⚠️ Warning: This is a draft ⚠️
This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.
If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.
{{wikipedia|Mandelbrot_set}} {{task|Fractals}} [[Category:Graphics]] [[Category:Raster graphics operations]]
;Task: Generate and draw the [[wp:Mandelbrot set|Mandelbrot set]].
Note that there are [http://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/Mandelbrot_set many algorithms] to draw Mandelbrot set and there are [http://en.wikibooks.org/wiki/Pictures_of_Julia_and_Mandelbrot_sets many functions] which generate it .
ACL2
(defun abs-sq (z) (+ (expt (realpart z) 2) (expt (imagpart z) 2))) (defun round-decimal (x places) (/ (floor (* x (expt 10 places)) 1) (expt 10 places))) (defun round-complex (z places) (complex (round-decimal (realpart z) places) (round-decimal (imagpart z) places))) (defun mandel-point-r (z c limit) (declare (xargs :measure (nfix limit))) (cond ((zp limit) 0) ((> (abs-sq z) 4) limit) (t (mandel-point-r (+ (round-complex (* z z) 15) c) c (1- limit))))) (defun mandel-point (z iters) (- 5 (floor (mandel-point-r z z iters) (/ iters 5)))) (defun draw-mandel-row (im re cols width iters) (declare (xargs :measure (nfix cols))) (if (zp cols) nil (prog2$ (cw (coerce (list (case (mandel-point (complex re im) iters) (5 #\#) (4 #\*) (3 #\.) (2 #\.) (otherwise #\Space))) 'string)) (draw-mandel-row im (+ re (/ (/ width 3))) (1- cols) width iters)))) (defun draw-mandel (im rows width height iters) (if (zp rows) nil (progn$ (draw-mandel-row im -2 width width iters) (cw "~%") (draw-mandel (- im (/ (/ height 2))) (1- rows) width height iters)))) (defun draw-mandelbrot (width iters) (let ((height (floor (* 1000 width) 3333))) (draw-mandel 1 height width height iters)))
{{out}}
> (draw-mandelbrot 60 100)
#
..
.####
. # .##.
##*###############.
#.##################
.######################.
######. #######################
##########.######################
##############################################
##########.######################
######. #######################
.######################.
#.##################
##*###############.
. # .##.
.####
..
Ada
{{libheader|Lumen}} mandelbrot.adb:
with Lumen.Binary;
package body Mandelbrot is
function Create_Image (Width, Height : Natural) return Lumen.Image.Descriptor is
use type Lumen.Binary.Byte;
Result : Lumen.Image.Descriptor;
X0, Y0 : Float;
X, Y, Xtemp : Float;
Iteration : Float;
Max_Iteration : constant Float := 1000.0;
Color : Lumen.Binary.Byte;
begin
Result.Width := Width;
Result.Height := Height;
Result.Complete := True;
Result.Values := new Lumen.Image.Pixel_Matrix (1 .. Width, 1 .. Height);
for Screen_X in 1 .. Width loop
for Screen_Y in 1 .. Height loop
X0 := -2.5 + (3.5 / Float (Width) * Float (Screen_X));
Y0 := -1.0 + (2.0 / Float (Height) * Float (Screen_Y));
X := 0.0;
Y := 0.0;
Iteration := 0.0;
while X * X + Y * Y <= 4.0 and then Iteration < Max_Iteration loop
Xtemp := X * X - Y * Y + X0;
Y := 2.0 * X * Y + Y0;
X := Xtemp;
Iteration := Iteration + 1.0;
end loop;
if Iteration = Max_Iteration then
Color := 255;
else
Color := 0;
end if;
Result.Values (Screen_X, Screen_Y) := (R => Color, G => Color, B => Color, A => 0);
end loop;
end loop;
return Result;
end Create_Image;
end Mandelbrot;
mandelbrot.ads:
with Lumen.Image;
package Mandelbrot is
function Create_Image (Width, Height : Natural) return Lumen.Image.Descriptor;
end Mandelbrot;
test_mandelbrot.adb:
with System.Address_To_Access_Conversions;
with Lumen.Window;
with Lumen.Image;
with Lumen.Events;
with GL;
with Mandelbrot;
procedure Test_Mandelbrot is
Program_End : exception;
Win : Lumen.Window.Handle;
Image : Lumen.Image.Descriptor;
Tx_Name : aliased GL.GLuint;
Wide, High : Natural := 400;
-- Create a texture and bind a 2D image to it
procedure Create_Texture is
use GL;
package GLB is new System.Address_To_Access_Conversions (GLubyte);
IP : GLpointer;
begin -- Create_Texture
-- Allocate a texture name
glGenTextures (1, Tx_Name'Unchecked_Access);
-- Bind texture operations to the newly-created texture name
glBindTexture (GL_TEXTURE_2D, Tx_Name);
-- Select modulate to mix texture with color for shading
glTexEnvi (GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_MODULATE);
-- Wrap textures at both edges
glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT);
glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_REPEAT);
-- How the texture behaves when minified and magnified
glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST);
-- Create a pointer to the image. This sort of horror show is going to
-- be disappearing once Lumen includes its own OpenGL bindings.
IP := GLB.To_Pointer (Image.Values.all'Address).all'Unchecked_Access;
-- Build our texture from the image we loaded earlier
glTexImage2D (GL_TEXTURE_2D, 0, GL_RGBA, GLsizei (Image.Width), GLsizei (Image.Height), 0,
GL_RGBA, GL_UNSIGNED_BYTE, IP);
end Create_Texture;
-- Set or reset the window view parameters
procedure Set_View (W, H : in Natural) is
use GL;
begin -- Set_View
GL.glEnable (GL.GL_TEXTURE_2D);
glClearColor (0.8, 0.8, 0.8, 1.0);
glMatrixMode (GL_PROJECTION);
glLoadIdentity;
glViewport (0, 0, GLsizei (W), GLsizei (H));
glOrtho (0.0, GLdouble (W), GLdouble (H), 0.0, -1.0, 1.0);
glMatrixMode (GL_MODELVIEW);
glLoadIdentity;
end Set_View;
-- Draw our scene
procedure Draw is
use GL;
begin -- Draw
-- clear the screen
glClear (GL_COLOR_BUFFER_BIT or GL_DEPTH_BUFFER_BIT);
GL.glBindTexture (GL.GL_TEXTURE_2D, Tx_Name);
-- fill with a single textured quad
glBegin (GL_QUADS);
begin
glTexCoord2f (1.0, 0.0);
glVertex2i (GLint (Wide), 0);
glTexCoord2f (0.0, 0.0);
glVertex2i (0, 0);
glTexCoord2f (0.0, 1.0);
glVertex2i (0, GLint (High));
glTexCoord2f (1.0, 1.0);
glVertex2i (GLint (Wide), GLint (High));
end;
glEnd;
-- flush rendering pipeline
glFlush;
-- Now show it
Lumen.Window.Swap (Win);
end Draw;
-- Simple event handler routine for keypresses and close-window events
procedure Quit_Handler (Event : in Lumen.Events.Event_Data) is
begin -- Quit_Handler
raise Program_End;
end Quit_Handler;
-- Simple event handler routine for Exposed events
procedure Expose_Handler (Event : in Lumen.Events.Event_Data) is
pragma Unreferenced (Event);
begin -- Expose_Handler
Draw;
end Expose_Handler;
-- Simple event handler routine for Resized events
procedure Resize_Handler (Event : in Lumen.Events.Event_Data) is
begin -- Resize_Handler
Wide := Event.Resize_Data.Width;
High := Event.Resize_Data.Height;
Set_View (Wide, High);
-- Image := Mandelbrot.Create_Image (Width => Wide, Height => High);
-- Create_Texture;
Draw;
end Resize_Handler;
begin
-- Create Lumen window, accepting most defaults; turn double buffering off
-- for simplicity
Lumen.Window.Create (Win => Win,
Name => "Mandelbrot fractal",
Width => Wide,
Height => High,
Events => (Lumen.Window.Want_Exposure => True,
Lumen.Window.Want_Key_Press => True,
others => False));
-- Set up the viewport and scene parameters
Set_View (Wide, High);
-- Now create the texture and set up to use it
Image := Mandelbrot.Create_Image (Width => Wide, Height => High);
Create_Texture;
-- Enter the event loop
declare
use Lumen.Events;
begin
Select_Events (Win => Win,
Calls => (Key_Press => Quit_Handler'Unrestricted_Access,
Exposed => Expose_Handler'Unrestricted_Access,
Resized => Resize_Handler'Unrestricted_Access,
Close_Window => Quit_Handler'Unrestricted_Access,
others => No_Callback));
end;
exception
when Program_End =>
null;
end Test_Mandelbrot;
{{out}} [[File:Ada_Mandelbrot.gif]]
ALGOL 68
{{works with|Algol 68 Genie 1.19.0}}
Plot part of the Mandelbrot set as a pseudo-gif image.
INT pix = 300, max iter = 256, REAL zoom = 0.33 / pix;
[-pix : pix, -pix : pix] INT plane;
COMPL ctr = 0.05 I 0.75 # center of set #;
# Compute the length of an orbit. #
PROC iterate = (COMPL z0) INT:
BEGIN COMPL z := 0, INT iter := 1;
WHILE (iter +:= 1) < max iter # not converged # AND ABS z < 2 # not diverged #
DO z := z * z + z0
OD;
iter
END;
# Compute set and find maximum orbit length. #
INT max col := 0;
FOR x FROM -pix TO pix
DO FOR y FROM -pix TO pix
DO COMPL z0 = ctr + (x * zoom) I (y * zoom);
IF (plane [x, y] := iterate (z0)) < max iter
THEN (plane [x, y] > max col | max col := plane [x, y])
FI
OD
OD;
# Make a plot. #
FILE plot;
INT num pix = 2 * pix + 1;
make device (plot, "gif", whole (num pix, 0) + "x" + whole (num pix, 0));
open (plot, "mandelbrot.gif", stand draw channel);
FOR x FROM -pix TO pix
DO FOR y FROM -pix TO pix
DO INT col = (plane [x, y] > max col | max col | plane [x, y]);
REAL c = sqrt (1- col / max col); # sqrt to enhance contrast #
draw colour (plot, c, c, c);
draw point (plot, (x + pix) / (num pix - 1), (y + pix) / (num pix - 1))
OD
OD;
close (plot)
ALGOL W
Generates an ASCII Mandelbrot Set. Translated from the sample program in the Compiler/AST Interpreter task.
begin
% This is an integer ascii Mandelbrot generator, translated from the %
% Compiler/AST Interpreter Task's ASCII Mandelbrot Set example program %
integer leftEdge, rightEdge, topEdge, bottomEdge, xStep, yStep, maxIter;
leftEdge := -420;
rightEdge := 300;
topEdge := 300;
bottomEdge := -300;
xStep := 7;
yStep := 15;
maxIter := 200;
for y0 := topEdge step - yStep until bottomEdge do begin
for x0 := leftEdge step xStep until rightEdge do begin
integer x, y, i;
string(1) theChar;
y := 0;
x := 0;
theChar := " ";
i := 0;
while i < maxIter do begin
integer x_x, y_y;
x_x := (x * x) div 200;
y_y := (y * y) div 200;
if x_x + y_y > 800 then begin
theChar := code( decode( "0" ) + i );
if i > 9 then theChar := "@";
i := maxIter
end;
y := x * y div 100 + y0;
x := x_x - y_y + x0;
i := i + 1
end while_i_lt_maxIter ;
writeon( theChar );
end for_x0 ;
write();
end for_y0
end.
{{out}}
1111111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222211111
1111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222211
1111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222
1111111111111111222222222222222222233333333333333333333333222222222222222222222222222222222222222222222
1111111111111112222222222222333333333333333333333333333333333333222222222222222222222222222222222222222
1111111111111222222222233333333333333333333333344444456655544443333332222222222222222222222222222222222
1111111111112222222233333333333333333333333444444445567@@6665444444333333222222222222222222222222222222
11111111111222222333333333333333333333334444444445555679@@@@7654444443333333222222222222222222222222222
1111111112222223333333333333333333333444444444455556789@@@@98755544444433333332222222222222222222222222
1111111122223333333333333333333333344444444445556668@@@ @@@76555544444333333322222222222222222222222
1111111222233333333333333333333344444444455566667778@@ @987666555544433333333222222222222222222222
111111122333333333333333333333444444455556@@@@@99@@@@@@ @@@@@@877779@5443333333322222222222222222222
1111112233333333333333333334444455555556679@ @@@ @@@@@@ 8544333333333222222222222222222
1111122333333333333333334445555555556666789@@@ @86554433333333322222222222222222
1111123333333333333444456666555556666778@@ @ @@87655443333333332222222222222222
111123333333344444455568@887789@8777788@@@ @@@@65444333333332222222222222222
111133334444444455555668@@@@@@@@@@@@99@@@ @@765444333333333222222222222222
111133444444445555556778@@@ @@@@ @855444333333333222222222222222
11124444444455555668@99@@ @ @655444433333333322222222222222
11134555556666677789@@ @86655444433333333322222222222222
111 @@876555444433333333322222222222222
11134555556666677789@@ @86655444433333333322222222222222
11124444444455555668@99@@ @ @655444433333333322222222222222
111133444444445555556778@@@ @@@@ @855444333333333222222222222222
111133334444444455555668@@@@@@@@@@@@99@@@ @@765444333333333222222222222222
111123333333344444455568@887789@8777788@@@ @@@@65444333333332222222222222222
1111123333333333333444456666555556666778@@ @ @@87655443333333332222222222222222
1111122333333333333333334445555555556666789@@@ @86554433333333322222222222222222
1111112233333333333333333334444455555556679@ @@@ @@@@@@ 8544333333333222222222222222222
111111122333333333333333333333444444455556@@@@@99@@@@@@ @@@@@@877779@5443333333322222222222222222222
1111111222233333333333333333333344444444455566667778@@ @987666555544433333333222222222222222222222
1111111122223333333333333333333333344444444445556668@@@ @@@76555544444333333322222222222222222222222
1111111112222223333333333333333333333444444444455556789@@@@98755544444433333332222222222222222222222222
11111111111222222333333333333333333333334444444445555679@@@@7654444443333333222222222222222222222222222
1111111111112222222233333333333333333333333444444445567@@6665444444333333222222222222222222222222222222
1111111111111222222222233333333333333333333333344444456655544443333332222222222222222222222222222222222
1111111111111112222222222222333333333333333333333333333333333333222222222222222222222222222222222222222
1111111111111111222222222222222222233333333333333333333333222222222222222222222222222222222222222222222
1111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222
1111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222211
1111111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222211111
Applesoft BASIC
This version takes into account the Apple II's funky 280×192 6-color display, which has an effective resolution of only 140×192 in color.
10 HGR2
20 XC = -0.5 : REM CENTER COORD X
30 YC = 0 : REM " " Y
40 S = 2 : REM SCALE
45 IT = 20 : REM ITERATIONS
50 XR = S * (280 / 192): REM TOTAL RANGE OF X
60 YR = S : REM " " " Y
70 X0 = XC - (XR/2) : REM MIN VALUE OF X
80 X1 = XC + (XR/2) : REM MAX " " X
90 Y0 = YC - (YR/2) : REM MIN " " Y
100 Y1 = YC + (YR/2) : REM MAX " " Y
110 XM = XR / 279 : REM SCALING FACTOR FOR X
120 YM = YR / 191 : REM " " " Y
130 FOR YI = 0 TO 3 : REM INTERLEAVE
140 FOR YS = 0+YI TO 188+YI STEP 4 : REM Y SCREEN COORDINATE
145 HCOLOR=3 : HPLOT 0,YS TO 279,YS
150 FOR XS = 0 TO 278 STEP 2 : REM X SCREEN COORDINATE
170 X = XS * XM + X0 : REM TRANSL SCREEN TO TRUE X
180 Y = YS * YM + Y0 : REM TRANSL SCREEN TO TRUE Y
190 ZX = 0
200 ZY = 0
210 XX = 0
220 YY = 0
230 FOR I = 0 TO IT
240 ZY = 2 * ZX * ZY + Y
250 ZX = XX - YY + X
260 XX = ZX * ZX
270 YY = ZY * ZY
280 C = IT-I
290 IF XX+YY >= 4 GOTO 301
300 NEXT I
301 IF C >= 8 THEN C = C - 8 : GOTO 301
310 HCOLOR = C : HPLOT XS, YS TO XS+1, YS
320 NEXT XS
330 NEXT YS
340 NEXT YI
By making the following modifications, the same code will render the Mandelbrot set in monochrome at full 280×192 resolution.
150 FOR XS = 0 TO 279
301 C = (C - INT(C/2)*2)*3
310 HCOLOR = C: HPLOT XS, YS
AutoHotkey
Max_Iteration := 256
Width := Height := 400
File := "MandelBrot." Width ".bmp"
Progress, b2 w400 fs9, Creating Colours ...
Gosub, CreateColours
Gosub, CreateBitmap
Progress, Off
Gui, -Caption
Gui, Margin, 0, 0
Gui, Add, Picture,, %File%
Gui, Show,, MandelBrot
Return
GuiClose:
GuiEscape:
ExitApp
;---------------------------------------------------------------------------
CreateBitmap: ; create and save a 32bit bitmap file
;---------------------------------------------------------------------------
; define header details
HeaderBMP := 14
HeaderDIB := 40
DataOffset := HeaderBMP + HeaderDIB
ImageSize := Width * Height * 4 ; 32bit
FileSize := DataOffset + ImageSize
Resolution := 3780 ; from mspaint
; create bitmap header
VarSetCapacity(IMAGE, FileSize, 0)
NumPut(Asc("B") , IMAGE, 0x00, "Char")
NumPut(Asc("M") , IMAGE, 0x01, "Char")
NumPut(FileSize , IMAGE, 0x02, "UInt")
NumPut(DataOffset , IMAGE, 0x0A, "UInt")
NumPut(HeaderDIB , IMAGE, 0x0E, "UInt")
NumPut(Width , IMAGE, 0x12, "UInt")
NumPut(Height , IMAGE, 0x16, "UInt")
NumPut(1 , IMAGE, 0x1A, "Short") ; Planes
NumPut(32 , IMAGE, 0x1C, "Short") ; Bits per Pixel
NumPut(ImageSize , IMAGE, 0x22, "UInt")
NumPut(Resolution , IMAGE, 0x26, "UInt")
NumPut(Resolution , IMAGE, 0x2A, "UInt")
; fill in Data
Gosub, CreatePixels
; save Bitmap to file
FileDelete, %File%
Handle := DllCall("CreateFile", "Str", File, "UInt", 0x40000000
, "UInt", 0, "UInt", 0, "UInt", 2, "UInt", 0, "UInt", 0)
DllCall("WriteFile", "UInt", Handle, "UInt", &IMAGE, "UInt"
, FileSize, "UInt *", Bytes, "UInt", 0)
DllCall("CloseHandle", "UInt", Handle)
Return
;---------------------------------------------------------------------------
CreatePixels: ; create pixels for [-2 < x < 1] [-1.5 < y < 1.5]
;---------------------------------------------------------------------------
Loop, % Height // 2 + 1 {
yi := A_Index - 1
y0 := -1.5 + yi / Height * 3 ; range -1.5 .. +1.5
Progress, % 200*yi // Height, % "Current line: " 2*yi " / " Height
Loop, %Width% {
xi := A_Index - 1
x0 := -2 + xi / Width * 3 ; range -2 .. +1
Gosub, Mandelbrot
p1 := DataOffset + 4 * (Width * yi + xi)
NumPut(Colour, IMAGE, p1, "UInt")
p2 := DataOffset + 4 * (Width * (Height-yi) + xi)
NumPut(Colour, IMAGE, p2, "UInt")
}
}
Return
;---------------------------------------------------------------------------
Mandelbrot: ; calculate a colour for each pixel
;---------------------------------------------------------------------------
x := y := Iteration := 0
While, (x*x + y*y <= 4) And (Iteration < Max_Iteration) {
xtemp := x*x - y*y + x0
y := 2*x*y + y0
x := xtemp
Iteration++
}
Colour := Iteration = Max_Iteration ? 0 : Colour_%Iteration%
Return
;---------------------------------------------------------------------------
CreateColours: ; borrowed from PureBasic example
;---------------------------------------------------------------------------
Loop, 64 {
i4 := (i3 := (i2 := (i1 := A_Index - 1) + 64) + 64) + 64
Colour_%i1% := RGB(4*i1 + 128, 4*i1, 0)
Colour_%i2% := RGB(64, 255, 4*i1)
Colour_%i3% := RGB(64, 255 - 4*i1, 255)
Colour_%i4% := RGB(64, 0, 255 - 4*i1)
}
Return
;---------------------------------------------------------------------------
RGB(r, g, b) { ; return 24bit color value
;---------------------------------------------------------------------------
Return, (r&0xFF)<<16 | g<<8 | b
}
AWK
BEGIN {
XSize=59; YSize=21;
MinIm=-1.0; MaxIm=1.0;MinRe=-2.0; MaxRe=1.0;
StepX=(MaxRe-MinRe)/XSize; StepY=(MaxIm-MinIm)/YSize;
for(y=0;y<YSize;y++)
{
Im=MinIm+StepY*y;
for(x=0;x<XSize;x++)
{
Re=MinRe+StepX*x; Zr=Re; Zi=Im;
for(n=0;n<30;n++)
{
a=Zr*Zr; b=Zi*Zi;
if(a+b>4.0) break;
Zi=2*Zr*Zi+Im; Zr=a-b+Re;
}
printf "%c",62-n;
}
print "";
}
exit;
}
{{out}}
>>>>>>
### ==<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<=======
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<
### =
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<======
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<====
>>==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<===
>>=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<==
>=<<<<<<<<;;;:599999999886 %78:;;<<<<<<=
><<<<;;;;;:::972456-567763 +9;;<<<<<<<
><;;;;;;::::9875& .3 *9;;;<<<<<<
>;;;;;;::997564' ' 8:;;;<<<<<<
>::988897735/ &89:;;;<<<<<<
>::988897735/ &89:;;;<<<<<<
>;;;;;;::997564' ' 8:;;;<<<<<<
><;;;;;;::::9875& .3 *9;;;<<<<<<
><<<<;;;;;:::972456-567763 +9;;<<<<<<<
>=<<<<<<<<;;;:599999999886 %78:;;<<<<<<=
>>=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<==
>>==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<===
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<====
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<======
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<
### =
B
This implements a 16bit fixed point arithmetic Mandelbrot set calculation. {{works with|The Amsterdam Compiler Kit - B|V6.1pre1}}
main() {
auto cx,cy,x,y,x2,y2;
auto iter;
auto xmin,xmax,ymin,ymax,maxiter,dx,dy;
xmin = -8601;
xmax = 2867;
ymin = -4915;
ymax = 4915;
maxiter = 32;
dx = (xmax-xmin)/79;
dy = (ymax-ymin)/24;
cy=ymin;
while( cy<=ymax ) {
cx=xmin;
while( cx<=xmax ) {
x = 0;
y = 0;
x2 = 0;
y2 = 0;
iter=0;
while( iter<maxiter ) {
if( x2+y2>16384 ) break;
y = ((x*y)>>11)+cy;
x = x2-y2+cx;
x2 = (x*x)>>12;
y2 = (y*y)>>12;
iter++;
}
putchar(' '+iter);
cx =+ dx;
}
putchar(13);
putchar(10);
cy =+ dy;
}
return(0);
}
{{out}}
!!!!!!!!!!!!!!!"""""""""""""####################################""""""""""""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$$%'+)%%%$$$$$#####"""""""""""
!!!!!!!!!!!"""""""#######################$$$$$$$$%%%&&(+,)++&%$$$$$$######""""""
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*5:/+('&%%$$$$$$#######"""
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''),@@@@@@@,'&%%%%%$$$$########
!!!!!!!"""####################$$$$$$$$%%%&'())((())*,@@@@@@/+))('&&&&)'%$$######
!!!!!!""###################$$$$$%%%%%%&&&'+.@@=/<@@@@@@@@@@@@@@@/[email protected]%%$#####
!!!!!"################$$$%%%%%%%%%%&&&&'),+2@@@@@@@@@@@@@@@@@@@@@@@@@1(&&%$$####
!!!!"##########$$$$$%%&(-(''''''''''''(*,5@@@@@@@@@@@@@@@@@@@@@@@@@@@@+)-&%$$###
!!!!####$$$$$$$$%%%%%&'(*-@1.+.@-4+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4-(&%$$$##
!!!!#$$$$$$$$$%%%%%%'''++.6@@@@@@@@@8/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@3(%%$$$$#
!!!#$$$$$$$%&&&&''()/-5.5@@@@@@@@@@@@@>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@?'&%%$$$$#
!!!(**+/+<523/80/46@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4+)'&&%%$$$$#
!!!#$$$$$$$%&&&&''().-2.@@@@@@@@@@@@@@?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'&%%$$$$#
!!!!#$$$$$$$$$%%%%%&'''/,.7@@@@@@@@@;/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0'%%$$$$#
!!!!####$$$$$$$$%%%%%&'(*-:2.,/?-5+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4+(&%$$$##
!!!!"##########$$$$$%%&(-(''''(''''''((*,4@@@@@@@@@@@@@@@@@@@@@@@@@@@4+).&%$$###
!!!!!"################$$$%%%%%%%%%%&&&&')<,4@@@@@@@@@@@@@@@@@@@@@@@@@/('&%%$####
!!!!!!""##################$$$$$$%%%%%%&&&'*.@@@0@@@@@@@@@@@@@@@@1,,@//9)%%$#####
!!!!!!!"""####################$$$$$$$$%%%&(())((()**-@@@@@@/+)))'&&&')'%$$######
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''(,@@@@@@@+'&&%%%%%$$$########
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*7@0+('&%%%$$$$$#######"""
!!!!!!!!!!!"""""""######################$$$$$$$$$%%%&&(+-).*&%$$$$$$######""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$%%'3(%%%$$$$$######""""""""""
!!!!!!!!!!!!!!!""""""""""""#####################################""""""""""""""""
BASIC
{{works with|QBasic}}
This is almost exactly the same as the pseudocode from [[wp:Mandelbrot set#For_programmers|the Wikipedia entry's "For programmers" section]] (which it's closely based on, of course). The image generated is very blocky ("low-res") due to the selected video mode, but it's fairly accurate.
SCREEN 13
WINDOW (-2, 1.5)-(2, -1.5)
FOR x0 = -2 TO 2 STEP .01
FOR y0 = -1.5 TO 1.5 STEP .01
x = 0
y = 0
iteration = 0
maxIteration = 223
WHILE (x * x + y * y <= (2 * 2) AND iteration < maxIteration)
xtemp = x * x - y * y + x0
y = 2 * x * y + y0
x = xtemp
iteration = iteration + 1
WEND
IF iteration <> maxIteration THEN
c = iteration
ELSE
c = 0
END IF
PSET (x0, y0), c + 32
NEXT
NEXT
=
BASIC256
=
graphsize 384,384 refresh kt = 319 : m = 4.0 xmin = -2.1 : xmax = 0.6 : ymin = -1.35 : ymax = 1.35 dx = (xmax - xmin) / graphwidth : dy = (ymax - ymin) / graphheight
for x = 0 to graphwidth jx = xmin + x * dx for y = 0 to graphheight jy = ymin + y * dy k = 0 : wx = 0.0 : wy = 0.0 do tx = wx * wx - wy * wy + jx ty = 2.0 * wx * wy + jy wx = tx wy = ty r = wx * wx + wy * wy k = k + 1 until r > m or k > kt
if k > kt then color black else if k < 16 then color k * 8, k * 8, 128 + k * 4 if k >= 16 and k < 64 then color 128 + k - 16, 128 + k - 16, 192 + k - 16 if k >= 64 then color kt - k, 128 + (kt - k) / 2, kt - k end if plot x, y next y refresh
next x imgsave "Mandelbrot_BASIC-256.png", "PNG"
{{out|Image generated by the script}}
[[File:Mandelbrot BASIC-256.jpg|220px]]
=
## BBC BASIC
=
{{works with|BBC BASIC for Windows}}
```bbcbasic
sizex% = 300 : sizey% = 300
maxiter% = 128
VDU 23,22,sizex%;sizey%;8,8,16,128
ORIGIN 0,sizey%
GCOL 1
FOR X% = 0 TO 2*sizex%-2 STEP 2
xi = X%/200 - 2
FOR Y% = 0 TO sizey%-2 STEP 2
yi = Y% / 200
x = 0
y = 0
FOR I% = 1 TO maxiter%
IF x*x+y*y > 4 EXIT FOR
xt = xi + x*x-y*y
y = yi + 2*x*y
x = xt
NEXT
IF I%>maxiter% I%=0
COLOUR 1,I%*15,I%*8,0
PLOT X%,Y% : PLOT X%,-Y%
NEXT
NEXT X%
[[File:Mandelbrot_bbc.gif]]
=
Liberty BASIC
= Any words of description go outside of lang tags.
nomainwin
WindowWidth =440
WindowHeight =460
open "Mandelbrot Set" for graphics_nsb_nf as #w
#w "trapclose [quit]"
#w "down"
for x0 = -2 to 1 step .0033
for y0 = -1.5 to 1.5 step .0075
x = 0
y = 0
iteration = 0
maxIteration = 255
while ( ( x *x +y *y) <=4) and ( iteration <maxIteration)
xtemp =x *x -y *y +x0
y =2 *x *y +y0
x = xtemp
iteration = iteration + 1
wend
if iteration <>maxIteration then
c =iteration
else
c =0
end if
call pSet x0, y0, c
scan
next
next
#w "flush"
wait
sub pSet x, y, c
xScreen = 10 +( x +2) /3 *400
yScreen = 10 +( y +1.5) /3 *400
if c =0 then
col$ ="red"
else
if c mod 2 =1 then col$ ="lightgray" else col$ ="white"
end if
#w "color "; col$
#w "set "; xScreen; " "; yScreen
end sub
[quit]
close #w
end
=
OS/8 BASIC
= Works under BASIC on a PDP-8 running OS/8. Various emulators exist including simh's PDP-8 emulator and the [http://www.bernhard-baehr.de/pdp8e/pdp8e.html PDP-8/E Simulator] for Classic Macintosh and OS X.
10 X1=59\Y1=21
20 I1=-1.0\I2=1.0\R1=-2.0\R2=1.0
30 S1=(R2-R1)/X1\S2=(I2-I1)/Y1
40 FOR Y=0 TO Y1
50 I3=I1+S2*Y
60 FOR X=0 TO X1
70 R3=R1+S1*X\Z1=R3\Z2=I3
80 FOR N=0 TO 30
90 A=Z1*Z1\B=Z2*Z2
100 IF A+B>4.0 GOTO 130
110 Z2=2*Z1*Z2+I3\Z1=A-B+R3
120 NEXT N
130 PRINT CHR$(62-N);
140 NEXT X
150 PRINT
160 NEXT Y
170 END
{{out}}
>>>>>>
### ==<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<========
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<
### ==
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<
### =
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<=====
>>==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<====
>>=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<===
>=<<<<<<<<;;;:599999999886 %78:;;<<<<<<==
><<<<;;;;;:::972456-567763 +9;;<<<<<<<=
><;;;;;;::::9875& .3 *9;;;<<<<<<=
>;;;;;;::997564' ' 8:;;;<<<<<<=
>::988897735/ &89:;;;<<<<<<=
>::988897735/ &89:;;;<<<<<<=
>;;;;;;::997564' ' 8:;;;<<<<<<=
><;;;;;;::::9875& .3 *9;;;<<<<<<=
><<<<;;;;;:::972456-567763 +9;;<<<<<<<=
>=<<<<<<<<;;;:599999999886 %78:;;<<<<<<==
>>=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<===
>>==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<====
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<=====
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<
### =
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<
### ==
>>>>>>
### ==<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<========
=
Quite BASIC
=
1000 REM Mandelbrot Set Project
1010 REM Quite BASIC Math Project
1015 REM 'http://www.quitebasic.com/prj/math/mandelbrot/
1020 REM ------------------------
1030 CLS
1040 PRINT "This program plots a graphical representation of the famous Mandelbrot set. It takes a while to finish so have patience and don't have too high expectations; the graphics resolution is not very high on our canvas."
2000 REM Initialize the color palette
2010 GOSUB 3000
2020 REM L is the maximum iterations to try
2030 LET L = 100
2040 FOR I = 0 TO 100
2050 FOR J = 0 TO 100
2060 REM Map from pixel coordinates (I,J) to math (U,V)
2060 LET U = I / 50 - 1.5
2070 LET V = J / 50 - 1
2080 LET X = U
2090 LET Y = V
2100 LET N = 0
2110 REM Inner iteration loop starts here
2120 LET R = X * X
2130 LET Q = Y * Y
2140 IF R + Q > 4 OR N >= L THEN GOTO 2190
2150 LET Y = 2 * X * Y + V
2160 LET X = R - Q + U
2170 LET N = N + 1
2180 GOTO 2120
2190 REM Compute the color to plot
2200 IF N < 10 THEN LET C = "black" ELSE LET C = P[ROUND(8 * (N-10) / (L-10))]
2210 PLOT I, J, C
2220 NEXT J
2230 NEXT I
2240 END
3000 REM Subroutine -- Set up Palette
3010 ARRAY P
3020 LET P[0] = "black"
3030 LET P[1] = "magenta"
3040 LET P[2] = "blue"
3050 LET P[3] = "green"
3060 LET P[4] = "cyan"
3070 LET P[5] = "red"
3080 LET P[6] = "orange"
3090 LET P[7] = "yellow"
3090 LET P[8] = "white"
3100 RETURN
=
Run BASIC
=
'Mandelbrot V4 for RunBasic
'Based on LibertyBasic solution
'copy the code and go to runbasic.com
'http://rosettacode.org/wiki/Mandelbrot_set#Liberty_BASIC
'May 2015 (updated 29 Apr 2018)
'
'Note - we only get so much processing time on the server, so the
'graph is computed in three or four pieces
'
WindowWidth = 320 'RunBasic max size 800 x 600
WindowHeight = 320
'print zone -2 to 1 (X)
'print zone -1.5 to 1.5 (Y)
a = -1.5 'graph -1.5 to -0.75, first "loop"
b = -0.75 'adjust for max processor time (y0 for loop below)
'open "Mandelbrot Set" for graphics_nsb_nf as #w not used in RunBasic
graphic #w, WindowWidth, WindowHeight
'#w "trapclose [quit]" not used in RunBasic
'#w "down" not used in RunBasic
cls
'#w flush()
#w cls("black")
render #w
'#w flush()
input "OK, hit enter to continue"; guess
cls
[man_calc]
'3/screen size 3/800 = 0.00375 ** 3/790 = 0.0037974
'3/screen size (y) 3/600 = .005 ** 3/590 = 0.0050847
'3/215 = .0139 .0068 = 3/440
cc = 3/299
'
for x0 = -2 to 1 step cc
for y0 = a to b step cc
x = 0
y = 0
iteration = 0
maxIteration = 255
while ( ( x *x +y *y) <=4) and ( iteration <maxIteration)
xtemp =x *x -y *y +x0
y =2 *x *y +y0
x = xtemp
iteration = iteration + 1
wend
if iteration <>maxIteration then
c =iteration
else
c =0
end if
call pSet x0, y0, c
'scan why scan? (wait for user input) with RunBasic ?
next
next
'#w flush() 'what is flush? RunBasic uses the render command.
render #w
input "OK, hit enter to continue"; guess
cls
a = a + 0.75
b = b + 0.75
if b > 1.6 then goto[quit] else goto[man_calc]
sub pSet x, y, c
xScreen = 5+(x +2) /3 * 300 'need positive screen number
yScreen = 5+(y +1.5) /3 * 300 'and 5x5 boarder
if c =0 then
col$ ="red"
else
if c mod 2 =1 then col$ ="lightgray" else col$ ="white"
end if
#w "color "; col$
#w "set "; xScreen; " "; yScreen
end sub
[quit]
'cls
print
print "This is a Mandelbrot Graph output from www.runbasic.com"
render #w
print "All done, good bye."
end
=
Sinclair ZX81 BASIC
= {{trans|QBasic}} Requires at least 2k of RAM.
Glacially slow, but does eventually produce a tolerable low-resolution image (screenshot [http://edmundgriffiths.com/zxmandelbrot.jpg here]). You can adjust the constants in lines 30 and 40 to zoom in on a particular area, if you like.
10 FOR I=0 TO 63
20 FOR J=43 TO 0 STEP -1
30 LET X=(I-52)/31
40 LET Y=(J-22)/31
50 LET XA=0
60 LET YA=0
70 LET ITER=0
80 LET XTEMP=XA*XA-YA*YA+X
90 LET YA=2*XA*YA+Y
100 LET XA=XTEMP
110 LET ITER=ITER+1
120 IF XA*XA+YA*YA<=4 AND ITER<200 THEN GOTO 80
130 IF ITER=200 THEN PLOT I, J
140 NEXT J
150 NEXT I
=
Microsoft Small Basic
=
GraphicsWindow.Show()
size = 500
half = 250
GraphicsWindow.Width = size * 1.5
GraphicsWindow.Height = size
GraphicsWindow.Title = "Mandelbrot"
For px = 1 To size * 1.5
x_0 = px/half - 2
For py = 1 To size
y_0 = py/half - 1
x = x_0
y = y_0
i = 0
While(c <= 2 AND i<100)
x_1 = Math.Power(x, 2) - Math.Power(y, 2) + x_0
y_1 = 2 * x * y + y_0
c = Math.Power(Math.Power(x_1, 2) + Math.Power(y_1, 2), 0.5)
x = x_1
y = y_1
i = i + 1
EndWhile
If i < 99 Then
GraphicsWindow.SetPixel(px, py, GraphicsWindow.GetColorFromRGB((255/25)*i, (255/25)*i, (255/5)*i))
Else
GraphicsWindow.SetPixel(px, py, "black")
EndIf
c=0
EndFor
EndFor
=
Visual BASIC for Applications on Excel
= {{works with|Excel 2013}} Based on the BBC BASIC version. Create a spreadsheet with -2 to 2 in row 1 and -2 to 2 in the A column (in steps of your choosing). In the cell B2, call the function with =mandel(B$1,$A2) and copy the cell to all others in the range. Conditionally format the cells to make the colours pleasing (eg based on values, 3-color scale, min value 2 [colour red], midpoint number 10 [green] and highest value black. Then format the cells with the custom type "";"";"" to remove the numbers.
Function mandel(xi As Double, yi As Double)
maxiter = 256
x = 0
y = 0
For i = 1 To maxiter
If ((x * x) + (y * y)) > 4 Then Exit For
xt = xi + ((x * x) - (y * y))
y = yi + (2 * x * y)
x = xt
Next
mandel = i
End Function
[[File:vbamandel.png]] Edit: I don't seem to be able to upload the screenshot, so I've shared it here: https://goo.gl/photos/LkezpuQziJPAtdnd9
==={{header|Microsoft Super Extended Color BASIC (Tandy Color Computer 3)}}===
1 REM MANDELBROT SET - TANDY COCO 3
2 POKE 65497,1
10 HSCREEN 2
20 HCLS
30 X1=319:Y1=191
40 I1=-1.0:I2=1.0:R1=-2:R2=1.0
50 S1=(R2-R1)/X1:S2=(I2-I1)/Y1
60 FOR Y=0 TO Y1
70 I3=I1+S2*Y
80 FOR X=0 TO X1
90 R3=R1+S1*X:Z1=R3:Z2=I3
100 FOR N=0 TO 30
110 A=Z1*Z1:B=Z2*Z2
120 IF A+B>4.0 GOTO 150
130 Z2=2*Z1*Z2+I3:Z1=A-B+R3
140 NEXT N
150 HSET(X,Y,N-16*INT(N/16))
160 NEXT X
170 NEXT Y
180 GOTO 180
Befunge
Using 14-bit fixed point arithmetic for simplicity and portability. It should work in most interpreters, but the exact output is implementation dependent, and some will be unbearably slow.
X scale is (-2.0, 0.5); Y scale is (-1, 1); Max iterations 94 with the ASCII character set as the "palette".
:00p58*`#@_0>:01p78vv$$<
@^+1g00,+55_v# !`\+*9<>4v$
@v30p20"?~^"< ^+1g10,+*8<$
@>p0\>\::*::882**02g*0v >^
`*:*" d":+*:-*"[Z"+g3 < |<
v-*"[Z"+g30*g20**288\--\<#
>2**5#>8*:*/00g"P"*58*:*v^
v*288 p20/**288:+*"[Z"+-<:
>*%03 p58*:*/01g"3"* v>::^
\_^#!:-1\+-*2*:*85<^
{{out}}
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}}|{{{{{{{{{{zzzzzzyyxwsuwwwwwwwwwwwwwvvurn[ ptuox
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Bourne Again SHell
{{works with|BASH|4}}
((xmin=-8601)) # int(-2.1*4096) ((xmax=2867)) # int( 0.7*4096) ((ymin=-4915)) # int(-1.2*4096) ((ymax=4915)) # int( 1.2*4096) ((maxiter=30)) ((dx=(xmax-xmin)/72)) ((dy=(ymax-ymin)/24)) C='0123456789' ((lC=${#C})) for((cy=ymax;cy>=ymin;cy-=dy)) ; do for((cx=xmin;cx<=xmax;cx+=dx)) ; do ((x=0,y=0,x2=0,y2=0)) for((iter=0;iter<maxiter && x2+y2<=16384;iter++)) ; do ((y=((x*y)>>11)+cy,x=x2-y2+cx,x2=(x*x)>>12,y2=(y*y)>>12)) done ((c=iter%lC)) echo -n ${C:$c:1} done echo done
{{out}}
1111111111111222222222222333333333333333333333333333333333222222222222222
1111111111112222222233333333333333333333344444456015554444333332222222222
1111111111222222333333333333333333333444444445556704912544444433333222222
1111111112222333333333333333333333444444444555678970508655544444333333222
1111111222233333333333333333333444444444556667807000002076555544443333333
1111112223333333333333333333444444455577898889016000003099766662644333333
1111122333333333333333334444455555566793000800000000000000931045875443333
1111123333333333333344455555555566668014000000000000000000000009865544333
1111233333333344445568277777777777880600000000000000000000000009099544433
1111333344444445555678041513450199023000000000000000000000000000807544433
1112344444445555556771179000000000410000000000000000000000000000036544443
1114444444566667782404400000000000000000000000000000000000000000775544443
1119912160975272040000000000000000000000000000000000000000000219765544443
1114444444566667792405800000000000000000000000000000000000000000075544443
1113344444445555556773270000000000500000000000000000000000000000676544443
1111333344444445555678045623255199020000000000000000000000000000707544433
1111233333333444445568177777877777881500000000000000000000000009190544433
1111123333333333333344455555555566668126000000000000000000000009865544333
1111122333333333333333334444455555566793000100000000000000941355975443333
1111112223333333333333333334444444455588908889016000003099876670654433333
1111111222233333333333333333334444444445556667800000002976555554443333333
1111111112222333333333333333333333444444444555679060608655544444333333222
1111111111222222333333333333333333333444444445556702049544444433333222222
1111111111112222222233333333333333333333344444456205554444333333222222222
1111111111111222222222222333333333333333333333333333333333222222222222222
Brace
This is a simple Mandelbrot plotter. A longer version based on this smooths colors, and avoids calculating the time-consuming black pixels: http://sam.ai.ki/brace/examples/mandelbrot.d/1
#!/usr/bin/env bx
use b
Main():
num outside = 16, ox = -0.5, oy = 0, r = 1.5
long i, max_i = 100, rb_i = 30
space()
uint32_t *px = pixel()
num d = 2*r/h, x0 = ox-d*w_2, y0 = oy+d*h_2
for(y, 0, h):
cmplx c = x0 + (y0-d*y)*I
repeat(w):
cmplx w = 0
for i=0; i < max_i && cabs(w) < outside; ++i
w = w*w + c
*px++ = i < max_i ? rainbow(i*359 / rb_i % 360) : black
c += d
An example plot from the longer version:
[[File:brace-mandelbrot-small.png]]
=={{header|Brainfuck}}==
{{out}}
```txt
AAAAAAAAAAAAAAAABBBBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDEGFFEEEEDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
AAAAAAAAAAAAAAABBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDEEEFGIIGFFEEEDDDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBBB
AAAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDEEEEFFFI KHGGGHGEDDDDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBB
AAAAAAAAAAAABBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDEEEEEFFGHIMTKLZOGFEEDDDDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBB
AAAAAAAAAAABBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDEEEEEEFGGHHIKPPKIHGFFEEEDDDDDDDDDCCCCCCCCCCBBBBBBBBBBBBBBBBBB
AAAAAAAAAABBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEEFFGHIJKS X KHHGFEEEEEDDDDDDDDDCCCCCCCCCCBBBBBBBBBBBBBBBB
AAAAAAAAABBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEEFFGQPUVOTY ZQL[MHFEEEEEEEDDDDDDDCCCCCCCCCCCBBBBBBBBBBBBBB
AAAAAAAABBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEFFFFFGGHJLZ UKHGFFEEEEEEEEDDDDDCCCCCCCCCCCCBBBBBBBBBBBB
AAAAAAABBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDEEEEFFFFFFGGGGHIKP KHHGGFFFFEEEEEEDDDDDCCCCCCCCCCCBBBBBBBBBBB
AAAAAAABBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDEEEEEFGGHIIHHHHHIIIJKMR VMKJIHHHGFFFFFFGSGEDDDDCCCCCCCCCCCCBBBBBBBBB
AAAAAABBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDEEEEEEFFGHK MKJIJO N R X YUSR PLV LHHHGGHIOJGFEDDDCCCCCCCCCCCCBBBBBBBB
AAAAABBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDEEEEEEEEEFFFFGH O TN S NKJKR LLQMNHEEDDDCCCCCCCCCCCCBBBBBBB
AAAAABBCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDEEEEEEEEEEEEFFFFFGHHIN Q UMWGEEEDDDCCCCCCCCCCCCBBBBBB
AAAABBCCCCCCCCCCCCCCCCCCCCCCCCCDDDDEEEEEEEEEEEEEEEFFFFFFGHIJKLOT [JGFFEEEDDCCCCCCCCCCCCCBBBBB
AAAABCCCCCCCCCCCCCCCCCCCCCCDDDDEEEEEEEEEEEEEEEEFFFFFFGGHYV RQU QMJHGGFEEEDDDCCCCCCCCCCCCCBBBB
AAABCCCCCCCCCCCCCCCCCDDDDDDDEEFJIHFFFFFFFFFFFFFFGGGGGGHIJN JHHGFEEDDDDCCCCCCCCCCCCCBBB
AAABCCCCCCCCCCCDDDDDDDDDDEEEEFFHLKHHGGGGHHMJHGGGGGGHHHIKRR UQ L HFEDDDDCCCCCCCCCCCCCCBB
AABCCCCCCCCDDDDDDDDDDDEEEEEEFFFHKQMRKNJIJLVS JJKIIIIIIJLR YNHFEDDDDDCCCCCCCCCCCCCBB
AABCCCCCDDDDDDDDDDDDEEEEEEEFFGGHIJKOU O O PR LLJJJKL OIHFFEDDDDDCCCCCCCCCCCCCCB
AACCCDDDDDDDDDDDDDEEEEEEEEEFGGGHIJMR RMLMN NTFEEDDDDDDCCCCCCCCCCCCCB
AACCDDDDDDDDDDDDEEEEEEEEEFGGGHHKONSZ QPR NJGFEEDDDDDDCCCCCCCCCCCCCC
ABCDDDDDDDDDDDEEEEEFFFFFGIPJIIJKMQ VX HFFEEDDDDDDCCCCCCCCCCCCCC
ACDDDDDDDDDDEFFFFFFFGGGGHIKZOOPPS HGFEEEDDDDDDCCCCCCCCCCCCCC
ADEEEEFFFGHIGGGGGGHHHHIJJLNY TJHGFFEEEDDDDDDDCCCCCCCCCCCCC
A PLJHGGFFEEEDDDDDDDCCCCCCCCCCCCC
ADEEEEFFFGHIGGGGGGHHHHIJJLNY TJHGFFEEEDDDDDDDCCCCCCCCCCCCC
ACDDDDDDDDDDEFFFFFFFGGGGHIKZOOPPS HGFEEEDDDDDDCCCCCCCCCCCCCC
ABCDDDDDDDDDDDEEEEEFFFFFGIPJIIJKMQ VX HFFEEDDDDDDCCCCCCCCCCCCCC
AACCDDDDDDDDDDDDEEEEEEEEEFGGGHHKONSZ QPR NJGFEEDDDDDDCCCCCCCCCCCCCC
AACCCDDDDDDDDDDDDDEEEEEEEEEFGGGHIJMR RMLMN NTFEEDDDDDDCCCCCCCCCCCCCB
AABCCCCCDDDDDDDDDDDDEEEEEEEFFGGHIJKOU O O PR LLJJJKL OIHFFEDDDDDCCCCCCCCCCCCCCB
AABCCCCCCCCDDDDDDDDDDDEEEEEEFFFHKQMRKNJIJLVS JJKIIIIIIJLR YNHFEDDDDDCCCCCCCCCCCCCBB
AAABCCCCCCCCCCCDDDDDDDDDDEEEEFFHLKHHGGGGHHMJHGGGGGGHHHIKRR UQ L HFEDDDDCCCCCCCCCCCCCCBB
AAABCCCCCCCCCCCCCCCCCDDDDDDDEEFJIHFFFFFFFFFFFFFFGGGGGGHIJN JHHGFEEDDDDCCCCCCCCCCCCCBBB
AAAABCCCCCCCCCCCCCCCCCCCCCCDDDDEEEEEEEEEEEEEEEEFFFFFFGGHYV RQU QMJHGGFEEEDDDCCCCCCCCCCCCCBBBB
AAAABBCCCCCCCCCCCCCCCCCCCCCCCCCDDDDEEEEEEEEEEEEEEEFFFFFFGHIJKLOT [JGFFEEEDDCCCCCCCCCCCCCBBBBB
AAAAABBCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDEEEEEEEEEEEEFFFFFGHHIN Q UMWGEEEDDDCCCCCCCCCCCCBBBBBB
AAAAABBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDEEEEEEEEEFFFFGH O TN S NKJKR LLQMNHEEDDDCCCCCCCCCCCCBBBBBBB
AAAAAABBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDEEEEEEFFGHK MKJIJO N R X YUSR PLV LHHHGGHIOJGFEDDDCCCCCCCCCCCCBBBBBBBB
AAAAAAABBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDEEEEEFGGHIIHHHHHIIIJKMR VMKJIHHHGFFFFFFGSGEDDDDCCCCCCCCCCCCBBBBBBBBB
AAAAAAABBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDEEEEFFFFFFGGGGHIKP KHHGGFFFFEEEEEEDDDDDCCCCCCCCCCCBBBBBBBBBBB
AAAAAAAABBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEFFFFFGGHJLZ UKHGFFEEEEEEEEDDDDDCCCCCCCCCCCCBBBBBBBBBBBB
AAAAAAAAABBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEEFFGQPUVOTY ZQL[MHFEEEEEEEDDDDDDDCCCCCCCCCCCBBBBBBBBBBBBBB
AAAAAAAAAABBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEEFFGHIJKS X KHHGFEEEEEDDDDDDDDDCCCCCCCCCCBBBBBBBBBBBBBBBB
AAAAAAAAAAABBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDEEEEEEFGGHHIKPPKIHGFFEEEDDDDDDDDDCCCCCCCCCCBBBBBBBBBBBBBBBBBB
AAAAAAAAAAAABBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDEEEEEFFGHIMTKLZOGFEEDDDDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBB
AAAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDEEEEFFFI KHGGGHGEDDDDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBB
AAAAAAAAAAAAAAABBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDEEEFGIIGFFEEEDDDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBBB
C
PPM non interactive
Here is one file program. It directly creates ppm file.
/* c program: -------------------------------- 1. draws Mandelbrot set for Fc(z)=z*z +c using Mandelbrot algorithm ( boolean escape time ) ------------------------------- 2. technique of creating ppm file is based on the code of Claudio Rocchini http://en.wikipedia.org/wiki/Image:Color_complex_plot.jpg create 24 bit color graphic file , portable pixmap file = PPM see http://en.wikipedia.org/wiki/Portable_pixmap to see the file use external application ( graphic viewer) */ #include <stdio.h> #include <math.h> int main() { /* screen ( integer) coordinate */ int iX,iY; const int iXmax = 800; const int iYmax = 800; /* world ( double) coordinate = parameter plane*/ double Cx,Cy; const double CxMin=-2.5; const double CxMax=1.5; const double CyMin=-2.0; const double CyMax=2.0; /* */ double PixelWidth=(CxMax-CxMin)/iXmax; double PixelHeight=(CyMax-CyMin)/iYmax; /* color component ( R or G or B) is coded from 0 to 255 */ /* it is 24 bit color RGB file */ const int MaxColorComponentValue=255; FILE * fp; char *filename="new1.ppm"; char *comment="# ";/* comment should start with # */ static unsigned char color[3]; /* Z=Zx+Zy*i ; Z0 = 0 */ double Zx, Zy; double Zx2, Zy2; /* Zx2=Zx*Zx; Zy2=Zy*Zy */ /* */ int Iteration; const int IterationMax=200; /* bail-out value , radius of circle ; */ const double EscapeRadius=2; double ER2=EscapeRadius*EscapeRadius; /*create new file,give it a name and open it in binary mode */ fp= fopen(filename,"wb"); /* b - binary mode */ /*write ASCII header to the file*/ fprintf(fp,"P6\n %s\n %d\n %d\n %d\n",comment,iXmax,iYmax,MaxColorComponentValue); /* compute and write image data bytes to the file*/ for(iY=0;iY<iYmax;iY++) { Cy=CyMin + iY*PixelHeight; if (fabs(Cy)< PixelHeight/2) Cy=0.0; /* Main antenna */ for(iX=0;iX<iXmax;iX++) { Cx=CxMin + iX*PixelWidth; /* initial value of orbit = critical point Z= 0 */ Zx=0.0; Zy=0.0; Zx2=Zx*Zx; Zy2=Zy*Zy; /* */ for (Iteration=0;Iteration<IterationMax && ((Zx2+Zy2)<ER2);Iteration++) { Zy=2*Zx*Zy + Cy; Zx=Zx2-Zy2 +Cx; Zx2=Zx*Zx; Zy2=Zy*Zy; }; /* compute pixel color (24 bit = 3 bytes) */ if (Iteration==IterationMax) { /* interior of Mandelbrot set = black */ color[0]=0; color[1]=0; color[2]=0; } else { /* exterior of Mandelbrot set = white */ color[0]=255; /* Red*/ color[1]=255; /* Green */ color[2]=255;/* Blue */ }; /*write color to the file*/ fwrite(color,1,3,fp); } } fclose(fp); return 0; }</lang > ### PPM Interactive [[file:mandel-C-GL.png|center|400px]] Infinitely zoomable OpenGL program. Adjustable colors, max iteration, black and white, screen dump, etc. Compile with <code>gcc mandelbrot.c -lglut -lGLU -lGL -lm</code> * [[OpenBSD]] users, install freeglut package, and compile with <code>make mandelbrot CPPFLAGS='-I/usr/local/include `pkg-config glu --cflags`' LDLIBS='-L/usr/local/lib -lglut `pkg-config glu --libs` -lm'</code> {{libheader|GLUT}} ```c #include <stdio.h> #include <stdlib.h> #include <math.h> #include <GL/glut.h> #include <GL/gl.h> #include <GL/glu.h> void set_texture(); typedef struct {unsigned char r, g, b;} rgb_t; rgb_t **tex = 0; int gwin; GLuint texture; int width, height; int tex_w, tex_h; double scale = 1./256; double cx = -.6, cy = 0; int color_rotate = 0; int saturation = 1; int invert = 0; int max_iter = 256; void render() { double x = (double)width /tex_w, y = (double)height/tex_h; glClear(GL_COLOR_BUFFER_BIT); glTexEnvi(GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_REPLACE); glBindTexture(GL_TEXTURE_2D, texture); glBegin(GL_QUADS); glTexCoord2f(0, 0); glVertex2i(0, 0); glTexCoord2f(x, 0); glVertex2i(width, 0); glTexCoord2f(x, y); glVertex2i(width, height); glTexCoord2f(0, y); glVertex2i(0, height); glEnd(); glFlush(); glFinish(); } int dump = 1; void screen_dump() { char fn[100]; int i; sprintf(fn, "screen%03d.ppm", dump++); FILE *fp = fopen(fn, "w"); fprintf(fp, "P6\n%d %d\n255\n", width, height); for (i = height - 1; i >= 0; i--) fwrite(tex[i], 1, width * 3, fp); fclose(fp); printf("%s written\n", fn); } void keypress(unsigned char key, int x, int y) { switch(key) { case 'q': glFinish(); glutDestroyWindow(gwin); return; case 27: scale = 1./256; cx = -.6; cy = 0; break; case 'r': color_rotate = (color_rotate + 1) % 6; break; case '>': case '.': max_iter += 128; if (max_iter > 1 << 15) max_iter = 1 << 15; printf("max iter: %d\n", max_iter); break; case '<': case ',': max_iter -= 128; if (max_iter < 128) max_iter = 128; printf("max iter: %d\n", max_iter); break; case 'c': saturation = 1 - saturation; break; case 's': screen_dump(); return; case 'z': max_iter = 4096; break; case 'x': max_iter = 128; break; case ' ': invert = !invert; } set_texture(); } void hsv_to_rgb(int hue, int min, int max, rgb_t *p) { if (min == max) max = min + 1; if (invert) hue = max - (hue - min); if (!saturation) { p->r = p->g = p->b = 255 * (max - hue) / (max - min); return; } double h = fmod(color_rotate + 1e-4 + 4.0 * (hue - min) / (max - min), 6); # define VAL 255 double c = VAL * saturation; double X = c * (1 - fabs(fmod(h, 2) - 1)); p->r = p->g = p->b = 0; switch((int)h) { case 0: p->r = c; p->g = X; return; case 1: p->r = X; p->g = c; return; case 2: p->g = c; p->b = X; return; case 3: p->g = X; p->b = c; return; case 4: p->r = X; p->b = c; return; default:p->r = c; p->b = X; } } void calc_mandel() { int i, j, iter, min, max; rgb_t *px; double x, y, zx, zy, zx2, zy2; min = max_iter; max = 0; for (i = 0; i < height; i++) { px = tex[i]; y = (i - height/2) * scale + cy; for (j = 0; j < width; j++, px++) { x = (j - width/2) * scale + cx; iter = 0; zx = hypot(x - .25, y); if (x < zx - 2 * zx * zx + .25) iter = max_iter; if ((x + 1)*(x + 1) + y * y < 1/16) iter = max_iter; zx = zy = zx2 = zy2 = 0; for (; iter < max_iter && zx2 + zy2 < 4; iter++) { zy = 2 * zx * zy + y; zx = zx2 - zy2 + x; zx2 = zx * zx; zy2 = zy * zy; } if (iter < min) min = iter; if (iter > max) max = iter; *(unsigned short *)px = iter; } } for (i = 0; i < height; i++) for (j = 0, px = tex[i]; j < width; j++, px++) hsv_to_rgb(*(unsigned short*)px, min, max, px); } void alloc_tex() { int i, ow = tex_w, oh = tex_h; for (tex_w = 1; tex_w < width; tex_w <<= 1); for (tex_h = 1; tex_h < height; tex_h <<= 1); if (tex_h != oh || tex_w != ow) tex = realloc(tex, tex_h * tex_w * 3 + tex_h * sizeof(rgb_t*)); for (tex[0] = (rgb_t *)(tex + tex_h), i = 1; i < tex_h; i++) tex[i] = tex[i - 1] + tex_w; } void set_texture() { alloc_tex(); calc_mandel(); glEnable(GL_TEXTURE_2D); glBindTexture(GL_TEXTURE_2D, texture); glTexImage2D(GL_TEXTURE_2D, 0, 3, tex_w, tex_h, 0, GL_RGB, GL_UNSIGNED_BYTE, tex[0]); glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST); glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST); render(); } void mouseclick(int button, int state, int x, int y) { if (state != GLUT_UP) return; cx += (x - width / 2) * scale; cy -= (y - height/ 2) * scale; switch(button) { case GLUT_LEFT_BUTTON: /* zoom in */ if (scale > fabs(x) * 1e-16 && scale > fabs(y) * 1e-16) scale /= 2; break; case GLUT_RIGHT_BUTTON: /* zoom out */ scale *= 2; break; /* any other button recenters */ } set_texture(); } void resize(int w, int h) { printf("resize %d %d\n", w, h); width = w; height = h; glViewport(0, 0, w, h); glOrtho(0, w, 0, h, -1, 1); set_texture(); } void init_gfx(int *c, char **v) { glutInit(c, v); glutInitDisplayMode(GLUT_RGB); glutInitWindowSize(640, 480); glutDisplayFunc(render); gwin = glutCreateWindow("Mandelbrot"); glutKeyboardFunc(keypress); glutMouseFunc(mouseclick); glutReshapeFunc(resize); glGenTextures(1, &texture); set_texture(); } int main(int c, char **v) { init_gfx(&c, v); printf("keys:\n\tr: color rotation\n\tc: monochrome\n\ts: screen dump\n\t" "<, >: decrease/increase max iteration\n\tq: quit\n\tmouse buttons to zoom\n"); glutMainLoop(); return 0; }
ASCII
Not mine, found it on Ken Perlin's homepage, this deserves a place here to illustrate how awesome C can be:
main(k){float i,j,r,x,y=-16;while(puts(""),y++<15)for(x =0;x++<84;putchar(" .:-;!/>)|&IH%*#"[k&15]))for(i=k=r=0; j=r*r-i*i-2+x/25,i=2*r*i+y/10,j*j+i*i<11&&k++<111;r=j);}
There may be warnings on compiling but disregard them, the output will be produced nevertheless. Such programs are called obfuscated and C excels when it comes to writing such cryptic programs. Google IOCCC for more.
.............::::::::::::::::::::::::::::::::::::::::::::::::.......................
.........::::::::::::::::::::::::::::::::::::::::::::::::::::::::...................
.....::::::::::::::::::::::::::::::::::-----------:::::::::::::::::::...............
...:::::::::::::::::::::::::::::------------------------:::::::::::::::.............
:::::::::::::::::::::::::::-------------;;;!:H!!;;;--------:::::::::::::::..........
::::::::::::::::::::::::-------------;;;;!!/>&*|I !;;;--------::::::::::::::........
::::::::::::::::::::-------------;;;;;;!!/>)|.*#|>/!!;;;;-------::::::::::::::......
::::::::::::::::-------------;;;;;;!!!!//>|: !:|//!!!;;;;-----::::::::::::::.....
::::::::::::------------;;;;;;;!!/>)I>>)||I# H&))>////*!;;-----:::::::::::::....
::::::::----------;;;;;;;;;;!!!//)H: #| IH&*I#/;;-----:::::::::::::...
:::::---------;;;;!!!!!!!!!!!//>|.H: #I>/!;;-----:::::::::::::..
:----------;;;;!/||>//>>>>//>>)|% %|&/!;;----::::::::::::::.
--------;;;;;!!//)& .;I*-H#&||&/ *)/!;;-----::::::::::::::
-----;;;;;!!!//>)IH:- ## #&!!;;-----::::::::::::::
;;;;!!!!!///>)H%.** * )/!;;;------:::::::::::::
&)/!!;;;------:::::::::::::
;;;;!!!!!///>)H%.** * )/!;;;------:::::::::::::
-----;;;;;!!!//>)IH:- ## #&!!;;-----::::::::::::::
--------;;;;;!!//)& .;I*-H#&||&/ *)/!;;-----::::::::::::::
:----------;;;;!/||>//>>>>//>>)|% %|&/!;;----::::::::::::::.
:::::---------;;;;!!!!!!!!!!!//>|.H: #I>/!;;-----:::::::::::::..
::::::::----------;;;;;;;;;;!!!//)H: #| IH&*I#/;;-----:::::::::::::...
::::::::::::------------;;;;;;;!!/>)I>>)||I# H&))>////*!;;-----:::::::::::::....
::::::::::::::::-------------;;;;;;!!!!//>|: !:|//!!!;;;;-----::::::::::::::.....
::::::::::::::::::::-------------;;;;;;!!/>)|.*#|>/!!;;;;-------::::::::::::::......
::::::::::::::::::::::::-------------;;;;!!/>&*|I !;;;--------::::::::::::::........
:::::::::::::::::::::::::::-------------;;;!:H!!;;;--------:::::::::::::::..........
...:::::::::::::::::::::::::::::------------------------:::::::::::::::.............
.....::::::::::::::::::::::::::::::::::-----------:::::::::::::::::::...............
.........::::::::::::::::::::::::::::::::::::::::::::::::::::::::...................
.............::::::::::::::::::::::::::::::::::::::::::::::::.......................
C++
This generic function assumes that the image can be accessed like a two-dimensional array of colors. It may be passed a true array (in which case the Mandelbrot set will simply be drawn into that array, which then might be saved as image file), or a class which maps the subscript operator to the pixel drawing routine of some graphics library. In the latter case, there must be functions get_first_dimension and get_second_dimension defined for that type, to be found by argument dependent lookup. The code provides those functions for built-in arrays.
#include <cstdlib> #include <complex> // get dimensions for arrays template<typename ElementType, std::size_t dim1, std::size_t dim2> std::size_t get_first_dimension(ElementType (&a)[dim1][dim2]) { return dim1; } template<typename ElementType, std::size_t dim1, std::size_t dim2> std::size_t get_second_dimension(ElementType (&a)[dim1][dim2]) { return dim2; } template<typename ColorType, typename ImageType> void draw_Mandelbrot(ImageType& image, //where to draw the image ColorType set_color, ColorType non_set_color, //which colors to use for set/non-set points double cxmin, double cxmax, double cymin, double cymax,//the rect to draw in the complex plane unsigned int max_iterations) //the maximum number of iterations { std::size_t const ixsize = get_first_dimension(image); std::size_t const iysize = get_first_dimension(image); for (std::size_t ix = 0; ix < ixsize; ++ix) for (std::size_t iy = 0; iy < iysize; ++iy) { std::complex<double> c(cxmin + ix/(ixsize-1.0)*(cxmax-cxmin), cymin + iy/(iysize-1.0)*(cymax-cymin)); std::complex<double> z = 0; unsigned int iterations; for (iterations = 0; iterations < max_iterations && std::abs(z) < 2.0; ++iterations) z = z*z + c; image[ix][iy] = (iterations == max_iterations) ? set_color : non_set_color; } }
Note this code has not been executed.
Cixl
Displays a zooming Mandelbrot using ANSI graphics.
use: cx;
define: max 4.0;
define: max-iter 570;
let: (max-x max-y) screen-size;
let: max-cx $max-x 2.0 /;
let: max-cy $max-y 2.0 /;
let: rows Stack<Str> new;
let: buf Buf new;
let: zoom 0 ref;
func: render()()
$rows clear
$max-y 2 / {
let: y;
$buf 0 seek
$max-x {
let: x;
let: (zx zy) 0.0 ref %%;
let: cx $x $max-cx - $zoom deref /;
let: cy $y $max-cy - $zoom deref /;
let: i #max-iter ref;
{
let: nzx $zx deref ** $zy deref ** - $cx +;
$zy $zx deref *2 $zy deref * $cy + set
$zx $nzx set
$i &-- set-call
$nzx ** $zy deref ** + #max < $i deref and
} while
let: c $i deref % -7 bsh bor 256 mod;
$c {$x 256 mod $y 256 mod} {0 0} if-else $c new-rgb $buf set-bg
@@s $buf print
} for
$rows $buf str push
} for
1 1 #out move-to
$rows {#out print} for
$rows riter {#out print} for;
#out hide-cursor
raw-mode
let: poll Poll new;
let: is-done #f ref;
$poll #in {
#in read-char _
$is-done #t set
} on-read
{
$zoom &++ set-call
render
$poll 0 wait _
$is-done deref !
} while
#out reset-style
#out clear-screen
1 1 #out move-to
#out show-cursor
normal-mode
C#
using System; using System.Drawing; using System.Drawing.Imaging; using System.Threading; using System.Windows.Forms; /// <summary> /// Generates bitmap of Mandelbrot Set and display it on the form. /// </summary> public class MandelbrotSetForm : Form { const double MaxValueExtent = 2.0; Thread thread; static double CalcMandelbrotSetColor(ComplexNumber c) { // from http://en.wikipedia.org/w/index.php?title=Mandelbrot_set const int MaxIterations = 1000; const double MaxNorm = MaxValueExtent * MaxValueExtent; int iteration = 0; ComplexNumber z = new ComplexNumber(); do { z = z * z + c; iteration++; } while (z.Norm() < MaxNorm && iteration < MaxIterations); if (iteration < MaxIterations) return (double)iteration / MaxIterations; else return 0; // black } static void GenerateBitmap(Bitmap bitmap) { double scale = 2 * MaxValueExtent / Math.Min(bitmap.Width, bitmap.Height); for (int i = 0; i < bitmap.Height; i++) { double y = (bitmap.Height / 2 - i) * scale; for (int j = 0; j < bitmap.Width; j++) { double x = (j - bitmap.Width / 2) * scale; double color = CalcMandelbrotSetColor(new ComplexNumber(x, y)); bitmap.SetPixel(j, i, GetColor(color)); } } } static Color GetColor(double value) { const double MaxColor = 256; const double ContrastValue = 0.2; return Color.FromArgb(0, 0, (int)(MaxColor * Math.Pow(value, ContrastValue))); } public MandelbrotSetForm() { // form creation this.Text = "Mandelbrot Set Drawing"; this.BackColor = System.Drawing.Color.Black; this.BackgroundImageLayout = System.Windows.Forms.ImageLayout.Stretch; this.MaximizeBox = false; this.StartPosition = FormStartPosition.CenterScreen; this.FormBorderStyle = FormBorderStyle.FixedDialog; this.ClientSize = new Size(640, 640); this.Load += new System.EventHandler(this.MainForm_Load); } void MainForm_Load(object sender, EventArgs e) { thread = new Thread(thread_Proc); thread.IsBackground = true; thread.Start(this.ClientSize); } void thread_Proc(object args) { // start from small image to provide instant display for user Size size = (Size)args; int width = 16; while (width * 2 < size.Width) { int height = width * size.Height / size.Width; Bitmap bitmap = new Bitmap(width, height, PixelFormat.Format24bppRgb); GenerateBitmap(bitmap); this.BeginInvoke(new SetNewBitmapDelegate(SetNewBitmap), bitmap); width *= 2; Thread.Sleep(200); } // then generate final image Bitmap finalBitmap = new Bitmap(size.Width, size.Height, PixelFormat.Format24bppRgb); GenerateBitmap(finalBitmap); this.BeginInvoke(new SetNewBitmapDelegate(SetNewBitmap), finalBitmap); } void SetNewBitmap(Bitmap image) { if (this.BackgroundImage != null) this.BackgroundImage.Dispose(); this.BackgroundImage = image; } delegate void SetNewBitmapDelegate(Bitmap image); static void Main() { Application.Run(new MandelbrotSetForm()); } } struct ComplexNumber { public double Re; public double Im; public ComplexNumber(double re, double im) { this.Re = re; this.Im = im; } public static ComplexNumber operator +(ComplexNumber x, ComplexNumber y) { return new ComplexNumber(x.Re + y.Re, x.Im + y.Im); } public static ComplexNumber operator *(ComplexNumber x, ComplexNumber y) { return new ComplexNumber(x.Re * y.Re - x.Im * y.Im, x.Re * y.Im + x.Im * y.Re); } public double Norm() { return Re * Re + Im * Im; } }
Clojure
{{trans|Perl}}
(ns mandelbrot (:refer-clojure :exclude [+ * <]) (:use (clojure.contrib complex-numbers) (clojure.contrib.generic [arithmetic :only [+ *]] [comparison :only [<]] [math-functions :only [abs]]))) (defn mandelbrot? [z] (loop [c 1 m (iterate #(+ z (* % %)) 0)] (if (and (> 20 c) (< (abs (first m)) 2) ) (recur (inc c) (rest m)) (if (= 20 c) true false)))) (defn mandelbrot [] (for [y (range 1 -1 -0.05) x (range -2 0.5 0.0315)] (if (mandelbrot? (complex x y)) "#" " "))) (println (interpose \newline (map #(apply str %) (partition 80 (mandelbrot)))))
COBOL
EBCDIC art.
IDENTIFICATION DIVISION.
PROGRAM-ID. MANDELBROT-SET-PROGRAM.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 COMPLEX-ARITHMETIC.
05 X PIC S9V9(9).
05 Y PIC S9V9(9).
05 X-A PIC S9V9(6).
05 X-B PIC S9V9(6).
05 Y-A PIC S9V9(6).
05 X-A-SQUARED PIC S9V9(6).
05 Y-A-SQUARED PIC S9V9(6).
05 SUM-OF-SQUARES PIC S9V9(6).
05 ROOT PIC S9V9(6).
01 LOOP-COUNTERS.
05 I PIC 99.
05 J PIC 99.
05 K PIC 999.
77 PLOT-CHARACTER PIC X.
PROCEDURE DIVISION.
CONTROL-PARAGRAPH.
PERFORM OUTER-LOOP-PARAGRAPH
VARYING I FROM 1 BY 1 UNTIL I IS GREATER THAN 24.
STOP RUN.
OUTER-LOOP-PARAGRAPH.
PERFORM INNER-LOOP-PARAGRAPH
VARYING J FROM 1 BY 1 UNTIL J IS GREATER THAN 64.
DISPLAY ''.
INNER-LOOP-PARAGRAPH.
MOVE SPACE TO PLOT-CHARACTER.
MOVE ZERO TO X-A.
MOVE ZERO TO Y-A.
MULTIPLY J BY 0.0390625 GIVING X.
SUBTRACT 1.5 FROM X.
MULTIPLY I BY 0.083333333 GIVING Y.
SUBTRACT 1 FROM Y.
PERFORM ITERATION-PARAGRAPH VARYING K FROM 1 BY 1
UNTIL K IS GREATER THAN 100 OR PLOT-CHARACTER IS EQUAL TO '#'.
DISPLAY PLOT-CHARACTER WITH NO ADVANCING.
ITERATION-PARAGRAPH.
MULTIPLY X-A BY X-A GIVING X-A-SQUARED.
MULTIPLY Y-A BY Y-A GIVING Y-A-SQUARED.
SUBTRACT Y-A-SQUARED FROM X-A-SQUARED GIVING X-B.
ADD X TO X-B.
MULTIPLY X-A BY Y-A GIVING Y-A.
MULTIPLY Y-A BY 2 GIVING Y-A.
SUBTRACT Y FROM Y-A.
MOVE X-B TO X-A.
ADD X-A-SQUARED TO Y-A-SQUARED GIVING SUM-OF-SQUARES.
MOVE FUNCTION SQRT (SUM-OF-SQUARES) TO ROOT.
IF ROOT IS GREATER THAN 2 THEN MOVE '#' TO PLOT-CHARACTER.
{{out}}
################################################################
################################# ############################
################################ ###########################
############################## ## ############################
######################## # ######################
######################## ##################
##################### #################
#################### ###############
######## ## ##### ################
####### # ################
###### # #################
####################
###### # #################
####### # ################
######## ## ##### ################
#################### ###############
##################### #################
######################## ##################
######################## # ######################
############################## ## ############################
################################ ###########################
################################# ############################
################################################################
################################################################
Common Lisp
(defpackage #:mandelbrot (:use #:cl)) (in-package #:mandelbrot) (deftype pixel () '(unsigned-byte 8)) (deftype image () '(array pixel)) (defun write-pgm (image filespec) (declare (image image)) (with-open-file (s filespec :direction :output :element-type 'pixel :if-exists :supersede) (let* ((width (array-dimension image 1)) (height (array-dimension image 0)) (header (format nil "P5~A~D ~D~A255~A" #\Newline width height #\Newline #\Newline))) (loop for c across header do (write-byte (char-code c) s)) (dotimes (row height) (dotimes (col width) (write-byte (aref image row col) s)))))) (defparameter *x-max* 800) (defparameter *y-max* 800) (defparameter *cx-min* -2.5) (defparameter *cx-max* 1.5) (defparameter *cy-min* -2.0) (defparameter *cy-max* 2.0) (defparameter *escape-radius* 2) (defparameter *iteration-max* 40) (defun mandelbrot (filespec) (let ((pixel-width (/ (- *cx-max* *cx-min*) *x-max*)) (pixel-height (/ (- *cy-max* *cy-min*) *y-max*)) (image (make-array (list *y-max* *x-max*) :element-type 'pixel :initial-element 0))) (loop for y from 0 below *y-max* for cy from *cy-min* by pixel-height do (loop for x from 0 below *x-max* for cx from *cx-min* by pixel-width for iteration = (loop with c = (complex cx cy) for iteration from 0 below *iteration-max* for z = c then (+ (* z z) c) while (< (abs z) *escape-radius*) finally (return iteration)) for pixel = (round (* 255 (/ (- *iteration-max* iteration) *iteration-max*))) do (setf (aref image y x) pixel))) (write-pgm image filespec)))
D
Textual Version
This uses std.complex because D built-in complex numbers are deprecated.
void main() { import std.stdio, std.complex; for (real y = -1.2; y < 1.2; y += 0.05) { for (real x = -2.05; x < 0.55; x += 0.03) { auto z = 0.complex; foreach (_; 0 .. 100) z = z ^^ 2 + complex(x, y); write(z.abs < 2 ? '#' : '.'); } writeln; } }
{{out}}
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
................................................................##.....................
.............................................................######....................
.............................................................#######...................
..............................................................######...................
..........................................................#.#.###..#.#.................
...................................................##....################..............
..................................................###.######################.###.......
...................................................############################........
................................................###############################........
................................................################################.......
.............................................#####################################.....
..............................................###################################......
..............................##.####.#......####################################......
..............................###########....####################################......
............................###############.######################################.....
............................###############.#####################################......
........................##.#####################################################.......
......#.#####################################################################..........
........................##.#####################################################.......
............................###############.#####################################......
............................###############.######################################.....
..............................###########....####################################......
..............................##.####.#......####################################......
..............................................###################################......
.............................................#####################################.....
................................................################################.......
................................................###############################........
...................................................############################........
..................................................###.######################.###.......
...................................................##....################..............
..........................................................#.#.###..#.#.................
..............................................................######...................
.............................................................#######...................
.............................................................######....................
................................................................##.....................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
More Functional Textual Version
The output is similar.
void main() { import std.stdio, std.complex, std.range, std.algorithm; foreach (immutable y; iota(-1.2, 1.2, 0.05)) iota(-2.05, 0.55, 0.03).map!(x => 0.complex .recurrence!((a, n) => a[n - 1] ^^ 2 + complex(x, y)) .drop(100).front.abs < 2 ? '#' : '.').writeln; }
Graphical Version
{{libheader|QD}} {{libheader|SDL}} {{libheader|Phobos}}
import qd; double lensqr(cdouble c) { return c.re * c.re + c.im * c.im; } const Limit = 150; void main() { screen(640, 480); for (int y = 0; y < screen.h; ++y) { flip; events; for (int x = 0; x < screen.w; ++x) { auto c_x = x * 1.0 / screen.w - 0.5, c_y = y * 1.0 / screen.h - 0.5, c = c_y * 2.0i + c_x * 3.0 - 1.0, z = 0.0i + 0.0, i = 0; for (; i < Limit; ++i) { z = z * z + c; if (lensqr(z) > 4) break; } auto value = cast(ubyte) (i * 255.0 / Limit); pset(x, y, rgb(value, value, value)); } } while (true) { flip; events; } }
Dart
Implementation in Google Dart works on http://try.dartlang.org/ (as of 10/18/2011) since the language is very new, it may break in the future.
The implementation uses a incomplete Complex class supporting operator overloading.
Complex(this._r,this._i); double get r => _r; double get i => _i; String toString() => "($r,$i)";
Complex operator +(Complex other) => new Complex(r+other.r,i+other.i); Complex operator (Complex other) => new Complex(rother.r-iother.i,rother.i+other.ri); double abs() => rr+i*i; }
void main() { double start_x=-1.5; double start_y=-1.0; double step_x=0.03; double step_y=0.1;
for(int y=0;y<20;y++) { String line=""; for(int x=0;x<70;x++) { Complex c=new Complex(start_x+step_xx,start_y+step_yy); Complex z=new Complex(0.0, 0.0); for(int i=0;i<100;i++) { z=z*(z)+c; if(z.abs()>2) { break; } } line+=z.abs()>2 ? " " : "*"; } print(line); } }
## Dc
### ASCII output
{{works with|GNU Dc}}
{{works with|OpenBSD Dc}}
This can be done in a more Dc-ish way, e.g. by moving the loop macros' definitions to the initialisations in the top instead of saving the macro definition of inner loops over and over again in outer loops.
```dc
_2.1 sx # xmin = -2.1
0.7 sX # xmax = 0.7
_1.2 sy # ymin = -1.2
1.2 sY # ymax = 1.2
32 sM # maxiter = 32
80 sW # image width
25 sH # image height
8 k # precision
[ q ] sq # quitter helper macro
# for h from 0 to H-1
0 sh
[
lh lH =q # quit if H reached
# for w from 0 to W-1
0 sw
[
lw lW =q # quit if W reached
# (w,h) -> (R,I)
# | |
# | ymin + h*(ymax-ymin)/(height-1)
# xmin + w*(xmax-xmin)/(width-1)
lX lx - lW 1 - / lw * lx + sR
lY ly - lH 1 - / lh * ly + sI
# iterate for (R,I)
0 sr # r:=0
0 si # i:=0
0 sa # a:=0 (r squared)
0 sb # b:=0 (i squared)
0 sm # m:=0
# do while m!=M and a+b=<4
[
lm lM =q # exit if m==M
la lb + 4<q # exit if >4
2 lr * li * lI + si # i:=2*r*i+I
la lb - lR + sr # r:=a-b+R
lm 1 + sm # m+=1
lr 2 ^ sa # a:=r*r
li 2 ^ sb # b:=i*i
l0 x # loop
] s0
l0 x
lm 32 + P # print "pixel"
lw 1 + sw # w+=1
l1 x # loop
] s1
l1 x
A P # linefeed
lh 1 + sh # h+=1
l2 x # loop
] s2
l2 x
{{out}}
!!!!!!!!!!!!!!!"""""""""""""####################################""""""""""""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$$%'0(%%%$$$$$#####"""""""""""
!!!!!!!!!!!"""""""#######################$$$$$$$$%%%&&(++)++&$$$$$$$######""""""
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*@;/*('&%%$$$$$$#######"""
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''),@@@@@@@+'&%%%%%$$$$########
!!!!!!!"""####################$$$$$$$$%%%&'())((())*-@@@@@@.+))('&&&&+&%$$######
!!!!!!""###################$$$$$%%%%%%&&&'+.@@@08@@@@@@@@@@@@@@@/+,@//@)%%$#####
!!!!!"################$$$%%%%%%%%%%&&&&')-+7@@@@@@@@@@@@@@@@@@@@@@@@@4(&&%$$####
!!!!"##########$$$$$%%&(,('''''''''''((*-5@@@@@@@@@@@@@@@@@@@@@@@@@@@3+)4&%$$###
!!!!####$$$$$$$$%%%%%&'(*-@1.+/@-4+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@3+'&%$$$##
!!!!#$$$$$$$$$%%%%%%'''++.7@@@@@@@@@9/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@<6'%%$$$$#
!!!#$$$$$$$%&&&&''().-2.6@@@@@@@@@@@@@>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'&%%$$$$#
!!!@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@2+)'&&%%$$$$#
!!!#$$$$$$$%&&&&''().-2.6@@@@@@@@@@@@@>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'&%%$$$$#
!!!!#$$$$$$$$$%%%%%%'''++.7@@@@@@@@@9/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@<6'%%$$$$#
!!!!####$$$$$$$$%%%%%&'(*-@1.+/@-4+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@3+'&%$$$##
!!!!"##########$$$$$%%&(,('''''''''''((*-5@@@@@@@@@@@@@@@@@@@@@@@@@@@3+)4&%$$###
!!!!!"################$$$%%%%%%%%%%&&&&')-+7@@@@@@@@@@@@@@@@@@@@@@@@@4(&&%$$####
!!!!!!""###################$$$$$%%%%%%&&&'+.@@@08@@@@@@@@@@@@@@@/+,@//@)%%$#####
!!!!!!!"""####################$$$$$$$$%%%&'())((())*-@@@@@@.+))('&&&&+&%$$######
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''),@@@@@@@+'&%%%%%$$$$########
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*@;/*('&%%$$$$$$#######"""
!!!!!!!!!!!"""""""#######################$$$$$$$$%%%&&(++)++&$$$$$$$######""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$$%'0(%%%$$$$$#####"""""""""""
!!!!!!!!!!!!!!!"""""""""""""####################################""""""""""""""""
===PGM (P5) output=== This is a condensed version of the ASCII output variant modified to generate a PGM (P5) image.
_2.1 sx 0.7 sX _1.2 sy 1.2 sY
32 sM
640 sW 480 sH
8 k
[P5] P A P
lW n 32 P lH n A P
lM 1 - n A P
[ q ] sq
0 sh
[
lh lH =q
0 sw
[
lw lW =q
lX lx - lW 1 - / lw * lx + sR
lY ly - lH 1 - / lh * ly + sI
0 sr 0 si 0 sa 0 sb 0 sm
[
lm lM =q
la lb + 4<q
2 lr * li * lI + si
la lb - lR + sr
lm 1 + sm
lr 2 ^ sa
li 2 ^ sb
l0 x
] s0
l0 x
lm 1 - P
lw 1 + sw
l1 x
] s1
l1 x
lh 1 + sh
l2 x
] s2
l2 x
=={{header|DEC BASIC-PLUS}}==
Works under RSTS/E v7.0 on the [[wp:SIMH|simh]] PDP-11 emulator. For installation procedures for RSTS/E, see [http://www.eecis.udel.edu/~mader/delta/downloadrsts.html here].
{{out}}
```txt
>>>>>>
### ==<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<========
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<
### ==
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<
### =
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<=====
>>==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<====
>>=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<===
>=<<<<<<<<;;;:599999999886 %78:;;<<<<<<==
><<<<;;;;;:::972456-567763 +9;;<<<<<<<=
><;;;;;;::::9875& .3 *9;;;<<<<<<=
>;;;;;;::997564' ' 8:;;;<<<<<<=
>::988897735/ &89:;;;<<<<<<=
>::988897735/ &89:;;;<<<<<<=
>;;;;;;::997564' ' 8:;;;<<<<<<=
><;;;;;;::::9875& .3 *9;;;<<<<<<=
><<<<;;;;;:::972456-567763 +9;;<<<<<<<=
>=<<<<<<<<;;;:599999999886 %78:;;<<<<<<==
>>=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<===
>>==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<====
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<=====
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<
### =
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<
### ==
>>>>>>
### ==<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<========
DWScript
{{trans|D}}
const maxIter = 256;
var x, y, i : Integer;
for y:=-39 to 39 do begin
for x:=-39 to 39 do begin
var c := Complex(y/40-0.5, x/40);
var z := Complex(0, 0);
for i:=1 to maxIter do begin
z := z*z + c;
if Abs(z)>=4 then Break;
end;
if i>=maxIter then
Print('#')
else Print('.');
end;
PrintLn('');
end;
EasyLang
[https://easylang.online/apps/mandelbrot.html Run it]
## eC
[[File:Mandelbrot4.png]]
[http://ecere.com/apps/mandelbrot/ (Try it in a WebApp)]
Drawing code:
```eC
void drawMandelbrot(Bitmap bmp, float range, Complex center, ColorAlpha * palette, int nPalEntries, int nIterations, float scale)
{
int x, y;
int w = bmp.width, h = bmp.height;
ColorAlpha * picture = (ColorAlpha *)bmp.picture;
double logOf2 = log(2);
Complex d
{
w > h ? range : range * w / h,
h > w ? range : range * h / w
};
Complex C0 { center.a - d.a/2, center.b - d.b/2 };
Complex C = C0;
double delta = d.a / w;
for(y = 0; y < h; y++, C.a = C0.a, C.b += delta)
{
for(x = 0; x < w; x++, picture++, C.a += delta)
{
Complex Z { };
int i;
double ii = 0;
bool out = false;
double Za2 = Z.a * Z.a, Zb2 = Z.b * Z.b;
for(i = 0; i < nIterations; i++)
{
double z2;
Z = { Za2 - Zb2, 2*Z.a*Z.b };
Z.a += C.a;
Z.b += C.b;
Za2 = Z.a * Z.a, Zb2 = Z.b * Z.b;
z2 = Za2 + Zb2;
if(z2 >= 2*2)
{
ii = (double)(i + 1 - log(0.5 * log(z2)) / logOf2);
out = true;
break;
}
}
if(out)
{
float si = (float)(ii * scale);
int i0 = ((int)si) % nPalEntries;
*picture = palette[i0];
}
else
*picture = black;
}
}
}
Interactive class with Rubberband Zoom:
class Mandelbrot : Window
{
caption = $"Mandelbrot";
borderStyle = sizable;
hasMaximize = true;
hasMinimize = true;
hasClose = true;
clientSize = { 600, 600 };
Point mouseStart, mouseEnd;
bool dragging;
bool needUpdate;
float scale;
int nIterations; nIterations = 256;
ColorAlpha * palette;
int nPalEntries;
Complex center { -0.75, 0 };
float range; range = 4;
Bitmap bmp { };
Mandelbrot()
{
static ColorKey keys[] =
{
{ navy, 0.0f },
{ Color { 146, 213, 237 }, 0.198606268f },
{ white, 0.3f },
{ Color { 255, 255, 124 }, 0.444250882f },
{ Color { 255, 100, 0 }, 0.634146333f },
{ navy, 1 }
};
nPalEntries = 30000;
palette = new ColorAlpha[nPalEntries];
scale = nPalEntries / 175.0f;
PaletteGradient(palette, nPalEntries, keys, sizeof(keys)/sizeof(keys[0]), 1.0);
needUpdate = true;
}
~Mandelbrot() { delete palette; }
void OnRedraw(Surface surface)
{
if(needUpdate)
{
drawMandelbrot(bmp, range, center, palette, nPalEntries, nIterations, scale);
needUpdate = false;
}
surface.Blit(bmp, 0,0, 0,0, bmp.width, bmp.height);
if(dragging)
{
surface.foreground = lime;
surface.Rectangle(mouseStart.x, mouseStart.y, mouseEnd.x, mouseEnd.y);
}
}
bool OnLeftButtonDown(int x, int y, Modifiers mods)
{
mouseEnd = mouseStart = { x, y };
Capture();
dragging = true;
Update(null);
return true;
}
bool OnLeftButtonUp(int x, int y, Modifiers mods)
{
if(dragging)
{
int dx = Abs(mouseEnd.x - mouseStart.x), dy = Abs(mouseEnd.y - mouseStart.y);
if(dx > 4 && dy > 4)
{
int w = clientSize.w, h = clientSize.h;
float rangeX = w > h ? range : range * w / h;
float rangeY = h > w ? range : range * h / w;
center.a += ((mouseStart.x + mouseEnd.x) - w) / 2.0f * rangeX / w;
center.b += ((mouseStart.y + mouseEnd.y) - h) / 2.0f * rangeY / h;
range = dy > dx ? dy * range / h : dx * range / w;
needUpdate = true;
Update(null);
}
ReleaseCapture();
dragging = false;
}
return true;
}
bool OnMouseMove(int x, int y, Modifiers mods)
{
if(dragging)
{
mouseEnd = { x, y };
Update(null);
}
return true;
}
bool OnRightButtonDown(int x, int y, Modifiers mods)
{
range = 4;
nIterations = 256;
center = { -0.75, 0 };
needUpdate = true;
Update(null);
return true;
}
void OnResize(int width, int height)
{
bmp.Allocate(null, width, height, 0, pixelFormat888, false);
needUpdate = true;
Update(null);
}
bool OnKeyHit(Key key, unichar ch)
{
switch(key)
{
case space: case keyPadPlus: case plus:
nIterations += 256;
needUpdate = true;
Update(null);
break;
}
return true;
}
}
Mandelbrot mandelbrotForm {};
EchoLisp
(lib 'math) ;; fractal function
(lib 'plot)
;; (fractal z zc n) iterates z := z^2 + c, n times
;; 100 iterations
(define (mset z) (if (= Infinity (fractal 0 z 100)) Infinity z))
;; plot function argument inside square (-2 -2), (2,2)
(plot-z-arg mset -2 -2)
;; result here [http://www.echolalie.org/echolisp/help.html#fractal]
Elixir
defmodule Mandelbrot do def set do xsize = 59 ysize = 21 minIm = -1.0 maxIm = 1.0 minRe = -2.0 maxRe = 1.0 stepX = (maxRe - minRe) / xsize stepY = (maxIm - minIm) / ysize Enum.each(0..ysize, fn y -> im = minIm + stepY * y Enum.map(0..xsize, fn x -> re = minRe + stepX * x 62 - loop(0, re, im, re, im, re*re+im*im) end) |> IO.puts end) end defp loop(n, _, _, _, _, _) when n>=30, do: n defp loop(n, _, _, _, _, v) when v>4.0, do: n-1 defp loop(n, re, im, zr, zi, _) do a = zr * zr b = zi * zi loop(n+1, re, im, a-b+re, 2*zr*zi+im, a+b) end end Mandelbrot.set
{{out}}
??????
### ==<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<========
?????===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<
### ==
????===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<
### =
???==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<=====
??==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<====
??=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<===
?=<<<<<<<<;;;:599999999886 %78:;;<<<<<<==
?<<<<;;;;;:::972456-567763 +9;;<<<<<<<=
?<;;;;;;::::9875& .3 *9;;;<<<<<<=
?;;;;;;::997564' ' 8:;;;<<<<<<=
?::988897735/ &89:;;;<<<<<<=
?::988897735/ &89:;;;<<<<<<=
?;;;;;;::997564' ' 8:;;;<<<<<<=
?<;;;;;;::::9875& .3 *9;;;<<<<<<=
?<<<<;;;;;:::972456-567763 +9;;<<<<<<<=
?=<<<<<<<<;;;:599999999886 %78:;;<<<<<<==
??=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<===
??==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<====
???==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<=====
????===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<
### =
?????===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<
### ==
??????
### ==<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<========
Erlang
{{trans|Haskell}}
Function ''seq_float/2'' is copied from [https://gist.github.com/andruby/241489 Andrew Fecheyr's GitHubGist].
Using module complex from [https://github.com/ghulette/mandelbrot-erlang/blob/master/simple/complex.erl Geoff Hulette's GitHub repository]
[https://github.com/ghulette/mandelbrot-erlang Geoff Hulette's GitHub repository] provides two alternative implementations which are very interesting.
-module(mandelbrot). -export([test/0]). magnitude(Z) -> R = complex:real(Z), I = complex:imaginary(Z), R * R + I * I. mandelbrot(A, MaxI, Z, I) -> case (I < MaxI) and (magnitude(Z) < 2.0) of true -> NZ = complex:add(complex:mult(Z, Z), A), mandelbrot(A, MaxI, NZ, I + 1); false -> case I of MaxI -> $*; _ -> $ end end. test() -> lists:map( fun(S) -> io:format("~s",[S]) end, [ [ begin Z = complex:make(X, Y), mandelbrot(Z, 50, Z, 1) end || X <- seq_float(-2, 0.5, 0.0315) ] ++ "\n" || Y <- seq_float(-1,1, 0.05) ] ), ok. % ************************************************** % Copied from https://gist.github.com/andruby/241489 % ************************************************** seq_float(Min, Max, Inc, Counter, Acc) when (Counter*Inc + Min) >= Max -> lists:reverse([Max|Acc]); seq_float(Min, Max, Inc, Counter, Acc) -> seq_float(Min, Max, Inc, Counter+1, [Inc * Counter + Min|Acc]). seq_float(Min, Max, Inc) -> seq_float(Min, Max, Inc, 0, []). % **************************************************
Output:
**
******
********
******
******** ** *
*** *****************
************************ ***
****************************
******************************
******************************
************************************
* **********************************
** ***** * **********************************
*********** ************************************
************** ************************************
***************************************************
*****************************************************
*****************************************************
*****************************************************
***************************************************
************** ************************************
*********** ************************************
** ***** * **********************************
* **********************************
************************************
******************************
******************************
****************************
************************ ***
*** *****************
******** ** *
******
********
******
**
ERRE
PROGRAM MANDELBROT
!$KEY
!$INCLUDE="PC.LIB"
BEGIN
SCREEN(7)
GR_WINDOW(-2,1.5,2,-1.5)
FOR X0=-2 TO 2 STEP 0.01 DO
FOR Y0=-1.5 TO 1.5 STEP 0.01 DO
X=0
Y=0
ITERATION=0
MAX_ITERATION=223
WHILE (X*X+Y*Y<=(2*2) AND ITERATION<MAX_ITERATION) DO
X_TEMP=X*X-Y*Y+X0
Y=2*X*Y+Y0
X=X_TEMP
ITERATION=ITERATION+1
END WHILE
IF ITERATION<>MAX_ITERATION THEN
C=ITERATION
ELSE
C=0
END IF
PSET(X0,Y0,C)
END FOR
END FOR
END PROGRAM
Note: This is a PC version which uses EGA 16-color 320x200. Graphic commands are taken from PC.LIB library.
=={{header|F Sharp|F#}}==
open System.Drawing open System.Windows.Forms type Complex = { re : float; im : float } let cplus (x:Complex) (y:Complex) : Complex = { re = x.re + y.re; im = x.im + y.im } let cmult (x:Complex) (y:Complex) : Complex = { re = x.re * y.re - x.im * y.im; im = x.re * y.im + x.im * y.re; } let norm (x:Complex) : float = x.re*x.re + x.im*x.im type Mandel = class inherit Form static member xPixels = 500 static member yPixels = 500 val mutable bmp : Bitmap member x.mandelbrot xMin xMax yMin yMax maxIter = let rec mandelbrotIterator z c n = if (norm z) > 2.0 then false else match n with | 0 -> true | n -> let z' = cplus ( cmult z z ) c in mandelbrotIterator z' c (n-1) let dx = (xMax - xMin) / (float (Mandel.xPixels)) let dy = (yMax - yMin) / (float (Mandel.yPixels)) in for xi = 0 to Mandel.xPixels-1 do for yi = 0 to Mandel.yPixels-1 do let c = {re = xMin + (dx * float(xi) ) ; im = yMin + (dy * float(yi) )} in if (mandelbrotIterator {re=0.;im=0.;} c maxIter) then x.bmp.SetPixel(xi,yi,Color.Azure) else x.bmp.SetPixel(xi,yi,Color.Black) done done member public x.generate () = x.mandelbrot (-1.5) 0.5 (-1.0) 1.0 200 ; x.Refresh() new() as x = {bmp = new Bitmap(Mandel.xPixels , Mandel.yPixels)} then x.Text <- "Mandelbrot set" ; x.Width <- Mandel.xPixels ; x.Height <- Mandel.yPixels ; x.BackgroundImage <- x.bmp; x.generate(); x.Show(); end let f = new Mandel() do Application.Run(f)
=== Alternate version, applicable to text and GUI === ''' Basic generation code '''
let getMandelbrotValues width height maxIter ((xMin,xMax),(yMin,yMax)) = let mandIter (cr:float,ci:float) = let next (zr,zi) = (cr + (zr * zr - zi * zi)), (ci + (zr * zi + zi * zr)) let rec loop = function | step,_ when step=maxIter->0 | step,(zr,zi) when ((zr * zr + zi * zi) > 2.0) -> step | step,z -> loop ((step + 1), (next z)) loop (0,(0.0, 0.0)) let forPos = let dx, dy = (xMax - xMin) / (float width), (yMax - yMin) / (float height) fun y x -> mandIter ((xMin + dx * float(x)), (yMin + dy * float(y))) [0..height-1] |> List.map(fun y->[0..width-1] |> List.map (forPos y))
''' Text display '''
getMandelbrotValues 80 25 50 ((-2.0,1.0),(-1.0,1.0)) |> List.map(fun row-> row |> List.map (function | 0 ->" " |_->".") |> String.concat "") |> List.iter (printfn "%s")
Results: {{out}}
................................................................................
................................................................................
................................................. .............................
................................................ ...........................
................................................. ...........................
....................................... . ......................
........................................ .................
.................................... ..................
.................................... .................
.......................... ...... ................
....................... ... ................
..................... . ................
................. .................
................. .................
..................... . ................
....................... ... ................
.......................... ...... ................
.................................... .................
.................................... ..................
........................................ .................
....................................... . ......................
................................................. ...........................
................................................ ...........................
................................................. .............................
................................................................................
''' Graphics display '''
open System.Drawing open System.Windows.Forms let showGraphic (colorForIter: int -> Color) (width: int) (height:int) maxIter view = new Form() |> fun frm -> frm.Width <- width frm.Height <- height frm.BackgroundImage <- new Bitmap(width,height) |> fun bmp -> getMandelbrotValues width height maxIter view |> List.mapi (fun y row->row |> List.mapi (fun x v->((x,y),v))) |> List.collect id |> List.iter (fun ((x,y),v) -> bmp.SetPixel(x,y,(colorForIter v))) bmp frm.Show() let toColor = (function | 0 -> (0,0,0) | n -> ((31 &&& n) |> fun x->(0, 18 + x * 5, 36 + x * 7))) >> Color.FromArgb showGraphic toColor 640 480 5000 ((-2.0,1.0),(-1.0,1.0))
Factor
! with ("::") or without (":") generalizations:
! : [a..b] ( steps a b -- a..b ) 2dup swap - 4 nrot 1 - / <range> ;
:: [a..b] ( steps a b -- a..b ) a b b a - steps 1 - / <range> ;
: >char ( n -- c )
dup -1 = [ drop 32 ] [ 26 mod CHAR: a + ] if ;
! iterates z' = z^2 + c, Factor does complex numbers!
: iter ( c z -- z' ) dup * + ;
: unbound ( c -- ? ) absq 4 > ;
:: mz ( c max i z -- n )
{
{ [ i max >= ] [ -1 ] }
{ [ z unbound ] [ i ] }
[ c max i 1 + c z iter mz ]
} cond ;
: mandelzahl ( c max -- n ) 0 0 mz ;
:: mandel ( w h max -- )
h -1. 1. [a..b] ! range over y
[ w -2. 1. [a..b] ! range over x
[ dupd swap rect> max mandelzahl >char ] map
>string print
drop ! old y
] each
;
70 25 1000 mandel
{{out}}
bbbbbbbcccccdddddddddddddddddddeeeeeeeffghjpjl feeeeedddddcccccccccccc
bbbbbbccccddddddddddddddddddeeeeeeeefffghikopjhgffeeeeedddddcccccccccc
bbbbbcccddddddddddddddddddeeeeeeeefffggjotx etiigfffeeeeddddddcccccccc
bbbbccddddddddddddddddddeeeeeeeffgggghhjq iihgggfffeedddddddcccccc
bbbccddddddddddddddddeeeeeefffghvasjjqqyqt upqlrjhhhkhfedddddddccccc
bbbcdddddddddddddddeeeeffffffgghks c qnbpfmgfedddddddcccc
bbcdddddddddddddeefffffffffgggipmt qhgfeedddddddccc
bbdddddddddeeeefhlggggggghhhhils ljigfeedddddddcc
bcddddeeeeeefffghmllkjiljjiijle yhfeedddddddcc
bddeeeeeeeffffghhjoj do clmq qlgfeeedddddddc
bdeeeeeefffffhiijpu sm ohffeeedddddddc
beffeefgggghhjocsu higffeeedddddddc
cmihgffeeedddddddd
beffeefgggghhjocsu higffeeedddddddc
bdeeeeeefffffhiijpu sd ohffeeedddddddc
bddeeeeeeeffffghhjoj do clmq qlgfeeedddddddc
bcddddeeeeeefffghmllkjiljjiijle yhfeedddddddcc
bbdddddddddeeeefhlggggggghhhhils ljigfeedddddddcc
bbcdddddddddddddeefffffffffgggipmt qhgfeedddddddccc
bbbcdddddddddddddddeeeeffffffgghks c qnbpfmgfedddddddcccc
bbbccddddddddddddddddeeeeeefffghvasjjqqyqt upqlrjhhhkhfedddddddccccc
bbbbccddddddddddddddddddeeeeeeeffgggghhjq iihgggfffeedddddddcccccc
bbbbbcccddddddddddddddddddeeeeeeeefffggjotx etiigfffeeeeddddddcccccccc
bbbbbbccccddddddddddddddddddeeeeeeeefffghikopjhgffeeeeedddddcccccccccc
bbbbbbbcccccdddddddddddddddddddeeeeeeeffghjpjl feeeeedddddcccccccccccc
=={{header|Fōrmulæ}}==
In [https://wiki.formulae.org/Mandelbrot_set this] page you can see the solution of this task.
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text ([http://wiki.formulae.org/Editing_F%C5%8Drmul%C3%A6_expressions more info]). Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for transportation effects more than visualization and edition.
The option to show Fōrmulæ programs and their results is showing images. Unfortunately images cannot be uploaded in Rosetta Code.
Forth
This uses [[grayscale image]] utilities.
500 value max-iter
: mandel ( gmp F: imin imax rmin rmax -- )
0e 0e { F: imin F: imax F: rmin F: rmax F: Zr F: Zi }
dup bheight 0 do
i s>f dup bheight s>f f/ imax imin f- f* imin f+ TO Zi
dup bwidth 0 do
i s>f dup bwidth s>f f/ rmax rmin f- f* rmin f+ TO Zr
Zr Zi max-iter
begin 1- dup
while fover fdup f* fover fdup f*
fover fover f+ 4e f<
while f- Zr f+
frot frot f* 2e f* Zi f+
repeat fdrop fdrop
drop 0 \ for a pretty grayscale image, replace with: 255 max-iter */
else drop 255
then fdrop fdrop
over i j rot g!
loop
loop drop ;
80 24 graymap
dup -1e 1e -2e 1e mandel
dup gshow
free bye
Fortran
{{Works with|Fortran|90 and later}}
program mandelbrot
implicit none
integer , parameter :: rk = selected_real_kind (9, 99)
integer , parameter :: i_max = 800
integer , parameter :: j_max = 600
integer , parameter :: n_max = 100
real (rk), parameter :: x_centre = -0.5_rk
real (rk), parameter :: y_centre = 0.0_rk
real (rk), parameter :: width = 4.0_rk
real (rk), parameter :: height = 3.0_rk
real (rk), parameter :: dx_di = width / i_max
real (rk), parameter :: dy_dj = -height / j_max
real (rk), parameter :: x_offset = x_centre - 0.5_rk * (i_max + 1) * dx_di
real (rk), parameter :: y_offset = y_centre - 0.5_rk * (j_max + 1) * dy_dj
integer, dimension (i_max, j_max) :: image
integer :: i
integer :: j
integer :: n
real (rk) :: x
real (rk) :: y
real (rk) :: x_0
real (rk) :: y_0
real (rk) :: x_sqr
real (rk) :: y_sqr
do j = 1, j_max
y_0 = y_offset + dy_dj * j
do i = 1, i_max
x_0 = x_offset + dx_di * i
x = 0.0_rk
y = 0.0_rk
n = 0
do
x_sqr = x ** 2
y_sqr = y ** 2
if (x_sqr + y_sqr > 4.0_rk) then
image (i, j) = 255
exit
end if
if (n == n_max) then
image (i, j) = 0
exit
end if
y = y_0 + 2.0_rk * x * y
x = x_0 + x_sqr - y_sqr
n = n + 1
end do
end do
end do
open (10, file = 'out.pgm')
write (10, '(a/ i0, 1x, i0/ i0)') 'P2', i_max, j_max, 255
write (10, '(i0)') image
close (10)
end program mandelbrot
Frink
This draws a graphical Mandelbrot set using Frink's built-in graphics and complex arithmetic.
// Maximum levels for each pixel.
levels = 60
// Create a random color for each level.
colors = new array[[levels]]
for a = 0 to levels-1
colors@a = new color[randomFloat[0,1], randomFloat[0,1], randomFloat[0,1]]
// Make this number smaller for higher resolution.
stepsize = .005
g = new graphics
g.antialiased[false]
for im = -1.2 to 1.2 step stepsize
{
imag = i * im
for real = -2 to 1 step stepsize
{
C = real + imag
z = 0
count = -1
do
{
z = z^2 + C
count=count+1;
} while abs[z] < 4 and count < levels
g.color[colors@((count-1) mod levels)]
g.fillRectSize[real, im, stepsize, stepsize]
}
}
g.show[]
Futhark
{{incorrect|Futhark|Futhark's syntax has changed, so this example will not compile}} Computes escapes for each pixel, but not the colour.
default(f32)
type complex = (f32, f32)
fun dot(c: complex): f32 =
let (r, i) = c
in r * r + i * i
fun multComplex(x: complex, y: complex): complex =
let (a, b) = x
let (c, d) = y
in (a*c - b * d,
a*d + b * c)
fun addComplex(x: complex, y: complex): complex =
let (a, b) = x
let (c, d) = y
in (a + c,
b + d)
fun divergence(depth: int, c0: complex): int =
loop ((c, i) = (c0, 0)) = while i < depth && dot(c) < 4.0 do
(addComplex(c0, multComplex(c, c)),
i + 1)
in i
fun mandelbrot(screenX: int, screenY: int, depth: int, view: (f32,f32,f32,f32)): [screenX][screenY]int =
let (xmin, ymin, xmax, ymax) = view
let sizex = xmax - xmin
let sizey = ymax - ymin
in map (fn (x: int): [screenY]int =>
map (fn (y: int): int =>
let c0 = (xmin + (f32(x) * sizex) / f32(screenX),
ymin + (f32(y) * sizey) / f32(screenY))
in divergence(depth, c0))
(iota screenY))
(iota screenX)
fun main(screenX: int, screenY: int, depth: int, xmin: f32, ymin: f32, xmax: f32, ymax: f32): [screenX][screenY]int =
mandelbrot(screenX, screenY, depth, (xmin, ymin, xmax, ymax))
GLSL
This example works directly on Shadertoy link[https://www.shadertoy.com/view/XsfGWS]
void main(void)
{
vec2 uv = gl_FragCoord.xy / iResolution.xy;
float scale = iResolution.y / iResolution.x;
uv=((uv-0.5)*5.5);
uv.y*=scale;
uv.y+=0.0;
uv.x-=0.5;
vec2 z = vec2(0.0, 0.0);
vec3 c = vec3(0.0, 0.0, 0.0);
float v;
for(int i=0;(i<170);i++)
{
if(((z.x*z.x+z.y*z.y) >= 4.0)) break;
z = vec2(z.x*z.x - z.y*z.y, 2.0*z.y*z.x) + uv;
if((z.x*z.x+z.y*z.y) >= 2.0)
{
c.b=float(i)/20.0;
c.r=sin((float(i)/5.0));
}
}
gl_FragColor = vec4(c,1.0);
}
gnuplot
The output from gnuplot is controlled by setting the appropriate values for the options terminal and output.
set terminal png
set output 'mandelbrot.png'
The following script draws an image of the number of iterations it takes to escape the circle with radius rmax with a maximum of nmax.
rmax = 2
nmax = 100
complex (x, y) = x * {1, 0} + y * {0, 1}
mandelbrot (z, z0, n) = n == nmax || abs (z) > rmax ? n : mandelbrot (z ** 2 + z0, z0, n + 1)
set samples 200
set isosamples 200
set pm3d map
set size square
splot [-2 : .8] [-1.4 : 1.4] mandelbrot (complex (0, 0), complex (x, y), 0) notitle
{{out}} [[File:mandelbrot.png]]
Go
;Text Prints an 80-char by 41-line depiction.
package main import "fmt" import "math/cmplx" func mandelbrot(a complex128) (z complex128) { for i := 0; i < 50; i++ { z = z*z + a } return } func main() { for y := 1.0; y >= -1.0; y -= 0.05 { for x := -2.0; x <= 0.5; x += 0.0315 { if cmplx.Abs(mandelbrot(complex(x, y))) < 2 { fmt.Print("*") } else { fmt.Print(" ") } } fmt.Println("") } }
;Graphical [[File:GoMandelbrot.png|thumb|right|.png image]]
package main import ( "fmt" "image" "image/color" "image/draw" "image/png" "math/cmplx" "os" ) const ( maxEsc = 100 rMin = -2. rMax = .5 iMin = -1. iMax = 1. width = 750 red = 230 green = 235 blue = 255 ) func mandelbrot(a complex128) float64 { i := 0 for z := a; cmplx.Abs(z) < 2 && i < maxEsc; i++ { z = z*z + a } return float64(maxEsc-i) / maxEsc } func main() { scale := width / (rMax - rMin) height := int(scale * (iMax - iMin)) bounds := image.Rect(0, 0, width, height) b := image.NewNRGBA(bounds) draw.Draw(b, bounds, image.NewUniform(color.Black), image.ZP, draw.Src) for x := 0; x < width; x++ { for y := 0; y < height; y++ { fEsc := mandelbrot(complex( float64(x)/scale+rMin, float64(y)/scale+iMin)) b.Set(x, y, color.NRGBA{uint8(red * fEsc), uint8(green * fEsc), uint8(blue * fEsc), 255}) } } f, err := os.Create("mandelbrot.png") if err != nil { fmt.Println(err) return } if err = png.Encode(f, b); err != nil { fmt.Println(err) } if err = f.Close(); err != nil { fmt.Println(err) } }
Haskell
{{trans|Ruby}}
import Data.Bool import Data.Complex (Complex((:+)), magnitude) mandelbrot :: RealFloat a => Complex a -> Complex a mandelbrot a = iterate ((a +) . (^ 2)) 0 !! 50 main :: IO () main = mapM_ putStrLn [ [ bool ' ' '*' (2 > magnitude (mandelbrot (x :+ y))) | x <- [-2,-1.9685 .. 0.5] ] | y <- [1,0.95 .. -1] ]
Save the code to file m.hs and run : runhaskell m.hs
{{Out}}
**
******
********
******
******** ** *
*** *****************
************************ ***
****************************
******************************
******************************
************************************
* **********************************
** ***** * **********************************
*********** ************************************
************** ************************************
***************************************************
*****************************************************
***********************************************************************
*****************************************************
***************************************************
************** ************************************
*********** ************************************
** ***** * **********************************
* **********************************
************************************
******************************
******************************
****************************
************************ ***
*** *****************
******** ** *
******
********
******
**
Haxe
This version compiles for flash version 9 or greater. The compilation command is
haxe -swf mandelbrot.swf -main Mandelbrot
class Mandelbrot extends flash.display.Sprite
{
inline static var MAX_ITER = 255;
public static function main() {
var w = flash.Lib.current.stage.stageWidth;
var h = flash.Lib.current.stage.stageHeight;
var mandelbrot = new Mandelbrot(w, h);
flash.Lib.current.stage.addChild(mandelbrot);
mandelbrot.drawMandelbrot();
}
var image:flash.display.BitmapData;
public function new(width, height) {
super();
var bitmap:flash.display.Bitmap;
image = new flash.display.BitmapData(width, height, false);
bitmap = new flash.display.Bitmap(image);
this.addChild(bitmap);
}
public function drawMandelbrot() {
image.lock();
var step_x = 3.0 / (image.width-1);
var step_y = 2.0 / (image.height-1);
for (i in 0...image.height) {
var ci = i * step_y - 1.0;
for (j in 0...image.width) {
var k = 0;
var zr = 0.0;
var zi = 0.0;
var cr = j * step_x - 2.0;
while (k <= MAX_ITER && (zr*zr + zi*zi) <= 4) {
var temp = zr*zr - zi*zi + cr;
zi = 2*zr*zi + ci;
zr = temp;
k ++;
}
paint(j, i, k);
}
}
image.unlock();
}
inline function paint(x, y, iter) {
var color = iter > MAX_ITER? 0 : iter * 0x100;
image.setPixel(x, y, color);
}
}
Huginn
#! /bin/sh
exec huginn -E "${0}" "${@}"
#! huginn
import Algorithms as algo;
import Mathematics as math;
import Terminal as term;
mandelbrot( x, y ) {
c = math.Complex( x, y );
z = math.Complex( 0., 0. );
s = -1;
for ( i : algo.range( 50 ) ) {
z = z * z + c;
if ( | z | > 2. ) {
s = i;
break;
}
}
return ( s );
}
main( argv_ ) {
imgSize = term_size( argv_ );
yRad = 1.2;
yScale = 2. * yRad / real( imgSize[0] );
xScale = 3.3 / real( imgSize[1] );
glyphTab = [ ".", ":", "-", "+", "+" ].resize( 12, "*" ).resize( 26, "%" ).resize( 50, "@" ).push( " " );
for ( y : algo.range( imgSize[0] ) ) {
line = "";
for ( x : algo.range( imgSize[1] ) ) {
line += glyphTab[ mandelbrot( xScale * real( x ) - 2.3, yScale * real( y ) - yRad ) ];
}
print( line + "\n" );
}
return ( 0 );
}
term_size( argv_ ) {
lines = 25;
columns = 80;
if ( size( argv_ ) == 3 ) {
lines = integer( argv_[1] );
columns = integer( argv_[2] );
} else {
lines = term.lines();
columns = term.columns();
if ( ( lines % 2 ) == 0 ) {
lines -= 1;
}
}
lines -= 1;
columns -= 1;
return ( ( lines, columns ) );
}
{{out}}
........................:::::::::::::::::::------------------------------------------------------::::::::::::::::::::::::::::::::::::
......................::::::::::::::::------------------------------------++++++++++++++++++++---------::::::::::::::::::::::::::::::
....................:::::::::::::-----------------------------------+++++++++++++*******+++++++++++--------::::::::::::::::::::::::::
...................:::::::::::----------------------------------++++++++++++++++****%%******++++++++++---------::::::::::::::::::::::
.................:::::::::----------------------------------++++++++++++++++++++******% %****++++++++++++---------:::::::::::::::::::
................::::::::---------------------------------+++++++++++++++++++++******%%%%%*****+++++++++++++----------::::::::::::::::
...............::::::---------------------------------++++++++++++++++++++*****%%%%% @%%%@***++++++++++++++----------::::::::::::::
..............:::::--------------------------------++++++++++++++++++***********@% @%******+++++++++++++-----------:::::::::::
.............::::-------------------------------+++++++++++++++++****************@ %%***************+++++------------:::::::::
............:::------------------------------+++++++++++++++++****@%%%****%@@%@% %%@ @%%%% %*% ********%**++++------------::::::::
...........:::----------------------------+++++++++++++++++********% @%@@ %%%**%@%%@@**+++++------------::::::
..........:::-------------------------+++++++++++++++++++**********% @ %%***++++++------------:::::
..........:----------------------+++++++++++++++++++++*********%%%% %%******++++++------------::::
.........:-----------------++++++++**************************** %*****+++++-------------:::
.........----------+++++++++++++++****%********%%*********** @%% % %%**++++++-------------::
........:------++++++++++++++++++*******%@@%%**%% %%%*******%% %%***+++++++-------------:
........---+++++++++++++++++++++********%@ @%%%**% %%***+++++++-------------:
.......:-+++++++++++++++++++++*******%%%% @%% @****++++++++-------------
.......-+++++++++++++***********%**@*%@ % %***+++++++++-------------
.......++++++*******************%% @ %*****+++++++++-------------
....... %%******++++++++++-------------
.......++++++*******************%% @ %*****+++++++++-------------
.......-+++++++++++++***********%**@*%@ % %***+++++++++-------------
.......:-+++++++++++++++++++++*******%%%% @%% @****++++++++-------------
........---+++++++++++++++++++++********%@ @%%%**% %%***+++++++-------------:
........:------++++++++++++++++++*******%@@%%**%% %%%*******%% %%***+++++++-------------:
.........----------+++++++++++++++****%********%%*********** @%% % %%**++++++-------------::
.........:-----------------++++++++**************************** %*****+++++-------------:::
..........:----------------------+++++++++++++++++++++*********%%%% %%******++++++------------::::
..........:::-------------------------+++++++++++++++++++**********% @ %%***++++++------------:::::
...........:::----------------------------+++++++++++++++++********% @%@@ %%%**%@%%@@**+++++------------::::::
............:::------------------------------+++++++++++++++++****@%%%****%@@%@% %%@ @%%%% %*% ********%**++++------------::::::::
.............::::-------------------------------+++++++++++++++++****************@ %%***************+++++------------:::::::::
..............:::::--------------------------------++++++++++++++++++***********@% @%******+++++++++++++-----------:::::::::::
...............::::::---------------------------------++++++++++++++++++++*****%%%%% @%%%@***++++++++++++++----------::::::::::::::
................::::::::---------------------------------+++++++++++++++++++++******%%%%%*****+++++++++++++----------::::::::::::::::
.................:::::::::----------------------------------++++++++++++++++++++******% %****++++++++++++---------:::::::::::::::::::
...................:::::::::::----------------------------------++++++++++++++++****%%******++++++++++---------::::::::::::::::::::::
....................:::::::::::::-----------------------------------+++++++++++++*******+++++++++++--------::::::::::::::::::::::::::
......................::::::::::::::::------------------------------------++++++++++++++++++++---------::::::::::::::::::::::::::::::
=={{header|Icon}} and {{header|Unicon}}==
link graphics
procedure main()
width := 750
height := 600
limit := 100
WOpen("size="||width||","||height)
every x:=1 to width & y:=1 to height do
{
z:=complex(0,0)
c:=complex(2.5*x/width-2.0,(2.0*y/height-1.0))
j:=0
while j<limit & cAbs(z)<2.0 do
{
z := cAdd(cMul(z,z),c)
j+:= 1
}
Fg(mColor(j,limit))
DrawPoint(x,y)
}
WriteImage("./mandelbrot.gif")
WDone()
end
procedure mColor(x,limit)
max_color := 2^16-1
color := integer(max_color*(real(x)/limit))
return(if x=limit
then "black"
else color||","||color||",0")
end
record complex(r,i)
procedure cAdd(x,y)
return complex(x.r+y.r,x.i+y.i)
end
procedure cMul(x,y)
return complex(x.r*y.r-x.i*y.i,x.r*y.i+x.i*y.r)
end
procedure cAbs(x)
return sqrt(x.r*x.r+x.i*x.i)
end
{{libheader|Icon Programming Library}} [http://www.cs.arizona.edu/icon/library/src/gprocs/graphics.icn graphics is required ]
{{improve|Unicon|The example is correct; however, Unicon implemented additional graphical features and a better example may be possible.}}
IDL
IDL - Interactive Data Language (free implementation: GDL - GNU Data Language http://gnudatalanguage.sourceforge.net)
PRO Mandelbrot,xRange,yRange,xPixels,yPixels,iterations
xPixelstartVec = Lindgen( xPixels) * Float(xRange[1]-xRange[0]) / $
xPixels + xRange[0]
yPixelstartVec = Lindgen( yPixels) * Float(YRANGE[1]-yrange[0])$
/ yPixels + yRange[0]
constArr = Complex( Rebin( xPixelstartVec, xPixels, yPixels),$
Rebin( Transpose(yPixelstartVec), xPixels, yPixels))
valArr = ComplexArr( xPixels, yPixels)
res = IntArr( xPixels, yPixels)
oriIndex = Lindgen( Long(xPixels) * yPixels)
FOR i = 0, iterations-1 DO BEGIN ; only one loop needed
; calculation for whole array at once
valArr = valArr^2 - constArr
whereIn = Where( Abs( valArr) LE 4.0d, COMPLEMENT=whereOut)
IF whereIn[0] EQ -1 THEN BREAK
valArr = valArr[ whereIn]
constArr = constArr[ whereIn]
IF whereOut[0] NE -1 THEN BEGIN
res[ oriIndex[ whereOut]] = i+1
oriIndex = oriIndex[ whereIn]
ENDIF
ENDFOR
tv,res ; open a window and show the result
END
Mandelbrot,[-1.,2.3],[-1.3,1.3],640,512,200
END
from the command line:
GDL>.run mandelbrot
or
GDL> Mandelbrot,[-1.,2.3],[-1.3,1.3],640,512,200
Inform 7
{{libheader|Glimmr Drawing Commands by Erik Temple}} {{works with|Glulx virtual machine}}
"Mandelbrot"
The story headline is "A Non-Interactive Set".
Include Glimmr Drawing Commands by Erik Temple.
[Q20 fixed-point or floating-point: see definitions below]
Use floating-point math.
Finished is a room.
The graphics-window is a graphics g-window spawned by the main-window.
The position is g-placeabove.
When play begins:
let f10 be 10 as float;
now min re is ( -20 as float ) fdiv f10;
now max re is ( 6 as float ) fdiv f10;
now min im is ( -12 as float ) fdiv f10;
now max im is ( 12 as float ) fdiv f10;
now max iterations is 100;
add color g-Black to the palette;
add color g-Red to the palette;
add hex "#FFA500" to the palette;
add color g-Yellow to the palette;
add color g-Green to the palette;
add color g-Blue to the palette;
add hex "#4B0082" to the palette;
add hex "#EE82EE" to the palette;
open up the graphics-window.
Min Re is a number that varies.
Max Re is a number that varies.
Min Im is a number that varies.
Max Im is a number that varies.
Max Iterations is a number that varies.
Min X is a number that varies.
Max X is a number that varies.
Min Y is a number that varies.
Max Y is a number that varies.
The palette is a list of numbers that varies.
[vertically mirrored version]
Window-drawing rule for the graphics-window when max im is fneg min im:
clear the graphics-window;
let point be { 0, 0 };
now min X is 0 as float;
now min Y is 0 as float;
let mX be the width of the graphics-window minus 1;
let mY be the height of the graphics-window minus 1;
now max X is mX as float;
now max Y is mY as float;
let L be the column order with max mX;
repeat with X running through L:
now entry 1 in point is X;
repeat with Y running from 0 to mY / 2:
now entry 2 in point is Y;
let the scaled point be the complex number corresponding to the point;
let V be the Mandelbrot result for the scaled point;
let C be the color corresponding to V;
if C is 0, next;
draw a rectangle (C) in the graphics-window at the point with size 1 by 1;
now entry 2 in point is mY - Y;
draw a rectangle (C) in the graphics-window at the point with size 1 by 1;
yield to VM;
rule succeeds.
[slower non-mirrored version]
Window-drawing rule for the graphics-window:
clear the graphics-window;
let point be { 0, 0 };
now min X is 0 as float;
now min Y is 0 as float;
let mX be the width of the graphics-window minus 1;
let mY be the height of the graphics-window minus 1;
now max X is mX as float;
now max Y is mY as float;
let L be the column order with max mX;
repeat with X running through L:
now entry 1 in point is X;
repeat with Y running from 0 to mY:
now entry 2 in point is Y;
let the scaled point be the complex number corresponding to the point;
let V be the Mandelbrot result for the scaled point;
let C be the color corresponding to V;
if C is 0, next;
draw a rectangle (C) in the graphics-window at the point with size 1 by 1;
yield to VM;
rule succeeds.
To decide which list of numbers is column order with max (N - number):
let L be a list of numbers;
let L2 be a list of numbers;
let D be 64;
let rev be false;
while D > 0:
let X be 0;
truncate L2 to 0 entries;
while X <= N:
if D is 64 or X / D is odd, add X to L2;
increase X by D;
if rev is true:
reverse L2;
let rev be false;
otherwise:
let rev be true;
add L2 to L;
let D be D / 2;
decide on L.
To decide which list of numbers is complex number corresponding to (P - list of numbers):
let R be a list of numbers;
extend R to 2 entries;
let X be entry 1 in P as float;
let X be (max re fsub min re) fmul (X fdiv max X);
let X be X fadd min re;
let Y be entry 2 in P as float;
let Y be (max im fsub min im) fmul (Y fdiv max Y);
let Y be Y fadd min im;
now entry 1 in R is X;
now entry 2 in R is Y;
decide on R.
To decide which number is Mandelbrot result for (P - list of numbers):
let c_re be entry 1 in P;
let c_im be entry 2 in P;
let z_re be 0 as float;
let z_im be z_re;
let threshold be 4 as float;
let runs be 0;
while 1 is 1:
[ z = z * z ]
let r2 be z_re fmul z_re;
let i2 be z_im fmul z_im;
let ri be z_re fmul z_im;
let z_re be r2 fsub i2;
let z_im be ri fadd ri;
[ z = z + c ]
let z_re be z_re fadd c_re;
let z_im be z_im fadd c_im;
let norm be (z_re fmul z_re) fadd (z_im fmul z_im);
increase runs by 1;
if norm is greater than threshold, decide on runs;
if runs is max iterations, decide on 0.
To decide which number is color corresponding to (V - number):
let L be the number of entries in the palette;
let N be the remainder after dividing V by L;
decide on entry (N + 1) in the palette.
Section - Fractional numbers (for Glulx only)
To decide which number is (N - number) as float: (- (numtof({N})) -).
To decide which number is (N - number) fadd (M - number): (- (fadd({N}, {M})) -).
To decide which number is (N - number) fsub (M - number): (- (fsub({N}, {M})) -).
To decide which number is (N - number) fmul (M - number): (- (fmul({N}, {M})) -).
To decide which number is (N - number) fdiv (M - number): (- (fdiv({N}, {M})) -).
To decide which number is fneg (N - number): (- (fneg({N})) -).
To yield to VM: (- glk_select_poll(gg_event); -).
Use Q20 fixed-point math translates as (- Constant Q20_MATH; -).
Use floating-point math translates as (- Constant FLOAT_MATH; -).
Include (-
#ifdef Q20_MATH;
! Q11.20 format: 1 sign bit, 11 integer bits, 20 fraction bits
[ numtof n r; @shiftl n 20 r; return r; ];
[ fadd n m; return n+m; ];
[ fsub n m; return n-m; ];
[ fmul n m; n = n + $$1000000000; @sshiftr n 10 n; m = m + $$1000000000; @sshiftr m 10 m; return n * m; ];
[ fdiv n m; @sshiftr m 20 m; return n / m; ];
[ fneg n; return -n; ];
#endif;
#ifdef FLOAT_MATH;
[ numtof f; @"S2:400" f f; return f; ];
[ fadd n m; @"S3:416" n m n; return n; ];
[ fsub n m; @"S3:417" n m n; return n; ];
[ fmul n m; @"S3:418" n m n; return n; ];
[ fdiv n m; @"S3:419" n m n; return n; ];
[ fneg n; @bitxor n $80000000 n; return n; ];
#endif;
-).
Newer Glulx interpreters provide 32-bit floating-point operations, but this solution also supports fixed-point math which is more widely supported and accurate enough for a zoomed-out view. Inform 6 inclusions are used for the low-level math functions in either case. The rendering process is extremely slow, since the graphics system is not optimized for pixel-by-pixel drawing, so this solution includes an optimization for vertical symmetry (as in the default view) and also includes extra logic to draw the lines in a more immediately useful order.
[[File:Mandelbrot-Inform7.png]]
J
The characteristic function of the Mandelbrot can be defined as follows:
mcf=. (<: 2:)@|@(] ((*:@] + [)^:((<: 2:)@|@])^:1000) 0:) NB. 1000 iterations test
The Mandelbrot set can be drawn as follows:
domain=. |.@|:@({.@[ + ] *~ j./&i.&>/@+.@(1j1 + ] %~ -~/@[))&>/
load 'viewmat'
viewmat mcf "0 @ domain (_2j_1 1j1) ; 0.01 NB. Complex interval and resolution
A smaller version, based on a black&white implementation of viewmat (and paraphrased, from html markup to wiki markup), is shown here:
viewmat mcf "0 @ domain (_2j_1 1j1) ; 0.1 NB. Complex interval and resolution
The output is HTML-heavy and can be found [[Mandelbrot_set/J/Output|here]] (split out to make editing this page easier).
Java
{{libheader|Swing}} {{libheader|AWT}}
import java.awt.Graphics; import java.awt.image.BufferedImage; import javax.swing.JFrame; public class Mandelbrot extends JFrame { private final int MAX_ITER = 570; private final double ZOOM = 150; private BufferedImage I; private double zx, zy, cX, cY, tmp; public Mandelbrot() { super("Mandelbrot Set"); setBounds(100, 100, 800, 600); setResizable(false); setDefaultCloseOperation(EXIT_ON_CLOSE); I = new BufferedImage(getWidth(), getHeight(), BufferedImage.TYPE_INT_RGB); for (int y = 0; y < getHeight(); y++) { for (int x = 0; x < getWidth(); x++) { zx = zy = 0; cX = (x - 400) / ZOOM; cY = (y - 300) / ZOOM; int iter = MAX_ITER; while (zx * zx + zy * zy < 4 && iter > 0) { tmp = zx * zx - zy * zy + cX; zy = 2.0 * zx * zy + cY; zx = tmp; iter--; } I.setRGB(x, y, iter | (iter << 8)); } } } @Override public void paint(Graphics g) { g.drawImage(I, 0, 0, this); } public static void main(String[] args) { new Mandelbrot().setVisible(true); } }
JavaScript
{{works with|Firefox|3.5.11}}
This needs the canvas tag of HTML 5 (it will not run on IE8 and lower or old browsers).
The code can be run directly from the Javascript console in modern browsers by copying and pasting it.
function mandelIter(cx, cy, maxIter) { var x = 0.0; var y = 0.0; var xx = 0; var yy = 0; var xy = 0; var i = maxIter; while (i-- && xx + yy <= 4) { xy = x * y; xx = x * x; yy = y * y; x = xx - yy + cx; y = xy + xy + cy; } return maxIter - i; } function mandelbrot(canvas, xmin, xmax, ymin, ymax, iterations) { var width = canvas.width; var height = canvas.height; var ctx = canvas.getContext('2d'); var img = ctx.getImageData(0, 0, width, height); var pix = img.data; for (var ix = 0; ix < width; ++ix) { for (var iy = 0; iy < height; ++iy) { var x = xmin + (xmax - xmin) * ix / (width - 1); var y = ymin + (ymax - ymin) * iy / (height - 1); var i = mandelIter(x, y, iterations); var ppos = 4 * (width * iy + ix); if (i > iterations) { pix[ppos] = 0; pix[ppos + 1] = 0; pix[ppos + 2] = 0; } else { var c = 3 * Math.log(i) / Math.log(iterations - 1.0); if (c < 1) { pix[ppos] = 255 * c; pix[ppos + 1] = 0; pix[ppos + 2] = 0; } else if ( c < 2 ) { pix[ppos] = 255; pix[ppos + 1] = 255 * (c - 1); pix[ppos + 2] = 0; } else { pix[ppos] = 255; pix[ppos + 1] = 255; pix[ppos + 2] = 255 * (c - 2); } } pix[ppos + 3] = 255; } } ctx.putImageData(img, 0, 0); } var canvas = document.createElement('canvas'); canvas.width = 900; canvas.height = 600; document.body.insertBefore(canvas, document.body.childNodes[0]); mandelbrot(canvas, -2, 1, -1, 1, 1000);
{{out}} with default parameters: [[File:Mandelbrot-Javascript.png]]
ES6/WebAssembly
With ES6 and WebAssembly, the program can run faster. Of course, this requires a compiled WASM file, but one can easily build one for instance with the [https://mbebenita.github.io/WasmExplorer/ WebAssembly explorer]
var mandelIter; fetch("./mandelIter.wasm") .then(res => { if (res.ok) return res.arrayBuffer(); throw new Error('Unable to fetch WASM.'); }) .then(bytes => { return WebAssembly.compile(bytes); }) .then(module => { return WebAssembly.instantiate(module); }) .then(instance => { WebAssembly.instance = instance; draw(); }) function mandelbrot(canvas, xmin, xmax, ymin, ymax, iterations) { // ... var i = WebAssembly.instance.exports.mandelIter(x, y, iterations); // ... } function draw() { // canvas initialization if necessary // ... mandelbrot(canvas, -2, 1, -1, 1, 1000); // ... }
jq
[[Image:Mandelbrot-Javascript.png|thumb|Thumbnail of SVG produced by jq program]] {{Works with|jq|1.4}}
The Mandelbrot function as defined here is similar to the JavaScript implementation but generates SVG. The resulting picture is the same.
'''Preliminaries'''
# SVG STUFF
def svg(id; width; height):
"<svg width='\(width // "100%")' height='\(height // "100%") '
id='\(id)'
xmlns='http://www.w3.org/2000/svg'>";
def pixel(x;y;r;g;b;a):
"<circle cx='\(x)' cy='\(y)' r='1' fill='rgb(\(r|floor),\(g|floor),\(b|floor))' />";
# "UNTIL"
# As soon as "condition" is true, then emit . and stop:
def do_until(condition; next):
def u: if condition then . else (next|u) end;
u;
def Mandeliter( cx; cy; maxiter ):
# [i, x, y, x^2+y^2]
[ maxiter, 0.0, 0.0, 0.0 ]
| do_until( .[0] == 0 or .[3] > 4;
.[1] as $x | .[2] as $y
| ($x * $y) as $xy
| ($x * $x) as $xx
| ($y * $y) as $yy
| [ (.[0] - 1), # i
($xx - $yy + cx), # x
($xy + $xy + cy), # y
($xx+$yy) # xx+yy
] )
| maxiter - .[0];
# width and height should be specified as the number of pixels.
# obj == { xmin: _, xmax: _, ymin: _, ymax: _ }
def Mandelbrot( obj; width; height; iterations ):
def pixies:
range(0; width) as $ix
| (obj.xmin + ((obj.xmax - obj.xmin) * $ix / (width - 1))) as $x
| range(0; height) as $iy
| (obj.ymin + ((obj.ymax - obj.ymin) * $iy / (height - 1))) as $y
| Mandeliter( $x; $y; iterations ) as $i
| if $i == iterations then
pixel($ix; $iy; 0; 0; 0; 255)
else
(3 * ($i|log)/((iterations - 1.0)|log)) as $c # redness
| if $c < 1 then
pixel($ix;$iy; 255*$c; 0; 0; 255)
elif $c < 2 then
pixel($ix;$iy; 255; 255*($c-1); 0; 255)
else
pixel($ix;$iy; 255; 255; 255*($c-2); 255)
end
end;
svg("mandelbrot"; "100%"; "100%"),
pixies,
"</svg>";
'''Example''':
Mandelbrot( {"xmin": -2, "xmax": 1, "ymin": -1, "ymax":1}; 900; 600; 1000 )
'''Execution:'''
$ jq -n -r -f mandelbrot.jq > mandelbrot.svg
The output can be viewed in a web browser such as Chrome, Firefox, or Safari.
Julia
Generates an ASCII representation:
function mandelbrot(a) z = 0 for i=1:50 z = z^2 + a end return z end for y=1.0:-0.05:-1.0 for x=-2.0:0.0315:0.5 abs(mandelbrot(complex(x, y))) < 2 ? print("*") : print(" ") end println() end
This generates a PNG image:
using Images @inline function hsv2rgb(h, s, v) const c = v * s const x = c * (1 - abs(((h/60) % 2) - 1)) const m = v - c const r,g,b = if h < 60 (c, x, 0) elseif h < 120 (x, c, 0) elseif h < 180 (0, c, x) elseif h < 240 (0, x, c) elseif h < 300 (x, 0, c) else (c, 0, x) end (r + m), (b + m), (g + m) end function mandelbrot() const w, h = 1000, 1000 const zoom = 0.5 const moveX = 0 const moveY = 0 const img = Array{RGB{Float64}}(h, w) const maxIter = 30 for x in 1:w for y in 1:h i = maxIter const c = Complex( (2*x - w) / (w * zoom) + moveX, (2*y - h) / (h * zoom) + moveY ) z = c while abs(z) < 2 && (i -= 1) > 0 z = z^2 + c end const r,g,b = hsv2rgb(i / maxIter * 360, 1, i / maxIter) img[y,x] = RGB{Float64}(r, g, b) end end save("mandelbrot_set.png", img) end mandelbrot()
Kotlin
{{trans|Java}}
// version 1.1.2 import java.awt.Graphics import java.awt.image.BufferedImage import javax.swing.JFrame class Mandelbrot: JFrame("Mandelbrot Set") { companion object { private const val MAX_ITER = 570 private const val ZOOM = 150.0 } private val img: BufferedImage init { setBounds(100, 100, 800, 600) isResizable = false defaultCloseOperation = EXIT_ON_CLOSE img = BufferedImage(width, height, BufferedImage.TYPE_INT_RGB) for (y in 0 until height) { for (x in 0 until width) { var zx = 0.0 var zy = 0.0 val cX = (x - 400) / ZOOM val cY = (y - 300) / ZOOM var iter = MAX_ITER while (zx * zx + zy * zy < 4.0 && iter > 0) { val tmp = zx * zx - zy * zy + cX zy = 2.0 * zx * zy + cY zx = tmp iter-- } img.setRGB(x, y, iter or (iter shl 7)) } } } override fun paint(g: Graphics) { g.drawImage(img, 0, 0, this) } } fun main(args: Array<String>) { Mandelbrot().isVisible = true }
LabVIEW
{{works with|LabVIEW|8.0 Full Development Suite}}
[[File:Mandelbrot_set_diagram.png|800px]]
[[File:Mandelbrot_set_panel.png|400px]]
Lang5
: d2c(*,*) 2 compress 'c dress ; # Make a complex number.
: iterate(c) [0 0](c) "dup * over +" steps reshape execute ;
: print_line(*) "#*+-. " "" split swap subscript "" join . "\n" . ;
75 iota 45 - 20 / # x coordinates
29 iota 14 - 10 / # y cordinates
'd2c outer # Make complex matrix.
10 'steps set # How many iterations?
iterate abs int 5 min 'print_line apply # Compute & print
Lasso
define mandelbrotBailout => 16
define mandelbrotMaxIterations => 1000
define mandelbrotIterate(x, y) => {
local(cr = #y - 0.5,
ci = #x,
zi = 0.0,
zr = 0.0,
i = 0,
temp, zr2, zi2)
{
++#i;
#temp = #zr * #zi
#zr2 = #zr * #zr
#zi2 = #zi * #zi
#zi2 + #zr2 > mandelbrotBailout?
return #i
#i > mandelbrotMaxIterations?
return 0
#zr = #zr2 - #zi2 + #cr
#zi = #temp + #temp + #ci
currentCapture->restart
}()
}
define mandelbrotTest() => {
local(x, y = -39.0)
{
stdout('\n')
#x = -39.0
{
mandelbrotIterate(#x / 40.0, #y / 40.0) == 0?
stdout('*')
| stdout(' ');
++#x
#x <= 39.0?
currentCapture->restart
}();
++#y
#y <= 39.0?
currentCapture->restart
}()
stdout('\n')
}
mandelbrotTest
{{out}}
*
*
*
*
*
***
*****
*****
***
*
*********
*************
***************
*********************
*********************
*******************
*******************
*******************
*******************
***********************
*******************
*******************
*********************
*******************
*******************
*****************
***************
*************
*********
*
***************
***********************
* ************************* *
*****************************
* ******************************* *
*********************************
***********************************
***************************************
*** ***************************************** ***
*************************************************
***********************************************
*********************************************
*********************************************
***********************************************
***********************************************
***************************************************
*************************************************
*************************************************
***************************************************
***************************************************
* *************************************************** *
***** *************************************************** *****
****** *************************************************** ******
******* *************************************************** *******
***********************************************************************
********* *************************************************** *********
****** *************************************************** ******
***** *************************************************** *****
***************************************************
***************************************************
***************************************************
***************************************************
*************************************************
*************************************************
***************************************************
***********************************************
***********************************************
*******************************************
*****************************************
*********************************************
**** ****************** ****************** ****
*** **************** **************** ***
* ************** ************** *
*********** ***********
** ***** ***** **
* * * *
LIL
From the source distribution. Produces a PBM, not shown here.
# # A mandelbrot generator that outputs a PBM file. This can be used to measure # performance differences between LIL versions and measure performance # bottlenecks (although keep in mind that LIL is not supposed to be a fast # language, but a small one which depends on C for the slow parts - in a real # program where for some reason mandelbrots are required, the code below would # be written in C). The code is based on the mandelbrot test for the Computer # Language Benchmarks Game at http://shootout.alioth.debian.org/ # # In my current computer (Intel Core2Quad Q9550 @ 2.83GHz) running x86 Linux # the results are (using the default 256x256 size): # # 2m3.634s - commit 1c41cdf89f4c1e039c9b3520c5229817bc6274d0 (Jan 10 2011) # # To test call # # time ./lil mandelbrot.lil > mandelbrot.pbm # # with an optimized version of lil (compiled with CFLAGS=-O3 make). # set width [expr $argv] if not $width { set width 256 } set height $width set bit_num 0 set byte_acc 0 set iter 50 set limit 2.0 write "P4\n${width} ${height}\n" for {set y 0} {$y < $height} {inc y} { for {set x 0} {$x < $width} {inc x} { set Zr 0.0 Zi 0.0 Tr 0.0 Ti 0.0 set Cr [expr 2.0 * $x / $width - 1.5] set Ci [expr 2.0 * $y / $height - 1.0] for {set i 0} {$i < $iter && $Tr + $Ti <= $limit * $limit} {inc i} { set Zi [expr 2.0 * $Zr * $Zi + $Ci] set Zr [expr $Tr - $Ti + $Cr] set Tr [expr $Zr * $Zr] set Ti [expr $Zi * $Zi] } set byte_acc [expr $byte_acc << 1] if [expr $Tr + $Ti <= $limit * $limit] { set byte_acc [expr $byte_acc | 1] } inc bit_num if [expr $bit_num == 8] { writechar $byte_acc set byte_acc 0 set bit_num 0 } {if [expr $x == $width - 1] { set byte_acc [expr 8 - $width % 8] writechar $byte_acc set byte_acc 0 set bit_num 0 }} } }
Logo
{{works with|UCB Logo}}
to mandelbrot :left :bottom :side :size
cs setpensize [1 1]
make "inc :side/:size
make "zr :left
repeat :size [
make "zr :zr + :inc
make "zi :bottom
pu
setxy repcount - :size/2 minus :size/2
pd
repeat :size [
make "zi :zi + :inc
setpencolor count.color calc :zr :zi
fd 1 ] ]
end
to count.color :count
;op (list :count :count :count)
if :count > 256 [op 0] ; black
if :count > 128 [op 7] ; white
if :count > 64 [op 5] ; magenta
if :count > 32 [op 6] ; yellow
if :count > 16 [op 4] ; red
if :count > 8 [op 2] ; green
if :count > 4 [op 1] ; blue
op 3 ; cyan
end
to calc :zr :zi [:count 0] [:az 0] [:bz 0]
if :az*:az + :bz*:bz > 4 [op :count]
if :count > 256 [op :count]
op (calc :zr :zi (:count + 1) (:zr + :az*:az - :bz*:bz) (:zi + 2*:az*:bz))
end
mandelbrot -2 -1.25 2.5 400
Lua
Needs LÖVE 2D Engine
Zoom in: drag the mouse; zoom out: right click
local maxIterations = 250 local minX, maxX, minY, maxY = -2.5, 2.5, -2.5, 2.5 local miX, mxX, miY, mxY function remap( x, t1, t2, s1, s2 ) local f = ( x - t1 ) / ( t2 - t1 ) local g = f * ( s2 - s1 ) + s1 return g; end function drawMandelbrot() local pts, a, as, za, b, bs, zb, cnt, clr = {} for j = 0, hei - 1 do for i = 0, wid - 1 do a = remap( i, 0, wid, minX, maxX ) b = remap( j, 0, hei, minY, maxY ) cnt = 0; za = a; zb = b while( cnt < maxIterations ) do as = a * a - b * b; bs = 2 * a * b a = za + as; b = zb + bs if math.abs( a ) + math.abs( b ) > 16 then break end cnt = cnt + 1 end if cnt == maxIterations then clr = 0 else clr = remap( cnt, 0, maxIterations, 0, 255 ) end pts[1] = { i, j, clr, clr, 0, 255 } love.graphics.points( pts ) end end end function startFractal() love.graphics.setCanvas( canvas ); love.graphics.clear() love.graphics.setColor( 255, 255, 255 ) drawMandelbrot(); love.graphics.setCanvas() end function love.load() wid, hei = love.graphics.getWidth(), love.graphics.getHeight() canvas = love.graphics.newCanvas( wid, hei ) startFractal() end function love.mousepressed( x, y, button, istouch ) if button == 1 then startDrag = true; miX = x; miY = y else minX = -2.5; maxX = 2.5; minY = minX; maxY = maxX startFractal() startDrag = false end end function love.mousereleased( x, y, button, istouch ) if startDrag then local l if x > miX then mxX = x else l = x; mxX = miX; miX = l end if y > miY then mxY = y else l = y; mxY = miY; miY = l end miX = remap( miX, 0, wid, minX, maxX ) mxX = remap( mxX, 0, wid, minX, maxX ) miY = remap( miY, 0, hei, minY, maxY ) mxY = remap( mxY, 0, hei, minY, maxY ) minX = miX; maxX = mxX; minY = miY; maxY = mxY startFractal() end end function love.draw() love.graphics.draw( canvas ) end
M2000 Interpreter
Console is a bitmap so we can plot on it. A subroutine plot different size of pixels so we get Mandelbrot image at final same size for 32X26 for a big pixel of 16x16 pixels to 512x416 for a 1:1 pixel. Iterations for each pixel set to 25. Module can get left top corner as twips, and the size factor from 1 to 16 (size of output is 512x416 pixels for any factor).
Module Mandelbrot(x=0&,y=0&,z=1&) {
If z<1 then z=1
If z>16 then z=16
Const iXmax=32*z
Const iYmax=26*z
Def single Cx, Cy, CxMin=-2.05, CxMax=0.85, CyMin=-1.2, CyMax=1.2
Const PixelWidth=(CxMax-CxMin)/iXmax, iXm=(iXmax-1)*PixelWidth
Const PixelHeight=(CyMax-CyMin)/iYmax,Ph2=PixelHeight/2
Const Iteration=25
Const EscRadious=2.5, ER2=EscRadious**2
Def single preview
preview=iXmax*twipsX*(z/16)
Def long yp, xp, dx, dy, dx1, dy1
Let dx=twipsx*(16/z), dx1=dx-1
Let dy=twipsy*(16/z), dy1=dy-1
yp=y
For iY=0 to (iYmax-1)*PixelHeight step PixelHeight {
Cy=CyMin+iY
xp=x
if abs(Cy)<Ph2 Then Cy=0
For iX=0 to iXm Step PixelWidth {
Let Cx=CxMin+iX,Zx=0,Zy=0,Zx2=Zx**2,Zy2=Zy**2
For It=Iteration to 1 {Let Zy=2*Zx*Zy+Cy,Zx=Zx2-Zy2+Cx,Zx2=Zx**2,Zy2=Zy**2 :if Zx2+Zy2>ER2 Then exit
}
if it>13 then {it-=13} else.if it=0 then SetPixel(xp,yp,0): xp+=dx : continue
it*=10:SetPixel(xp,yp,color(it, it,255)) :xp+=dx
} : yp+=dy
}
Sub SetPixel()
move number, number: fill dx1, dy1, number
End Sub
}
Cls 1,0
sz=(1,2,4,8,16)
i=each(sz)
While i {
Mandelbrot 250*twipsx,100*twipsy, array(i)
}
Version 2 without Subroutine. Also there is a screen refresh every 2 seconds.
Module Mandelbrot(x=0&,y=0&,z=1&) {
If z<1 then z=1
If z>16 then z=16
Const iXmax=32*z
Const iYmax=26*z
Def single Cx, Cy, CxMin=-2.05, CxMax=0.85, CyMin=-1.2, CyMax=1.2
Const PixelWidth=(CxMax-CxMin)/iXmax, iXm=(iXmax-1)*PixelWidth
Const PixelHeight=(CyMax-CyMin)/iYmax,Ph2=PixelHeight/2
Const Iteration=25
Const EscRadious=2.5, ER2=EscRadious**2
Def single preview
preview=iXmax*twipsX*(z/16)
Def long yp, xp, dx, dy, dx1, dy1
Let dx=twipsx*(16/z), dx1=dx-1
Let dy=twipsy*(16/z), dy1=dy-1
yp=y
Refresh 2000
For iY=0 to (iYmax-1)*PixelHeight step PixelHeight {
Cy=CyMin+iY
xp=x
if abs(Cy)<Ph2 Then Cy=0
move xp, yp
For iX=0 to iXm Step PixelWidth {
Let Cx=CxMin+iX,Zx=0,Zy=0,Zx2=Zx**2,Zy2=Zy**2
For It=Iteration to 1 {Let Zy=2*Zx*Zy+Cy,Zx=Zx2-Zy2+Cx,Zx2=Zx**2,Zy2=Zy**2 :if Zx2+Zy2>ER2 Then exit
}
if it>13 then {it-=13} else.if it=0 then fill dx1, dy1, 0: Step 0,-dy1: continue
it*=10:fill dx1, dy1, color(it, it,255): Step 0,-dy1
} : yp+=dy
}
}
Cls 1,0
sz=(1,2,4,8,16)
i=each(sz)
While i {
Mandelbrot 250*twipsx,100*twipsy, array(i)
}
Maple
=={{header|Mathematica}} / {{header|Wolfram Language}}==
The implementation could be better. But this is a start...
```mathematica
eTime[z0_, maxIter_Integer: 100] := (Length@NestWhileList[(# + z0)^2 &, 0, (Abs@# <= 2) &, 1, maxIter]) - 1
DistributeDefinitions[eTime];
mesh = ParallelTable[eTime[(x + I*y), 1000], {y, 1.2, -1.2, -0.01}, {x, -1.72, 1, 0.01}];
ReliefPlot[mesh, Frame -> False]
Faster version:
cf = With[{
mandel = Block[{z = #, c = #},
Catch@Do[If[Abs[z] > 2, Throw@i]; z = z^2 + c, {i, 100}]] &
},
Compile[{},Table[mandel[y + x I], {x, -1, 1, 0.005}, {y, -2, 0.5, 0.005}]]
];
ArrayPlot[cf[]]
Built-in function:
MandelbrotSetPlot[]
==Mathmap ==
filter mandelbrot (gradient coloration) c=ri:(xy/xy:[X,X]1.5-xy:[0.5,0]); z=ri:[0,0]; # initial value z0 = 0 # iteration of z iter=0; while abs(z)<2 && iter<31 do z=zz+c; # z(n+1) = fc(zn) iter=iter+1 end; coloration(iter/32) # color of pixel end
MATLAB
This solution uses the escape time algorithm to determine the coloring of the coordinates on the complex plane. The code can be reduced to a single line via vectorization after the Escape Time Algorithm function definition, but the code becomes unnecessarily obfuscated. Also, this code uses a lot of memory. You will need a computer with a lot of memory to compute the set with high resolution.
function [theSet,realAxis,imaginaryAxis] = mandelbrotSet(start,gridSpacing,last,maxIteration) %Define the escape time algorithm function escapeTime = escapeTimeAlgorithm(z0) escapeTime = 0; z = 0; while( (abs(z)<=2) && (escapeTime < maxIteration) ) z = (z + z0)^2; escapeTime = escapeTime + 1; end end %Define the imaginary axis imaginaryAxis = (imag(start):imag(gridSpacing):imag(last)); %Define the real axis realAxis = (real(start):real(gridSpacing):real(last)); %Construct the complex plane from the real and imaginary axes complexPlane = meshgrid(realAxis,imaginaryAxis) + meshgrid(imaginaryAxis(end:-1:1),realAxis)'.*i; %Apply the escape time algorithm to each point in the complex plane theSet = arrayfun(@escapeTimeAlgorithm, complexPlane); %Draw the set pcolor(realAxis,imaginaryAxis,theSet); shading flat; end
To use this function you must specify the:
- lower left hand corner of the complex plane from which to start the image,
- the grid spacing in both the imaginary and real directions,
- the upper right hand corner of the complex plane at which to end the image and
- the maximum iterations for the escape time algorithm.
For example:
- Lower Left Corner: -2.05-1.2i
- Grid Spacing: 0.004+0.0004i
- Upper Right Corner: 0.45+1.2i
- Maximum Iterations: 500
Sample usage:
mandelbrotSet(-2.05-1.2i,0.004+0.0004i,0.45+1.2i,500);
Metapost
prologues:=3;
outputtemplate:="%j-%c.svg";
outputformat:="svg";
def mandelbrot(expr maxX, maxY) =
max_iteration := 500;
color col[];
for i := 0 upto max_iteration:
t := i / max_iteration;
col[i] = (t,t,t);
endfor;
for px := 0 upto maxX:
for py := 0 upto maxY:
xz := px * 3.5 / maxX - 2.5; % (-2.5,1)
yz := py * 2 / maxY - 1; % (-1,1)
x := 0;
y := 0;
iteration := 0;
forever: exitunless ((x*x + y*y < 4) and (iteration < max_iteration));
xtemp := x*x - y*y + xz;
y := 2*x*y + yz;
x := xtemp;
iteration := iteration + 1;
endfor;
draw (px,py) withpen pencircle withcolor col[iteration];
endfor;
endfor;
enddef;
beginfig(1);
mandelbrot(200, 150);
endfig;
end
Sample usage:
mpost -numbersystem="double" mandelbrot.mp
MiniScript
ZOOM = 100
MAX_ITER = 40
gfx.clear color.black
for y in range(0,200)
for x in range(0,300)
zx = 0
zy = 0
cx = (x - 200) / ZOOM
cy = (y - 100) / ZOOM
for iter in range(MAX_ITER)
if zx*zx + zy*zy > 4 then break
tmp = zx * zx - zy * zy + cx
zy = 2 * zx * zy + cy
zx = tmp
end for
if iter then
gfx.setPixel x, y, rgb(255-iter*6, 0, iter*6)
end if
end for
end for
(Will upload an output image as soon as image uploading is fixed.)
=={{header|Modula-3}}==
MODULE Mandelbrot EXPORTS Main;
IMPORT Wr, Stdio, Fmt, Word;
CONST m = 50;
limit2 = 4.0;
TYPE UByte = BITS 8 FOR [0..16_FF];
VAR width := 200;
height := 200;
bitnum: CARDINAL := 0;
byteacc: UByte := 0;
isOverLimit: BOOLEAN;
Zr, Zi, Cr, Ci, Tr, Ti: REAL;
BEGIN
Wr.PutText(Stdio.stdout, "P4\n" & Fmt.Int(width) & " " & Fmt.Int(height) & "\n");
FOR y := 0 TO height - 1 DO
FOR x := 0 TO width - 1 DO
Zr := 0.0; Zi := 0.0;
Cr := 2.0 * FLOAT(x) / FLOAT(width) - 1.5;
Ci := 2.0 * FLOAT(y) / FLOAT(height) - 1.0;
FOR i := 1 TO m + 1 DO
Tr := Zr*Zr - Zi*Zi + Cr;
Ti := 2.0*Zr*Zi + Ci;
Zr := Tr; Zi := Ti;
isOverLimit := Zr*Zr + Zi*Zi > limit2;
IF isOverLimit THEN EXIT; END;
END;
IF isOverLimit THEN
byteacc := Word.Xor(Word.LeftShift(byteacc, 1), 16_00);
ELSE
byteacc := Word.Xor(Word.LeftShift(byteacc, 1), 16_01);
END;
INC(bitnum);
IF bitnum = 8 THEN
Wr.PutChar(Stdio.stdout, VAL(byteacc, CHAR));
byteacc := 0;
bitnum := 0;
ELSIF x = width - 1 THEN
byteacc := Word.LeftShift(byteacc, 8 - (width MOD 8));
Wr.PutChar(Stdio.stdout, VAL(byteacc, CHAR));
byteacc := 0;
bitnum := 0
END;
Wr.Flush(Stdio.stdout);
END;
END;
END Mandelbrot.
MySQL
See http://arbitraryscrawl.blogspot.co.uk/2012/06/fractsql.html for an explanation.
-- Table to contain all the data points
CREATE TABLE points (
c_re DOUBLE,
c_im DOUBLE,
z_re DOUBLE DEFAULT 0,
z_im DOUBLE DEFAULT 0,
znew_re DOUBLE DEFAULT 0,
znew_im DOUBLE DEFAULT 0,
steps INT DEFAULT 0,
active CHAR DEFAULT 1
);
DELIMITER |
-- Iterate over all the points in the table 'points'
CREATE PROCEDURE itrt (IN n INT)
BEGIN
label: LOOP
UPDATE points
SET
znew_re=POWER(z_re,2)-POWER(z_im,2)+c_re,
znew_im=2*z_re*z_im+c_im,
steps=steps+1
WHERE active=1;
UPDATE points SET
z_re=znew_re,
z_im=znew_im,
active=IF(POWER(z_re,2)+POWER(z_im,2)>4,0,1)
WHERE active=1;
SET n = n - 1;
IF n > 0 THEN
ITERATE label;
END IF;
LEAVE label;
END LOOP label;
END|
-- Populate the table 'points'
CREATE PROCEDURE populate (
r_min DOUBLE,
r_max DOUBLE,
r_step DOUBLE,
i_min DOUBLE,
i_max DOUBLE,
i_step DOUBLE)
BEGIN
DELETE FROM points;
SET @rl = r_min;
SET @a = 0;
rloop: LOOP
SET @im = i_min;
SET @b = 0;
iloop: LOOP
INSERT INTO points (c_re, c_im)
VALUES (@rl, @im);
SET @b=@b+1;
SET @im=i_min + @b * i_step;
IF @im < i_max THEN
ITERATE iloop;
END IF;
LEAVE iloop;
END LOOP iloop;
SET @a=@a+1;
SET @rl=r_min + @a * r_step;
IF @rl < r_max THEN
ITERATE rloop;
END IF;
LEAVE rloop;
END LOOP rloop;
END|
DELIMITER ;
-- Choose size and resolution of graph
-- R_min, R_max, R_step, I_min, I_max, I_step
CALL populate( -2.5, 1.5, 0.005, -2, 2, 0.005 );
-- Calculate 50 iterations
CALL itrt( 50 );
-- Create the image (/tmp/image.ppm)
-- Note, MySQL will not over-write an existing file and you may need
-- administrator access to delete or move it
SELECT @xmax:=COUNT(c_re) INTO @xmax FROM points GROUP BY c_im LIMIT 1;
SELECT @ymax:=COUNT(c_im) INTO @ymax FROM points GROUP BY c_re LIMIT 1;
SET group_concat_max_len=11*@xmax*@ymax;
SELECT
'P3', @xmax, @ymax, 200,
GROUP_CONCAT(
CONCAT(
IF( active=1, 0, 55+MOD(steps, 200) ), ' ',
IF( active=1, 0, 55+MOD(POWER(steps,3), 200) ), ' ',
IF( active=1, 0, 55+MOD(POWER(steps,2), 200) ) )
ORDER BY c_im ASC, c_re ASC SEPARATOR ' ' )
INTO OUTFILE '/tmp/image.ppm'
FROM points;
Nim
{{trans|Python}}
import complex proc mandelbrot(a: Complex): Complex = for i in 0 .. <50: result = result * result + a iterator stepIt(start, step: float, iterations: int): auto = for i in 0 .. iterations: yield start + float(i) * step var rows = "" for y in stepIt(1.0, -0.05, 41): for x in stepIt(-2.0, 0.0315, 80): if abs(mandelbrot((x,y))) < 2: rows.add('*') else: rows.add(' ') rows.add("\n") echo rows
OCaml
#load "graphics.cma";; let mandelbrot xMin xMax yMin yMax xPixels yPixels maxIter = let rec mandelbrotIterator z c n = if (Complex.norm z) > 2.0 then false else match n with | 0 -> true | n -> let z' = Complex.add (Complex.mul z z) c in mandelbrotIterator z' c (n-1) in Graphics.open_graph (" "^(string_of_int xPixels)^"x"^(string_of_int yPixels)); let dx = (xMax -. xMin) /. (float_of_int xPixels) and dy = (yMax -. yMin) /. (float_of_int yPixels) in for xi = 0 to xPixels - 1 do for yi = 0 to yPixels - 1 do let c = {Complex.re = xMin +. (dx *. float_of_int xi); Complex.im = yMin +. (dy *. float_of_int yi)} in if (mandelbrotIterator Complex.zero c maxIter) then (Graphics.set_color Graphics.white; Graphics.plot xi yi ) else (Graphics.set_color Graphics.black; Graphics.plot xi yi ) done done;; mandelbrot (-1.5) 0.5 (-1.0) 1.0 500 500 200;;
Octave
This code runs rather slowly and produces coloured Mandelbrot set by accident ([[Media:Mandel-Octave.jpg|output image]]).
#! /usr/bin/octave -qf
global width = 200;
global height = 200;
maxiter = 100;
z0 = 0;
global cmax = 1 + i;
global cmin = -2 - i;
function cs = pscale(c)
global cmax;
global cmin;
global width;
global height;
persistent px = (real(cmax-cmin))/width;
persistent py = (imag(cmax-cmin))/height;
cs = real(cmin) + px*real(c) + i*(imag(cmin) + py*imag(c));
endfunction
ms = zeros(width, height);
for x = 0:width-1
for y = 0:height-1
z0 = 0;
c = pscale(x+y*i);
for ic = 1:maxiter
z1 = z0^2 + c;
if ( abs(z1) > 2 ) break; endif
z0 = z1;
endfor
ms(x+1, y+1) = ic/maxiter;
endfor
endfor
saveimage("mandel.ppm", round(ms .* 255).', "ppm");
Ol
(define x-size 59)
(define y-size 21)
(define min-im -1)
(define max-im 1)
(define min-re -2)
(define max-re 1)
(define step-x (/ (- max-re min-re) x-size))
(define step-y (/ (- max-im min-im) y-size))
(for-each (lambda (y)
(let ((im (+ min-im (* step-y y))))
(for-each (lambda (x)
(let*((re (+ min-re (* step-x x)))
(zr (inexact re))
(zi (inexact im)))
(let loop ((n 0) (zi zi) (zr zr))
(let ((a (* zr zr))
(b (* zi zi)))
(cond
((> (+ a b) 4)
(display (string (- 62 n))))
((= n 30)
(display (string (- 62 n))))
(else
(loop (+ n 1) (+ (* 2 zr zi) im) (- (+ a re) b))))))))
(iota x-size))
(print)))
(iota y-size))
Output:
>>>>>>
### ==<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<=======
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<
### =
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<======
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<====
>>==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<===
>>=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<==
>=<<<<<<<<;;;:599999999886 %78:;;<<<<<<=
><<<<;;;;;:::972456-567763 +9;;<<<<<<<
><;;;;;;::::9875& .3 *9;;;<<<<<<
>;;;;;;::997564' ' 8:;;;<<<<<<
>::988897735/ &89:;;;<<<<<<
>::988897735/ &89:;;;<<<<<<
>;;;;;;::997564' ' 8:;;;<<<<<<
><;;;;;;::::9875& .3 *9;;;<<<<<<
><<<<;;;;;:::972456-567763 +9;;<<<<<<<
>=<<<<<<<<;;;:599999999886 %78:;;<<<<<<=
>>=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<==
>>==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<===
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<====
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<======
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<
### =
PARI/GP
Define function mandelbrot():
mandelbrot() =
{
forstep(y=-1, 1, 0.05,
forstep(x=-2, 0.5, 0.0315,
print1(((c)->my(z=c);for(i=1,20,z=z*z+c;if(abs(z)>2,return(" ")));"#")(x+y*I)));
print());
}
Output:
gp > mandelbrot()
#
# ### #
########
#########
######
## ## ############ #
### ################### #
#############################
############################
################################
################################
#################################### #
# # ###################################
########### ###################################
########### #####################################
############## ####################################
####################################################
######################################################
#########################################################################
######################################################
####################################################
############## ####################################
########### #####################################
########### ###################################
# # ###################################
#################################### #
################################
################################
############################
#############################
### ################### #
## ## ############ #
######
#########
########
# ### #
#
Pascal
{{trans|C}}
program mandelbrot; const ixmax = 800; iymax = 800; cxmin = -2.5; cxmax = 1.5; cymin = -2.0; cymax = 2.0; maxcolorcomponentvalue = 255; maxiteration = 200; escaperadius = 2; type colortype = record red : byte; green : byte; blue : byte; end; var ix, iy : integer; cx, cy : real; pixelwidth : real = (cxmax - cxmin) / ixmax; pixelheight : real = (cymax - cymin) / iymax; filename : string = 'new1.ppm'; comment : string = '# '; outfile : textfile; color : colortype; zx, zy : real; zx2, zy2 : real; iteration : integer; er2 : real = (escaperadius * escaperadius); begin {$I-} assign(outfile, filename); rewrite(outfile); if ioresult <> 0 then begin writeln(stderr, 'unable to open output file: ', filename); exit; end; writeln(outfile, 'P6'); writeln(outfile, ' ', comment); writeln(outfile, ' ', ixmax); writeln(outfile, ' ', iymax); writeln(outfile, ' ', maxcolorcomponentvalue); for iy := 1 to iymax do begin cy := cymin + (iy - 1)*pixelheight; if abs(cy) < pixelheight / 2 then cy := 0.0; for ix := 1 to ixmax do begin cx := cxmin + (ix - 1)*pixelwidth; zx := 0.0; zy := 0.0; zx2 := zx*zx; zy2 := zy*zy; iteration := 0; while (iteration < maxiteration) and (zx2 + zy2 < er2) do begin zy := 2*zx*zy + cy; zx := zx2 - zy2 + cx; zx2 := zx*zx; zy2 := zy*zy; iteration := iteration + 1; end; if iteration = maxiteration then begin color.red := 0; color.green := 0; color.blue := 0; end else begin color.red := 255; color.green := 255; color.blue := 255; end; write(outfile, chr(color.red), chr(color.green), chr(color.blue)); end; end; close(outfile); end.
Perl
translation / optimization of the ruby solution
use Math::Complex; sub mandelbrot { my ($z, $c) = @_[0,0]; for (1 .. 20) { $z = $z * $z + $c; return $_ if abs $z > 2; } } for (my $y = 1; $y >= -1; $y -= 0.05) { for (my $x = -2; $x <= 0.5; $x += 0.0315) {print mandelbrot($x + $y * i) ? ' ' : '#'} print "\n" }
Perl 6
{{Works with|rakudo|2016-05-01}} [[File:Mandel-perl6.png|thumb]] Variant of a Mandelbrot script from the [http://modules.perl6.org/ Perl 6 ecosystem]. Produces a [[Write ppm file|Portable Pixel Map]] to STDOUT. Redirect into a file to save it. Converted to a .png file for display here.
constant @color_map = map ~*.comb(/../).map({:16($_)}), <
000000 0000fc 4000fc 7c00fc bc00fc fc00fc fc00bc fc007c fc0040 fc0000 fc4000
fc7c00 fcbc00 fcfc00 bcfc00 7cfc00 40fc00 00fc00 00fc40 00fc7c 00fcbc 00fcfc
00bcfc 007cfc 0040fc 7c7cfc 9c7cfc bc7cfc dc7cfc fc7cfc fc7cdc fc7cbc fc7c9c
fc7c7c fc9c7c fcbc7c fcdc7c fcfc7c dcfc7c bcfc7c 9cfc7c 7cfc7c 7cfc9c 7cfcbc
7cfcdc 7cfcfc 7cdcfc 7cbcfc 7c9cfc b4b4fc c4b4fc d8b4fc e8b4fc fcb4fc fcb4e8
fcb4d8 fcb4c4 fcb4b4 fcc4b4 fcd8b4 fce8b4 fcfcb4 e8fcb4 d8fcb4 c4fcb4 b4fcb4
b4fcc4 b4fcd8 b4fce8 b4fcfc b4e8fc b4d8fc b4c4fc 000070 1c0070 380070 540070
700070 700054 700038 70001c 700000 701c00 703800 705400 707000 547000 387000
1c7000 007000 00701c 007038 007054 007070 005470 003870 001c70 383870 443870
543870 603870 703870 703860 703854 703844 703838 704438 705438 706038 707038
607038 547038 447038 387038 387044 387054 387060 387070 386070 385470 384470
505070 585070 605070 685070 705070 705068 705060 705058 705050 705850 706050
706850 707050 687050 607050 587050 507050 507058 507060 507068 507070 506870
506070 505870 000040 100040 200040 300040 400040 400030 400020 400010 400000
401000 402000 403000 404000 304000 204000 104000 004000 004010 004020 004030
004040 003040 002040 001040 202040 282040 302040 382040 402040 402038 402030
402028 402020 402820 403020 403820 404020 384020 304020 284020 204020 204028
204030 204038 204040 203840 203040 202840 2c2c40 302c40 342c40 3c2c40 402c40
402c3c 402c34 402c30 402c2c 40302c 40342c 403c2c 40402c 3c402c 34402c 30402c
2c402c 2c4030 2c4034 2c403c 2c4040 2c3c40 2c3440 2c3040
>;
constant MAX_ITERATIONS = 50;
my $width = my $height = +(@*ARGS[0] // 31);
sub cut(Range $r, UInt $n where $n > 1) {
$r.min, * + ($r.max - $r.min) / ($n - 1) ... $r.max
}
my @re = cut(-2 .. 1/2, $height);
my @im = cut( 0 .. 5/4, $width div 2 + 1) X* 1i;
sub mandelbrot(Complex $z is copy, Complex $c) {
for 1 .. MAX_ITERATIONS {
$z = $z*$z + $c;
return $_ if $z.abs > 2;
}
return 0;
}
say "P3";
say "$width $height";
say "255";
for @re -> $re {
put @color_map[|.reverse, |.[1..*]][^$width] given
my @ = map &mandelbrot.assuming(0i, *), $re «+« @im;
}
Phix
;Ascii This is included in the distribution (with some extra validation) as demo\mandle.exw
--
-- Mandlebrot set in ascii art demo.
--
constant b=" .:,;!/>)|&IH%*#"
atom r, i, c, C, z, Z, t, k
for y=30 to 0 by -1 do
C = y*0.1-1.5
puts(1,'\n')
for x=0 to 74 do
c = x*0.04-2
z = 0
Z = 0
r = c
i = C
k = 0
while k<112 do
t = z*z-Z*Z+r
Z = 2*z*Z+i
z = t
if z*z+Z*Z>10 then exit end if
k += 1
end while
puts(1,b[remainder(k,16)+1])
end for
end for
;Graphical This is included in the distribution as demo\arwendemo\mandel.exw
include arwen.ew
include ..\arwen\dib256.ew
constant HelpText = "Left-click drag with the mouse to move the image.\n"&
" (the image is currently only redrawn on mouseup).\n"&
"Right-click-drag with the mouse to select a region to zoom in to.\n"&
"Use the mousewheel to zoom in and out (nb: can be slow).\n"&
"Press F2 to select iterations, higher==more detail but slower.\n"&
"Resize the window as you please, but note that going fullscreen, \n"&
"especially at high iteration, may mean a quite long draw time.\n"&
"Press Escape to close the window."
procedure Help()
void = messageBox("Mandelbrot Set",HelpText,MB_OK)
end procedure
integer cWidth = 520 -- client area width
integer cHeight = 480 -- client area height
constant Main = create(Window, "Mandelbrot Set", 0, 0, 50, 50, cWidth+16, cHeight+38, 0),
mainHwnd = getHwnd(Main),
mainDC = getPrivateDC(Main),
mIter = create(Menu, "", 0, 0, 0,0,0,0,0),
iterHwnd = getHwnd(mIter),
mIter50 = create(MenuItem,"50 (fast, low detail)", 0, mIter, 0,0,0,0,0),
mIter100 = create(MenuItem,"100 (default)", 0, mIter, 0,0,0,0,0),
mIter500 = create(MenuItem,"500", 0, mIter, 0,0,0,0,0),
mIter1000 = create(MenuItem,"1000 (slow, high detail)",0, mIter, 0,0,0,0,0),
m50to1000 = {mIter50,mIter100,mIter500,mIter1000},
i50to1000 = { 50, 100, 500, 1000}
integer mainDib = 0
constant whitePen = c_func(xCreatePen, {0,1,BrightWhite})
constant NULL_BRUSH = 5,
NullBrushID = c_func(xGetStockObject,{NULL_BRUSH})
atom t0
integer iter
atom x0, y0 -- top-left coords to draw
atom scale -- controls width/zoom
procedure init()
x0 = -2
y0 = -1.25
scale = 2.5/cHeight
iter = 100
void = c_func(xSelectObject,{mainDC,whitePen})
void = c_func(xSelectObject,{mainDC,NullBrushID})
end procedure
init()
function in_set(atom x, atom y)
atom u,t
if x>-0.75 then
u = x-0.25
t = u*u+y*y
return ((2*t+u)*(2*t+u)>t)
else
return ((x+1)*(x+1)+y*y)>0.0625
end if
end function
function pixel_colour(atom x0, atom y0, integer iter)
integer count = 1
atom x = 0, y = 0
while (count<=iter) and (x*x+y*y<4) do
count += 1
{x,y} = {x*x-y*y+x0,2*x*y+y0}
end while
if count<=iter then return count end if
return 0
end function
procedure mandel(atom x0, atom y0, atom scale)
atom x,y
integer c
t0 = time()
y = y0
for yi=1 to cHeight do
x = x0
for xi=1 to cWidth do
c = 0 -- default to black
if in_set(x,y) then
c = pixel_colour(x,y,iter)
end if
setDibPixel(mainDib, xi, yi, c)
x += scale
end for
y += scale
end for
end procedure
integer firsttime = 1
integer drawBox = 0
integer drawTime = 0
procedure newDib()
sequence pal
if mainDib!=0 then
{} = deleteDib(mainDib)
end if
mainDib = createDib(cWidth, cHeight)
pal = repeat({0,0,0},256)
for i=2 to 256 do
pal[i][1] = i*5
pal[i][2] = 0
pal[i][3] = i*10
end for
setDibPalette(mainDib, 1, pal)
mandel(x0,y0,scale)
drawTime = 2
end procedure
procedure reDraw()
setText(Main,"Please Wait...")
mandel(x0,y0,scale)
drawTime = 2
repaintWindow(Main,False)
end procedure
procedure zoom(integer z)
while z do
if z>0 then
scale /= 1.1
z -= 1
else
scale *= 1.1
z += 1
end if
end while
reDraw()
end procedure
integer dx=0,dy=0 -- mouse down coords
integer mx=0,my=0 -- mouse move/up coords
function mainHandler(integer id, integer msg, atom wParam, object lParam)
integer x, y -- scratch vars
atom scale10
if msg=WM_SIZE then -- (also activate/firsttime)
{{},{},x,y} = getClientRect(Main)
if firsttime or cWidth!=x or cHeight!=y then
scale *= cWidth/x
{cWidth, cHeight} = {x,y}
newDib()
firsttime = 0
end if
elsif msg=WM_PAINT then
copyDib(mainDC, 0, 0, mainDib)
if drawBox then
void = c_func(xRectangle, {mainDC, dx, dy, mx, my})
end if
if drawTime then
if drawTime=2 then
setText(Main,sprintf("Mandelbrot Set [generated in %gs]",time()-t0))
else
setText(Main,"Mandelbrot Set")
end if
drawTime -= 1
end if
elsif msg=WM_CHAR then
if wParam=VK_ESCAPE then
closeWindow(Main)
elsif wParam='+' then zoom(+1)
elsif wParam='-' then zoom(-1)
end if
elsif msg=WM_LBUTTONDOWN
or msg=WM_RBUTTONDOWN then
{dx,dy} = lParam
elsif msg=WM_MOUSEMOVE then
if and_bits(wParam,MK_LBUTTON) then
{mx,my} = lParam
-- minus dx,dy (see WM_LBUTTONUP)
-- DEV maybe a timer to redraw, but probably too slow...
-- (this is where we need a background worker thread,
-- ideally one we can direct to abandon what it is
-- currently doing and start work on new x,y instead)
elsif and_bits(wParam,MK_RBUTTON) then
{mx,my} = lParam
drawBox = 1
repaintWindow(Main,False)
end if
elsif msg=WM_MOUSEWHEEL then
wParam = floor(wParam/#10000)
if wParam>=#8000 then -- sign bit set
wParam-=#10000
end if
wParam = floor(wParam/120) -- (gives +/-1, usually)
zoom(wParam)
elsif msg=WM_LBUTTONUP then
{mx,my} = lParam
drawBox = 0
x0 += (dx-mx)*scale
y0 += (dy-my)*scale
reDraw()
elsif msg=WM_RBUTTONUP then
{mx,my} = lParam
drawBox = 0
if mx!=dx and my!=dy then
x0 += min(mx,dx)*scale
y0 += min(my,dy)*scale
scale *= (abs(mx-dx))/cHeight
reDraw()
end if
elsif msg=WM_KEYDOWN then
if wParam=VK_F1 then
Help()
elsif wParam=VK_F2 then
{x,y} = getWindowRect(Main)
void = c_func(xTrackPopupMenu, {iterHwnd,TPM_LEFTALIGN,x+20,y+40,0,mainHwnd,NULL})
elsif find(wParam,{VK_UP,VK_DOWN,VK_LEFT,VK_RIGHT}) then
drawBox = 0
scale10 = scale*10
if wParam=VK_UP then
y0 += scale10
elsif wParam=VK_DOWN then
y0 -= scale10
elsif wParam=VK_LEFT then
x0 += scale10
elsif wParam=VK_RIGHT then
x0 -= scale10
end if
reDraw()
end if
elsif msg=WM_COMMAND then
id = find(id,m50to1000)
if id!=0 then
iter = i50to1000[id]
reDraw()
end if
end if
return 0
end function
setHandler({Main,mIter50,mIter100,mIter500,mIter1000}, routine_id("mainHandler"))
WinMain(Main,SW_NORMAL)
void = deleteDib(0)
PHP
{{libheader|GD Graphics Library}} {{works with|PHP|5.3.5}}
[[File:Mandel-php.png|thumb|right|Sample output]]
$min_x=-2; $max_x=1; $min_y=-1; $max_y=1; $dim_x=400; $dim_y=300; $im = @imagecreate($dim_x, $dim_y) or die("Cannot Initialize new GD image stream"); header("Content-Type: image/png"); $black_color = imagecolorallocate($im, 0, 0, 0); $white_color = imagecolorallocate($im, 255, 255, 255); for($y=0;$y<=$dim_y;$y++) { for($x=0;$x<=$dim_x;$x++) { $c1=$min_x+($max_x-$min_x)/$dim_x*$x; $c2=$min_y+($max_y-$min_y)/$dim_y*$y; $z1=0; $z2=0; for($i=0;$i<100;$i++) { $new1=$z1*$z1-$z2*$z2+$c1; $new2=2*$z1*$z2+$c2; $z1=$new1; $z2=$new2; if($z1*$z1+$z2*$z2>=4) { break; } } if($i<100) { imagesetpixel ($im, $x, $y, $white_color); } } } imagepng($im); imagedestroy($im);
PicoLisp
(scl 6)
(let Ppm (make (do 300 (link (need 400))))
(for (Y . Row) Ppm
(for (X . @) Row
(let (ZX 0 ZY 0 CX (*/ (- X 250) 1.0 150) CY (*/ (- Y 150) 1.0 150) C 570)
(while (and (> 4.0 (+ (*/ ZX ZX 1.0) (*/ ZY ZY 1.0))) (gt0 C))
(let Tmp (- (*/ ZX ZX 1.0) (*/ ZY ZY 1.0) (- CX))
(setq
ZY (+ (*/ 2 ZX ZY 1.0) CY)
ZX Tmp ) )
(dec 'C) )
(set (nth Ppm Y X) (list 0 C C)) ) ) )
(out "img.ppm"
(prinl "P6")
(prinl 400 " " 300)
(prinl 255)
(for Y Ppm (for X Y (apply wr X))) ) )
PostScript
%!PS-Adobe-2.0
%%BoundingBox: 0 0 300 200
%%EndComments
/origstate save def
/ld {load def} bind def
/m /moveto ld /g /setgray ld
/dot { currentpoint 1 0 360 arc fill } bind def
%%EndProlog
% param
/maxiter 200 def
% complex manipulation
/complex { 2 array astore } def
/real { 0 get } def
/imag { 1 get } def
/cmul { /a exch def /b exch def
a real b real mul
a imag b imag mul sub
a real b imag mul
a imag b real mul add
2 array astore
} def
/cadd { aload pop 3 -1 roll aload pop
3 -1 roll add
3 1 roll add exch 2 array astore
} def
/cconj { aload pop neg 2 array astore } def
/cabs2 { dup cconj cmul 0 get} def
% mandel
200 100 translate
-200 1 100 { /x exch def
-100 1 100 { /y exch def
/z0 0.0 0.0 complex def
0 1 maxiter { /iter exch def
x 100 div y 100 div complex
z0 z0 cmul
cadd dup /z0 exch def
cabs2 4 gt {exit} if
} for
iter maxiter div g
x y m dot
} for
} for
%
showpage
origstate restore
%%EOF
PowerShell
$x = $y = $i = $j = $r = -16 $colors = [Enum]::GetValues([System.ConsoleColor]) while(($y++) -lt 15) { for($x=0; ($x++) -lt 84; Write-Host " " -BackgroundColor ($colors[$k -band 15]) -NoNewline) { $i = $k = $r = 0 do { $j = $r * $r - $i * $i -2 + $x / 25 $i = 2 * $r * $i + $y / 10 $r = $j } while (($j * $j + $i * $i) -lt 11 -band ($k++) -lt 111) } Write-Host }
OpenEdge/Progress
<lang Progress (OpenEdge ABL)>DEFINE VARIABLE print_str AS CHAR NO-UNDO INIT ''. DEFINE VARIABLE X1 AS DECIMAL NO-UNDO INIT 50. DEFINE VARIABLE Y1 AS DECIMAL NO-UNDO INIT 21. DEFINE VARIABLE X AS DECIMAL NO-UNDO. DEFINE VARIABLE Y AS DECIMAL NO-UNDO. DEFINE VARIABLE N AS DECIMAL NO-UNDO. DEFINE VARIABLE I3 AS DECIMAL NO-UNDO. DEFINE VARIABLE R3 AS DECIMAL NO-UNDO. DEFINE VARIABLE Z1 AS DECIMAL NO-UNDO. DEFINE VARIABLE Z2 AS DECIMAL NO-UNDO. DEFINE VARIABLE A AS DECIMAL NO-UNDO. DEFINE VARIABLE B AS DECIMAL NO-UNDO. DEFINE VARIABLE I1 AS DECIMAL NO-UNDO INIT -1.0. DEFINE VARIABLE I2 AS DECIMAL NO-UNDO INIT 1.0. DEFINE VARIABLE R1 AS DECIMAL NO-UNDO INIT -2.0. DEFINE VARIABLE R2 AS DECIMAL NO-UNDO INIT 1.0. DEFINE VARIABLE S1 AS DECIMAL NO-UNDO. DEFINE VARIABLE S2 AS DECIMAL NO-UNDO.
S1 = (R2 - R1) / X1. S2 = (I2 - I1) / Y1. DO Y = 0 TO Y1 - 1: I3 = I1 + S2 * Y. DO X = 0 TO X1 - 1: R3 = R1 + S1 * X. Z1 = R3. Z2 = I3. DO N = 0 TO 29: A = Z1 * Z1. B = Z2 * Z2. IF A + B > 4.0 THEN LEAVE. Z2 = 2 * Z1 * Z2 + I3. Z1 = A - B + R3. END. print_str = print_str + CHR(62 - N). END. print_str = print_str + '~n'. END.
OUTPUT TO "C:\Temp\out.txt". MESSAGE print_str. OUTPUT CLOSE.
Example :<BR>
## Processing
```Prolog
// Following code is a zoomable Mandelbrot.
// Of course, you want to click on an interesting area
// with contrast and more colors to zoom in.
double x, y, zr, zi, zr2, zi2, cr, ci, n;
double zmx1, zmx2, zmy1, zmy2, f, di, dj;
double fn1, fn2, fn3, re, gr, bl, xt, yt, i, j;
void setup() {
size(500, 500);
di = 0;
dj = 0;
f = 10;
fn1 = random(20);
fn2 = random(20);
fn3 = random(20);
zmx1 = int(width / 4);
zmx2 = 2;
zmy1 = int(height / 4);
zmy2 = 2;
}
void draw() {
if (i <= width) i++;
x = (i + di)/ zmx1 - zmx2;
for ( j = 0; j <= height; j++) {
y = zmy2 - (j + dj) / zmy1;
zr = 0;
zi = 0;
zr2 = 0;
zi2 = 0;
cr = x;
ci = y;
n = 1;
while (n < 200 && (zr2 + zi2) < 4) {
zi2 = zi * zi;
zr2 = zr * zr;
zi = 2 * zi * zr + ci;
zr = zr2 - zi2 + cr;
n++;
}
re = (n * fn1) % 255;
gr = (n * fn2) % 255;
bl = (n * fn3) % 255;
stroke((float)re, (float)gr, (float)bl);
point((float)i, (float)j);
}
}
void mousePressed() {
background(200);
xt = mouseX;
yt = mouseY;
di = di + xt - float(width / 2);
dj = dj + yt - float(height / 2);
zmx1 = zmx1 * f;
zmx2 = zmx2 * (1 / f);
zmy1 = zmy1 * f;
zmy2 = zmy2 * (1 / f);
di = di * f;
dj = dj * f;
i = 0;
j = 0;
}
'''Output examples''' :
https://drive.google.com/open?id=0B8HXpZALHgx-WWV3dXJwRXdvbWs
https://drive.google.com/open?id=0B8HXpZALHgx-MktORkZKelFBbkU
Prolog
SWI-Prolog has a graphic interface XPCE :
:- use_module(library(pce)).
mandelbrot :-
new(D, window('Mandelbrot Set')),
send(D, size, size(700, 650)),
new(Img, image(@nil, width := 700, height := 650, kind := pixmap)),
forall(between(0,699, I),
( forall(between(0,649, J),
( get_RGB(I, J, R, G, B),
R1 is (R * 256) mod 65536,
G1 is (G * 256) mod 65536,
B1 is (B * 256) mod 65536,
send(Img, pixel(I, J, colour(@default, R1, G1, B1))))))),
new(Bmp, bitmap(Img)),
send(D, display, Bmp, point(0,0)),
send(D, open).
get_RGB(X, Y, R, G, B) :-
CX is (X - 350) / 150,
CY is (Y - 325) / 150,
Iter = 570,
compute_RGB(CX, CY, 0, 0, Iter, It),
IterF is It \/ It << 15,
R is IterF >> 16,
Iter1 is IterF - R << 16,
G is Iter1 >> 8,
B is Iter1 - G << 8.
compute_RGB(CX, CY, ZX, ZY, Iter, IterF) :-
ZX * ZX + ZY * ZY < 4,
Iter > 0,
!,
Tmp is ZX * ZX - ZY * ZY + CX,
ZY1 is 2 * ZX * ZY + CY,
Iter1 is Iter - 1,
compute_RGB(CX, CY, Tmp, ZY1, Iter1, IterF).
compute_RGB(_CX, _CY, _ZX, _ZY, Iter, Iter).
Example :
[[FILE:Mandelbrot.jpg]]
PureBasic
PureBasic forum: [http://www.purebasic.fr/german/viewtopic.php?f=4&t=22107 discussion]
EnableExplicit
#Window1 = 0
#Image1 = 0
#ImgGadget = 0
#max_iteration = 64
#width = 800
#height = 600
Define.d x0 ,y0 ,xtemp ,cr, ci
Define.i i, n, x, y ,Event ,color
Dim Color.l (255)
For n = 0 To 63
Color( 0 + n ) = RGB( n*4+128, 4 * n, 0 )
Color( 64 + n ) = RGB( 64, 255, 4 * n )
Color( 128 + n ) = RGB( 64, 255 - 4 * n , 255 )
Color( 192 + n ) = RGB( 64, 0, 255 - 4 * n )
Next
If OpenWindow(#Window1, 0, 0, #width, #height, "'Mandelbrot set' PureBasic Example", #PB_Window_SystemMenu )
If CreateImage(#Image1, #width, #height)
ImageGadget(#ImgGadget, 0, 0, #width, #height, ImageID(#Image1))
For y.i = 1 To #height -1
StartDrawing(ImageOutput(#Image1))
For x.i = 1 To #width -1
x0 = 0
y0 = 0;
cr = (x / #width)*2.5 -2
ci = (y / #height)*2.5 -1.25
i = 0
While (x0*x0 + y0*y0 <= 4.0) And i < #max_iteration
i +1
xtemp = x0*x0 - y0*y0 + cr
y0 = 2*x0*y0 + ci
x0 = xtemp
Wend
If i >= #max_iteration
Plot(x, y, 0 )
Else
Plot(x, y, Color(i & 255))
EndIf
Next
StopDrawing()
SetGadgetState(#ImgGadget, ImageID(#Image1))
Repeat
Event = WindowEvent()
If Event = #PB_Event_CloseWindow
End
EndIf
Until Event = 0
Next
EndIf
Repeat
Event = WaitWindowEvent()
Until Event = #PB_Event_CloseWindow
EndIf
Example:
[[File:Mandelbrot-PureBasic.png]]
Python
Translation of the ruby solution
# Python 3.0+ and 2.5+ try: from functools import reduce except: pass def mandelbrot(a): return reduce(lambda z, _: z * z + a, range(50), 0) def step(start, step, iterations): return (start + (i * step) for i in range(iterations)) rows = (("*" if abs(mandelbrot(complex(x, y))) < 2 else " " for x in step(-2.0, .0315, 80)) for y in step(1, -.05, 41)) print("\n".join("".join(row) for row in rows))
A more "Pythonic" version of the code:
import math def mandelbrot(z , c , n=40): if abs(z) > 1000: return float("nan") elif n > 0: return mandelbrot(z ** 2 + c, c, n - 1) else: return z ** 2 + c print("\n".join(["".join(["#" if not math.isnan(mandelbrot(0, x + 1j * y).real) else " " for x in [a * 0.02 for a in range(-80, 30)]]) for y in [a * 0.05 for a in range(-20, 20)]]) )
Finally, we can also use Matplotlib to visualize the Mandelbrot set with Python: {{libheader|matplotlib}} {{libheader|NumPy}}
from pylab import * from numpy import NaN def m(a): z = 0 for n in range(1, 100): z = z**2 + a if abs(z) > 2: return n return NaN X = arange(-2, .5, .002) Y = arange(-1, 1, .002) Z = zeros((len(Y), len(X))) for iy, y in enumerate(Y): print (iy, "of", len(Y)) for ix, x in enumerate(X): Z[iy,ix] = m(x + 1j * y) imshow(Z, cmap = plt.cm.prism, interpolation = 'none', extent = (X.min(), X.max(), Y.min(), Y.max())) xlabel("Re(c)") ylabel("Im(c)") savefig("mandelbrot_python.svg") show()
Another Numpy version using masks to avoid (explicit) nested loops. Runs about 16x faster for the same resolution.
import matplotlib.pyplot as plt import numpy as np npts = 300 max_iter = 100 X = np.linspace(-2, 1, 2 * npts) Y = np.linspace(-1, 1, npts) #broadcast X to a square array C = X[:, None] + 1J * Y #initial value is always zero Z = np.zeros_like(C) exit_times = max_iter * np.ones(C.shape, np.int32) mask = exit_times > 0 for k in range(max_iter): Z[mask] = Z[mask] * Z[mask] + C[mask] mask, old_mask = abs(Z) < 2, mask #use XOR to detect the area which has changed exit_times[mask ^ old_mask] = k plt.imshow(exit_times.T, cmap=plt.cm.prism, extent=(X.min(), X.max(), Y.min(), Y.max()))
R
iterate.until.escape <- function(z, c, trans, cond, max=50, response=dwell) { #we iterate all active points in the same array operation, #and keeping track of which points are still iterating. active <- seq_along(z) dwell <- z dwell[] <- 0 for (i in 1:max) { z[active] <- trans(z[active], c[active]); survived <- cond(z[active]) dwell[active[!survived]] <- i active <- active[survived] if (length(active) == 0) break } eval(substitute(response)) } re = seq(-2, 1, len=500) im = seq(-1.5, 1.5, len=500) c <- outer(re, im, function(x,y) complex(real=x, imaginary=y)) x <- iterate.until.escape(array(0, dim(c)), c, function(z,c)z^2+c, function(z)abs(z) <= 2, max=100) image(x)
Racket
#lang racket
(require racket/draw)
(define (iterations a z i)
(define z′ (+ (* z z) a))
(if (or (= i 255) (> (magnitude z′) 2))
i
(iterations a z′ (add1 i))))
(define (iter->color i)
(if (= i 255)
(make-object color% "black")
(make-object color% (* 5 (modulo i 15)) (* 32 (modulo i 7)) (* 8 (modulo i 31)))))
(define (mandelbrot width height)
(define target (make-bitmap width height))
(define dc (new bitmap-dc% [bitmap target]))
(for* ([x width] [y height])
(define real-x (- (* 3.0 (/ x width)) 2.25))
(define real-y (- (* 2.5 (/ y height)) 1.25))
(send dc set-pen (iter->color (iterations (make-rectangular real-x real-y) 0 0)) 1 'solid)
(send dc draw-point x y))
(send target save-file "mandelbrot.png" 'png))
(mandelbrot 300 200)
REXX
version 1
{{trans|AWK}} This REXX version doesn't depend on the ASCII sequence of glyphs; an internal character string was used that mimics a part of the ASCII glyph sequence.
/*REXX program generates and displays a Mandelbrot set as an ASCII art character image.*/
@ = '>=<;:9876543210/.-,+*)(''&%$#"!' /*the characters used in the display. */
Xsize = 59; minRE = -2; maxRE = +1; stepX = (maxRE-minRE) / Xsize
Ysize = 21; minIM = -1; maxIM = +1; stepY = (maxIM-minIM) / Ysize
do y=0 for ysize; im=minIM + stepY*y
$=
do x=0 for Xsize; re=minRE + stepX*x; zr=re; zi=im
do n=0 for 30; a=zr**2; b=zi**2; if a+b>4 then leave
zi=zr*zi*2 + im; zr=a-b+re
end /*n*/
$=$ || substr(@, n+1, 1) /*append number (as a char) to $ string*/
end /*x*/
say $ /*display a line of character output.*/
end /*y*/ /*stick a fork in it, we're all done. */
'''output''' using the internal defaults:
>>>>>>
### ==<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<=======
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<
### =
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<======
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<====
>>==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<===
>>=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<==
>=<<<<<<<<;;;:599999999886 %78:;;<<<<<<=
><<<<;;;;;:::972456-567763 +9;;<<<<<<<
><;;;;;;::::9875& .3 *9;;;<<<<<<
>;;;;;;::997564' ' 8:;;;<<<<<<
>::988897735/ &89:;;;<<<<<<
>::988897735/ &89:;;;<<<<<<
>;;;;;;::997564' ' 8:;;;<<<<<<
><;;;;;;::::9875& .3 *9;;;<<<<<<
><<<<;;;;;:::972456-567763 +9;;<<<<<<<
>=<<<<<<<<;;;:599999999886 %78:;;<<<<<<=
>>=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<==
>>==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<===
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<====
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<======
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<
### =
version 2
This REXX version uses glyphs that are "darker" (with a white background) around the output's peripheral.
/*REXX program generates and displays a Mandelbrot set as an ASCII art character image.*/
@ = '█▓▒░@9876543210=.-,+*)(·&%$#"!' /*the characters used in the display. */
Xsize = 59; minRE = -2; maxRE = +1; stepX = (maxRE-minRE) / Xsize
Ysize = 21; minIM = -1; maxIM = +1; stepY = (maxIM-minIM) / Ysize
do y=0 for ysize; im=minIM + stepY*y
$=
do x=0 for Xsize; re=minRE + stepX*x; zr=re; zi=im
do n=0 for 30; a=zr**2; b=zi**2; if a+b>4 then leave
zi=zr*zi*2 + im; zr=a-b+re
end /*n*/
$=$ || substr(@, n+1, 1) /*append number (as a char) to $ string*/
end /*x*/
say $ /*display a line of character output.*/
end /*y*/ /*stick a fork in it, we're all done. */
'''output''' using the internal defaults:
██████▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░@@@96032@░░░░▒▒▒▒▓▓▓▓▓▓▓▓▓▓
█████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░@@@873*079@@░░░░▒▒▒▒▒▓▓▓▓▓▓▓
████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░@@9974 (.9@@@@░░▒▒▒▒▒▓▓▓▓▓▓
███▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░@98888764 5789999@░░▒▒▒▒▒▓▓▓▓
██▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░@@@@996. &2 45335@░▒▒▒▒▒▒▓▓▓
██▓▒▒▒▒▒▒▒▒▒▒▒░░░@@@@@@999752 *79@░▒▒▒▒▒▒▓▓
█▓▒▒▒▒▒▒▒▒░░░@599999999886 %78@░░▒▒▒▒▒▒▓
█▒▒▒▒░░░░░@@@972456-567763 +9░░▒▒▒▒▒▒▒
█▒░░░░░░@@@@9875& .3 *9░░░▒▒▒▒▒▒
█░░░░░░@@997564· · 8@░░░▒▒▒▒▒▒
█@@988897735= &89@░░░▒▒▒▒▒▒
█@@988897735= &89@░░░▒▒▒▒▒▒
█░░░░░░@@997564· · 8@░░░▒▒▒▒▒▒
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█▒▒▒▒░░░░░@@@972456-567763 +9░░▒▒▒▒▒▒▒
█▓▒▒▒▒▒▒▒▒░░░@599999999886 %78@░░▒▒▒▒▒▒▓
██▓▒▒▒▒▒▒▒▒▒▒▒░░░@@@@@@999752 *79@░▒▒▒▒▒▒▓▓
██▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░@@@@996. &2 45335@░▒▒▒▒▒▒▓▓▓
███▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░@98888764 5789999@░░▒▒▒▒▒▓▓▓▓
████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░@@9974 (.9@@@@░░▒▒▒▒▒▓▓▓▓▓▓
█████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░@@@873*079@@░░░░▒▒▒▒▒▓▓▓▓▓▓▓
version 3
This REXX version produces a larger output (it uses the full width of the terminal screen (less one), and the height is one-half of the width.
/*REXX program generates and displays a Mandelbrot set as an ASCII art character image.*/
@ = '█▓▒░@9876543210=.-,+*)(·&%$#"!' /*the characters used in the display. */
parse arg Xsize Ysize . /*obtain optional arguments from the CL*/
if Xsize=='' then Xsize=linesize() - 1 /*X: the (usable) linesize (minus 1).*/
if Ysize=='' then Ysize=Xsize%2 + (Xsize//2==1) /*Y: half the linesize (make it even).*/
minRE = -2; maxRE = +1; stepX = (maxRE-minRE) / Xsize
minIM = -1; maxIM = +1; stepY = (maxIM-minIM) / Ysize
do y=0 for ysize; im=minIM + stepY*y
$=
do x=0 for Xsize; re=minRE + stepX*x; zr=re; zi=im
do n=0 for 30; a=zr**2; b=zi**2; if a+b>4 then leave
zi=zr*zi*2 + im; zr=a-b+re
end /*n*/
$=$ || substr(@, n+1, 1) /*append number (as a char) to $ string*/
end /*x*/
say $ /*display a line of character output.*/
end /*y*/ /*stick a fork in it, we're all done. */
'''output''' using the internal defaults:
████████▓▓▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░@@@@985164(9@░░░░░░▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓▓▓▓▓
███████▓▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░@@@@98763=5799@░░░░░░▒▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓▓▓
███████▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░@@@@98763.-2789@@@░░░░░░▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓▓
██████▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░@@@@985 2. 1448@@@@░░░░░░▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓
█████▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░@@@999874 *=79@@@@@░░░░▒▒▒▒▒▒▒▒▓▓▓▓▓▓▓▓
█████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░@@999998873 17899@@@@@░░░▒▒▒▒▒▒▒▒▓▓▓▓▓▓▓
████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░@@98888888764 #4678899999@@░░▒▒▒▒▒▒▒▒▓▓▓▓▓▓
████▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░@@@@9343,665 322= =215357888709@░░▒▒▒▒▒▒▒▒▓▓▓▓▓
███▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░@@@@@9986 + 32 ,56554)79@░▒▒▒▒▒▒▒▒▒▓▓▓▓
███▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░@@@@@@@999863 + 2· ",59@░░▒▒▒▒▒▒▒▒▓▓▓▓
███▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░@@@@@@@@@@9998763 $ 379@@░▒▒▒▒▒▒▒▒▒▓▓▓
██▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░@@@@@@@@@@999986.2 $ +689@@░░▒▒▒▒▒▒▒▒▒▓▓
██▓▒▒▒▒▒▒▒▒▒▒▒▒▒░░░@689999@@@99999887 05789@░░▒▒▒▒▒▒▒▒▒▓▓
██▒▒▒▒▒▒▒▒▒▒░░░░░@@9717888877888888763. 2558@░░░▒▒▒▒▒▒▒▒▒▓
█▓▒▒▒▒▒▒░░░░░░░@@@996)566761467777762 4@░░░▒▒▒▒▒▒▒▒▒▓
█▓▒▒▒▒░░░░░░░░@@@@99763 & 42&..366651· .68@░░░░▒▒▒▒▒▒▒▒▓
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█▒░░░░░░░░@@@@@9877650 - 289@░░░░▒▒▒▒▒▒▒▒▒
█░░░░░░░░@9999887%413+ % &69@@░░░░▒▒▒▒▒▒▒▒▒
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█@@99872676676422 5789@@░░░░▒▒▒▒▒▒▒▒▒
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██▒▒▒▒▒▒▒▒▒▒░░░░░@@9717888877888888763. 2558@░░░▒▒▒▒▒▒▒▒▒▓
██▓▒▒▒▒▒▒▒▒▒▒▒▒▒░░░@689999@@@99999887 05789@░░▒▒▒▒▒▒▒▒▒▓▓
██▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░@@@@@@@@@@999986.2 $ +689@@░░▒▒▒▒▒▒▒▒▒▓▓
███▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░@@@@@@@@@@9998763 $ 379@@░▒▒▒▒▒▒▒▒▒▓▓▓
███▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░@@@@@@@999863 + 2· ",59@░░▒▒▒▒▒▒▒▒▓▓▓▓
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████▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░@@@@9343,665 322= =215357888709@░░▒▒▒▒▒▒▒▒▓▓▓▓▓
████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░@@98888888764 #4678899999@@░░▒▒▒▒▒▒▒▒▓▓▓▓▓▓
█████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░@@999998873 17899@@@@@░░░▒▒▒▒▒▒▒▒▓▓▓▓▓▓▓
█████▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░@@@999874 *=79@@@@@░░░░▒▒▒▒▒▒▒▒▓▓▓▓▓▓▓▓
██████▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░@@@@985 2. 1448@@@@░░░░░░▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓
███████▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░@@@@98763.-2789@@@░░░░░░▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓▓
███████▓▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░@@@@98763=5799@░░░░░░▒▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓▓▓
This REXX program makes use of '''linesize''' REXX program (or BIF) which is used to determine the screen width (or linesize) of the terminal (console).
The '''LINESIZE.REX''' REXX program is included here ──► [[LINESIZE.REX]].
Ring
load "guilib.ring"
new qapp
{
win1 = new qwidget() {
setwindowtitle("Mandelbrot set")
setgeometry(100,100,500,500)
label1 = new qlabel(win1) {
setgeometry(10,10,400,400)
settext("")
}
new qpushbutton(win1) {
setgeometry(200,400,100,30)
settext("draw")
setclickevent("draw()")
}
show()
}
exec()
}
func draw
p1 = new qpicture()
color = new qcolor() {
setrgb(0,0,255,255)
}
pen = new qpen() {
setcolor(color)
setwidth(1)
}
new qpainter() {
begin(p1)
setpen(pen)
x1=300 y1=250
i1=-1 i2=1 r1=-2 r2=1
s1=(r2-r1)/x1 s2=(i2-i1)/y1
for y=0 to y1
i3=i1+s2*y
for x=0 to x1
r3=r1+s1*x z1=r3 z2=i3
for n=0 to 30
a=z1*z1 b=z2*z2
if a+b>4 exit ok
z2=2*z1*z2+i3 z1=a-b+r3
next
if n != 31 drawpoint(x,y) ok
next
next
endpaint()
}
label1 { setpicture(p1) show() }
Output:
[[File:CalmoSoftMandelbrot.jpg]]
Ruby
Text only, prints an 80-char by 41-line depiction. Found [http://www.xcombinator.com/2008/02/22/ruby-inject-and-the-mandelbrot-set/ here].
require 'complex' def mandelbrot(a) Array.new(50).inject(0) { |z,c| z*z + a } end (1.0).step(-1,-0.05) do |y| (-2.0).step(0.5,0.0315) do |x| print mandelbrot(Complex(x,y)).abs < 2 ? '*' : ' ' end puts end
{{trans|Tcl}}
Uses the text progress bar from [[Median filter#Ruby]]
class RGBColour def self.mandel_colour(i) self.new( 16*(i % 15), 32*(i % 7), 8*(i % 31) ) end end class Pixmap def self.mandelbrot(width, height) mandel = Pixmap.new(width,height) pb = ProgressBar.new(width) if $DEBUG width.times do |x| height.times do |y| x_ish = Float(x - width*11/15) / (width/3) y_ish = Float(y - height/2) / (height*3/10) mandel[x,y] = RGBColour.mandel_colour(mandel_iters(x_ish, y_ish)) end pb.update(x) if $DEBUG end pb.close if $DEBUG mandel end def self.mandel_iters(cx,cy) x = y = 0.0 count = 0 while Math.hypot(x,y) < 2 and count < 255 x, y = (x**2 - y**2 + cx), (2*x*y + cy) count += 1 end count end end Pixmap.mandelbrot(300,300).save('mandel.ppm')
Rust
Dependencies: image, num-complex
extern crate image; extern crate num_complex; use std::fs::File; use num_complex::Complex; fn main() { let max_iterations = 256u16; let img_side = 800u32; let cxmin = -2f32; let cxmax = 1f32; let cymin = -1.5f32; let cymax = 1.5f32; let scalex = (cxmax - cxmin) / img_side as f32; let scaley = (cymax - cymin) / img_side as f32; // Create a new ImgBuf let mut imgbuf = image::ImageBuffer::new(img_side, img_side); // Calculate for each pixel for (x, y, pixel) in imgbuf.enumerate_pixels_mut() { let cx = cxmin + x as f32 * scalex; let cy = cymin + y as f32 * scaley; let c = Complex::new(cx, cy); let mut z = Complex::new(0f32, 0f32); let mut i = 0; for t in 0..max_iterations { if z.norm() > 2.0 { break; } z = z * z + c; i = t; } *pixel = image::Luma([i as u8]); } // Save image let fout = &mut File::create("fractal.png").unwrap(); image::ImageLuma8(imgbuf).save(fout, image::PNG).unwrap(); }
Scala
{{works with|Scala|2.8}} Uses RgbBitmap from [[Basic_bitmap_storage#Scala|Basic Bitmap Storage]] task and Complex number class from [[Arithmetic/Complex#Scala|this]] programming task.
import org.rosettacode.ArithmeticComplex._ import java.awt.Color object Mandelbrot { def generate(width:Int =600, height:Int =400)={ val bm=new RgbBitmap(width, height) val maxIter=1000 val xMin = -2.0 val xMax = 1.0 val yMin = -1.0 val yMax = 1.0 val cx=(xMax-xMin)/width val cy=(yMax-yMin)/height for(y <- 0 until bm.height; x <- 0 until bm.width){ val c=Complex(xMin+x*cx, yMin+y*cy) val iter=itMandel(c, maxIter, 4) bm.setPixel(x, y, getColor(iter, maxIter)) } bm } def itMandel(c:Complex, imax:Int, bailout:Int):Int={ var z=Complex() for(i <- 0 until imax){ z=z*z+c; if(z.abs > bailout) return i } imax; } def getColor(iter:Int, max:Int):Color={ if (iter==max) return Color.BLACK var c=3*math.log(iter)/math.log(max-1.0) if(c<1) new Color((255*c).toInt, 0, 0) else if(c<2) new Color(255, (255*(c-1)).toInt, 0) else new Color(255, 255, (255*(c-2)).toInt) } }
Read–eval–print loop
import scala.swing._ import javax.swing.ImageIcon val imgMandel=Mandelbrot.generate() val mainframe=new MainFrame(){title="Test"; visible=true contents=new Label(){icon=new ImageIcon(imgMandel.image)} }
Scheme
This implementation writes an image of the Mandelbrot set to a plain pgm file. The set itself is drawn in white, while the exterior is drawn in black.
(define x-centre -0.5)
(define y-centre 0.0)
(define width 4.0)
(define i-max 800)
(define j-max 600)
(define n 100)
(define r-max 2.0)
(define file "out.pgm")
(define colour-max 255)
(define pixel-size (/ width i-max))
(define x-offset (- x-centre (* 0.5 pixel-size (+ i-max 1))))
(define y-offset (+ y-centre (* 0.5 pixel-size (+ j-max 1))))
(define (inside? z)
(define (*inside? z-0 z n)
(and (< (magnitude z) r-max)
(or (= n 0)
(*inside? z-0 (+ (* z z) z-0) (- n 1)))))
(*inside? z 0 n))
(define (boolean->integer b)
(if b colour-max 0))
(define (pixel i j)
(boolean->integer
(inside?
(make-rectangular (+ x-offset (* pixel-size i))
(- y-offset (* pixel-size j))))))
(define (plot)
(with-output-to-file file
(lambda ()
(begin (display "P2") (newline)
(display i-max) (newline)
(display j-max) (newline)
(display colour-max) (newline)
(do ((j 1 (+ j 1))) ((> j j-max))
(do ((i 1 (+ i 1))) ((> i i-max))
(begin (display (pixel i j)) (newline))))))))
(plot)
Scratch
[[File:scratch-mandelbrot.gif]]
Sass/SCSS
$canvasWidth: 200;
$canvasHeight: 200;
$iterations: 20;
$xCorner: -2;
$yCorner: -1.5;
$zoom: 3;
$data: ()!global;
@mixin plot ($x,$y,$count){
$index: ($y * $canvasWidth + $x) * 4;
$r: $count * -12 + 255;
$g: $count * -12 + 255;
$b: $count * -12 + 255;
$data: append($data, $x + px $y + px 0 rgb($r,$g,$b), comma)!global;
}
@for $x from 1 to $canvasWidth {
@for $y from 1 to $canvasHeight {
$count: 0;
$size: 0;
$cx: $xCorner + (($x * $zoom) / $canvasWidth);
$cy: $yCorner + (($y * $zoom) / $canvasHeight);
$zx: 0;
$zy: 0;
@while $count < $iterations and $size <= 4 {
$count: $count + 1;
$temp: ($zx * $zx) - ($zy * $zy);
$zy: (2 * $zx * $zy) + $cy;
$zx: $temp + $cx;
$size: ($zx * $zx) + ($zy * $zy);
}
@include plot($x, $y, $count);
}
}
.set {
height: 1px;
width: 1px;
position: absolute;
top: 50%;
left: 50%;
transform: translate($canvasWidth*0.5px, $canvasWidth*0.5px);
box-shadow: $data;
}
Seed7
$ include "seed7_05.s7i";
include "float.s7i";
include "complex.s7i";
include "draw.s7i";
include "keybd.s7i";
# Display the Mandelbrot set, that are points z[0] in the complex plane
# for which the sequence z[n+1] := z[n] ** 2 + z[0] (n >= 0) is bounded.
# Since this program is computing intensive it should be compiled with
# hi comp -O2 mandelbr
const integer: pix is 200;
const integer: max_iter is 256;
var array color: colorTable is max_iter times black;
const func integer: iterate (in complex: z0) is func
result
var integer: iter is 1;
local
var complex: z is complex.value;
begin
z := z0;
while sqrAbs(z) < 4.0 and # not diverged
iter < max_iter do # not converged
z *:= z;
z +:= z0;
incr(iter);
end while;
end func;
const proc: displayMandelbrotSet (in complex: center, in float: zoom) is func
local
var integer: x is 0;
var integer: y is 0;
var complex: z0 is complex.value;
begin
for x range -pix to pix do
for y range -pix to pix do
z0 := center + complex(flt(x) * zoom, flt(y) * zoom);
point(x + pix, y + pix, colorTable[iterate(z0)]);
end for;
end for;
end func;
const proc: main is func
local
const integer: num_pix is 2 * pix + 1;
var integer: col is 0;
begin
screen(num_pix, num_pix);
clear(curr_win, black);
KEYBOARD := GRAPH_KEYBOARD;
for col range 1 to pred(max_iter) do
colorTable[col] := color(65535 - (col * 5003) mod 65535,
(col * 257) mod 65535,
(col * 2609) mod 65535);
end for;
displayMandelbrotSet(complex(-0.75, 0.0), 1.3 / flt(pix));
DRAW_FLUSH;
readln(KEYBOARD);
end func;
Original source: [http://seed7.sourceforge.net/algorith/graphic.htm#mandelbr]
SequenceL
'''SequenceL Code for Computing and Coloring:'''
;
import <Utilities/Sequence.sl>;
import <Utilities/Math.sl>;
COLOR_STRUCT ::= (R: int(0), G: int(0), B: int(0));
rgb(r(0), g(0), b(0)) := (R: r, G: g, B: b);
RESULT_STRUCT ::= (FinalValue: Complex(0), Iterations: int(0));
makeResult(val(0), iters(0)) := (FinalValue: val, Iterations: iters);
zSquaredOperation(startingNum(0), currentNum(0)) :=
complexAdd(startingNum, complexMultiply(currentNum, currentNum));
zSquared(minX(0), maxX(0), resolutionX(0), minY(0), maxY(0), resolutionY(0), maxMagnitude(0), maxIters(0))[Y,X] :=
let
stepX := (maxX - minX) / resolutionX;
stepY := (maxY - minY) / resolutionY;
currentX := X * stepX + minX;
currentY := Y * stepY + minY;
in
operateUntil(zSquaredOperation, makeComplex(currentX, currentY), makeComplex(currentX, currentY), maxMagnitude, 0, maxIters)
foreach Y within 0 ... (resolutionY - 1),
X within 0 ... (resolutionX - 1);
operateUntil(operation(0), startingNum(0), currentNum(0), maxMagnitude(0), currentIters(0), maxIters(0)) :=
let
operated := operation(startingNum, currentNum);
in
makeResult(currentNum, maxIters) when currentIters >= maxIters
else
makeResult(currentNum, currentIters) when complexMagnitude(currentNum) >= maxMagnitude
else
operateUntil(operation, startingNum, operated, maxMagnitude, currentIters + 1, maxIters);
//region Smooth Coloring
COLOR_COUNT := size(colorSelections);
colorRange := range(0, 255, 1);
colors :=
let
first[i] := rgb(0, 0, i) foreach i within colorRange;
second[i] := rgb(i, i, 255) foreach i within colorRange;
third[i] := rgb(255, 255, i) foreach i within reverse(colorRange);
fourth[i] := rgb(255, i, 0) foreach i within reverse(colorRange);
fifth[i] := rgb(i, 0, 0) foreach i within reverse(colorRange);
red[i] := rgb(i, 0, 0) foreach i within colorRange;
redR[i] := rgb(i, 0, 0) foreach i within reverse(colorRange);
green[i] := rgb(0, i, 0) foreach i within colorRange;
greenR[i] :=rgb(0, i, 0) foreach i within reverse(colorRange);
blue[i] := rgb(0, 0, i) foreach i within colorRange;
blueR[i] := rgb(0, 0, i) foreach i within reverse(colorRange);
in
//red ++ redR ++ green ++ greenR ++ blue ++ blueR;
first ++ second ++ third ++ fourth ++ fifth;
//first ++ fourth;
colorSelections := range(1, size(colors), 30);
getSmoothColorings(zSquaredResult(2), maxIters(0))[Y,X] :=
let
current := zSquaredResult[Y,X];
zn := complexMagnitude(current.FinalValue);
nu := ln(ln(zn) / ln(2)) / ln(2);
result := abs(current.Iterations + 1 - nu);
index := floor(result);
rem := result - index;
color1 := colorSelections[(index mod COLOR_COUNT) + 1];
color2 := colorSelections[((index + 1) mod COLOR_COUNT) + 1];
in
rgb(0, 0, 0) when current.Iterations = maxIters
else
colors[color1] when color2 < color1
else
colors[floor(linearInterpolate(color1, color2, rem))];
linearInterpolate(v0(0), v1(0), t(0)) := (1 - t) * v0 + t * v1;
//endregion
'''C++ Driver Code:'''
{{libheader|CImg}}
#include "SL_Generated.h" #include "../../../ThirdParty/CImg/CImg.h" using namespace std; using namespace cimg_library; int main(int argc, char ** argv) { int cores = 0; Sequence<Sequence<_sl_RESULT_STRUCT> > computeResult; Sequence<Sequence<_sl_COLOR_STRUCT> > colorResult; sl_init(cores); int maxIters = 1000; int imageWidth = 1920; int imageHeight = 1200; double maxMag = 256; double xmin = -2.5; double xmax = 1.0; double ymin = -1.0; double ymax = 1.0; CImg<unsigned char> visu(imageWidth, imageHeight, 1, 3); CImgDisplay draw_disp(visu, "Mandelbrot Fractal in SequenceL"); bool redraw = true; SLTimer t; double computeTime; double colorTime; double renderTime; while(!draw_disp.is_closed()) { if(redraw) { redraw = false; t.start(); sl_zSquared(xmin, xmax, imageWidth, ymin, ymax, imageHeight, maxMag, maxIters, cores, computeResult); t.stop(); computeTime = t.getTime(); t.start(); sl_getSmoothColorings(computeResult, maxIters, cores, colorResult); t.stop(); colorTime = t.getTime(); t.start(); visu.fill(0); for(int i = 1; i <= colorResult.size(); i++) { for(int j = 1; j <= colorResult[i].size(); j++) { visu(j-1,i-1,0,0) = colorResult[i][j].R; visu(j-1,i-1,0,1) = colorResult[i][j].G; visu(j-1,i-1,0,2) = colorResult[i][j].B; } } visu.display(draw_disp); t.stop(); renderTime = t.getTime(); draw_disp.set_title("X:[%f, %f] Y:[%f, %f] | Mandelbrot Fractal in SequenceL | Compute Time: %f | Color Time: %f | Render Time: %f | Total FPS: %f", xmin, xmax, ymin, ymax, cores, computeTime, colorTime, renderTime, 1 / (computeTime + colorTime + renderTime)); } draw_disp.wait(); double xdiff = (xmax - xmin); double ydiff = (ymax - ymin); double xcenter = ((1.0 * draw_disp.mouse_x()) / imageWidth) * xdiff + xmin; double ycenter = ((1.0 * draw_disp.mouse_y()) / imageHeight) * ydiff + ymin; if(draw_disp.button()&1) { redraw = true; xmin = xcenter - (xdiff / 4); xmax = xcenter + (xdiff / 4); ymin = ycenter - (ydiff / 4); ymax = ycenter + (ydiff / 4); } else if(draw_disp.button()&2) { redraw = true; xmin = xcenter - xdiff; xmax = xcenter + xdiff; ymin = ycenter - ydiff; ymax = ycenter + ydiff; } } sl_done(); return 0; }
{{out}} [https://i.imgur.com/xeM4u9O.png Output Screenshot]
Sidef
func mandelbrot(z) { var c = z { z = (z*z + c) z.abs > 2 && return true } * 20 return false } for y range(1, -1, -0.05) { for x in range(-2, 0.5, 0.0315) { print(mandelbrot(x + y.i) ? ' ' : '#') } print "\n" }
Spin
{{works with|BST/BSTC}} {{works with|FastSpin/FlexSpin}} {{works with|HomeSpun}} {{works with|OpenSpin}}
con
_clkmode = xtal1+pll16x
_clkfreq = 80_000_000
xmin=-8601 ' int(-2.1*4096)
xmax=2867 ' int( 0.7*4096)
ymin=-4915 ' int(-1.2*4096)
ymax=4915 ' int( 1.2*4096)
maxiter=25
obj
ser : "FullDuplexSerial"
pub main | c,cx,cy,dx,dy,x,y,x2,y2,iter
ser.start(31, 30, 0, 115200)
dx:=(xmax-xmin)/79
dy:=(ymax-ymin)/24
cy:=ymin
repeat while cy=<ymax
cx:=xmin
repeat while cx=<xmax
x:=0
y:=0
x2:=0
y2:=0
iter:=0
repeat while iter=<maxiter and x2+y2=<16384
y:=((x*y)~>11)+cy
x:=x2-y2+cx
iter+=1
x2:=(x*x)~>12
y2:=(y*y)~>12
cx+=dx
ser.tx(iter+32)
cy+=dy
ser.str(string(13,10))
waitcnt(_clkfreq+cnt)
ser.stop
{{out}}
!!!!!!!!!!!!!!!"""""""""""""####################################""""""""""""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$$%'+)%%%$$$$$#####"""""""""""
!!!!!!!!!!!"""""""#######################$$$$$$$$%%%&&(+,)++&%$$$$$$######""""""
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*5:/+('&%%$$$$$$#######"""
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''),:::::::,'&%%%%%$$$$########
!!!!!!!"""####################$$$$$$$$%%%&'())((())*,::::::/+))('&&&&)'%$$######
!!!!!!""###################$$$$$%%%%%%&&&'+.:::/::::::::::::::::/++:..93%%$#####
!!!!!"################$$$%%%%%%%%%%&&&&'),+2:::::::::::::::::::::::::1(&&%$$####
!!!!"##########$$$$$%%&(-(''''''''''''(*,5::::::::::::::::::::::::::::+)-&%$$###
!!!!####$$$$$$$$%%%%%&'(*-:1.+.:-4+))**:::::::::::::::::::::::::::::::4-(&%$$$##
!!!!#$$$$$$$$$%%%%%%'''++.6:::::::::8/0::::::::::::::::::::::::::::::::3(%%$$$$#
!!!#$$$$$$$%&&&&''()/-5.5::::::::::::::::::::::::::::::::::::::::::::::'&%%$$$$#
!!!(**+/+:523/80/46::::::::::::::::::::::::::::::::::::::::::::::::4+)'&&%%$$$$#
!!!#$$$$$$$%&&&&''().-2.:::::::::::::::::::::::::::::::::::::::::::::::'&%%$$$$#
!!!!#$$$$$$$$$%%%%%&'''/,.7::::::::::/0::::::::::::::::::::::::::::::::0'%%$$$$#
!!!!####$$$$$$$$%%%%%&'(*-:2.,/:-5+))**:::::::::::::::::::::::::::::::4+(&%$$$##
!!!!"##########$$$$$%%&(-(''''(''''''((*,4:::::::::::::::::::::::::::4+).&%$$###
!!!!!"################$$$%%%%%%%%%%&&&&'):,4:::::::::::::::::::::::::/('&%%$####
!!!!!!""##################$$$$$$%%%%%%&&&'*.:::0::::::::::::::::1,,://9)%%$#####
!!!!!!!"""####################$$$$$$$$%%%&(())((()**-::::::/+)))'&&&')'%$$######
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''(,:::::::+'&&%%%%%$$$########
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*7:0+('&%%%$$$$$#######"""
!!!!!!!!!!!"""""""######################$$$$$$$$$%%%&&(+-).*&%$$$$$$######""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$%%'3(%%%$$$$$######""""""""""
!!!!!!!!!!!!!!!""""""""""""#####################################""""""""""""""""
SPL
w,h = #.scrsize()
sfx = -2.5; sfy = -2*h/w; fs = 4/w
#.aaoff()
> y, 1...h
> x, 1...w
fx = sfx + x*fs; fy = sfy + y*fs
#.drawpoint(x,y,color(fx,fy):3)
<
<
color(x,y)=
zr = x; zi = y; n = 0; maxn = 150
> zr*zr+zi*zi<4 & n<maxn
zrn = zr*zr-zi*zi+x; zin = 2*zr*zi+y
zr = zrn; zi = zin; n += 1
<
? n=maxn, <= 0,0,0
<= #.hsv2rgb(n/maxn*360,1,1):3
.
Tcl
{{libheader|Tk}} This code makes extensive use of Tk's built-in photo image system, which provides a 32-bit RGBA plotting surface that can be then quickly drawn in any number of places in the application. It uses a computational color scheme that was easy to code...
package require Tk proc mandelIters {cx cy} { set x [set y 0.0] for {set count 0} {hypot($x,$y) < 2 && $count < 255} {incr count} { set x1 [expr {$x*$x - $y*$y + $cx}] set y1 [expr {2*$x*$y + $cy}] set x $x1; set y $y1 } return $count } proc mandelColor {iter} { set r [expr {16*($iter % 15)}] set g [expr {32*($iter % 7)}] set b [expr {8*($iter % 31)}] format "#%02x%02x%02x" $r $g $b } image create photo mandel -width 300 -height 300 # Build picture in strips, updating as we go so we have "progress" monitoring # Also set the cursor to tell the user to wait while we work. pack [label .mandel -image mandel -cursor watch] update for {set x 0} {$x < 300} {incr x} { for {set y 0} {$y < 300} {incr y} { set i [mandelIters [expr {($x-220)/100.}] [expr {($y-150)/90.}]] mandel put [mandelColor $i] -to $x $y } update } .mandel configure -cursor {}
TeX
{{libheader|pst-fractal}}
The pst-fractal package includes a Mandelbrot set drawn by emitting [[PostScript]] code (using [[PSTricks]]), so the actual work done in the printer or PostScript interpreter.
% Plain TeX \input pst-fractal \psfractal[type=Mandel,xWidth=14cm,yWidth=12cm,maxIter=30,dIter=20] (-2.5,-1.5)(1,1.5) \end
The coordinates are a rectangle in the complex plane to draw, scaled up to xWidth,yWidth. More iterations with maxIter is higher resolution but slower. dIter is a scale factor for the colours.
The pstricks-examples package which is samples from the PSTricks book includes similar for [[LaTeX]] (25-02-6.ltx and 33-02-6.ltx).
{{libheader|PGF}}
The PGF shadings library includes a Mandelbrot set. In PGF 3.0 the calculations are done in [[PostScript]] code emitted, so the output size is small but it only does 10 iterations so is very low resolution.
\documentclass{article} \usepackage{tikz} \usetikzlibrary{shadings} \begin{document} \begin{tikzpicture} \shade[shading=Mandelbrot set] (0,0) rectangle (4,4); \end{tikzpicture} \end{document}
{{libheader|LuaTeX}} [[LuaLaTeX]] plus pgfplots code can be found at [http://texwelt.de/wissen/fragen/3960/fraktale-mit-pgfplots http://texwelt.de/wissen/fragen/3960/fraktale-mit-pgfplots]. The calculations are done by inline [[Lua]] code and the resulting bitmap shown with a PGF plot.
=={{header|TI-83 BASIC}}== Based on the [[Mandelbrot_set#BASIC|BASIC Version]]. Due to the TI-83's lack of power, it takes around 2 hours to complete at 16 iterations.
PROGRAM:MANDELBR
:Input "ITER. ",D
:For(A,Xmin,Xmax,ΔX)
:For(B,Ymin,Ymax,ΔY)
:0→X
:0→Y
:0→I
:D→M
:While X^2+Y^2≤4 and I<M
:X^2-Y^2+A→R
:2XY+B→Y
:R→X
:I+1→I
:End
:If I≠M
:Then
:I→C
:Else
:0→C
:End
:If C<1
:Pt-On(A,B)
:End
:End
:End
TXR
{{trans|Scheme}}
Creates same mandelbrot.pgm file.
(defvar x-centre -0.5)
(defvar y-centre 0.0)
(defvar width 4.0)
(defvar i-max 800)
(defvar j-max 600)
(defvar n 100)
(defvar r-max 2.0)
(defvar file "mandelbrot.pgm")
(defvar colour-max 255)
(defvar pixel-size (/ width i-max))
(defvar x-offset (- x-centre (* 0.5 pixel-size (+ i-max 1))))
(defvar y-offset (+ y-centre (* 0.5 pixel-size (+ j-max 1))))
;; with-output-to-file macro
(defmacro with-output-to-file (name . body)
^(let ((*stdout* (open-file ,name "w")))
(unwind-protect (progn ,*body) (close-stream *stdout*))))
;; complex number library
(defmacro cplx (x y) ^(cons ,x ,y))
(defmacro re (c) ^(car ,c))
(defmacro im (c) ^(cdr ,c))
(defsymacro c0 '(0 . 0))
(macro-time
(defun with-cplx-expand (specs body)
(tree-case specs
(((re im expr) . rest)
^(tree-bind (,re . ,im) ,expr ,(with-cplx-expand rest body)))
(() (tree-case body
((a b . rest) ^(progn ,a ,b ,*rest))
((a) a)
(x (error "with-cplx: invalid body ~s" body))))
(x (error "with-cplx: bad args ~s" x)))))
(defmacro with-cplx (specs . body)
(with-cplx-expand specs body))
(defun c+ (x y)
(with-cplx ((a b x) (c d y))
(cplx (+ a c) (+ b d))))
(defun c* (x y)
(with-cplx ((a b x) (c d y))
(cplx (- (* a c) (* b d)) (+ (* b c) (* a d)))))
(defun modulus (z)
(with-cplx ((a b z))
(sqrt (+ (* a a) (* b b)))))
;; Mandelbrot routines
(defun inside-p (z0 : (z c0) (n n))
(and (< (modulus z) r-max)
(or (zerop n)
(inside-p z0 (c+ (c* z z) z0) (- n 1)))))
(defmacro int-bool (b)
^(if ,b colour-max 0))
(defun pixel (i j)
(int-bool
(inside-p
(cplx (+ x-offset (* pixel-size i))
(- y-offset (* pixel-size j))))))
;; Mandelbrot loop and output
(defun plot ()
(with-output-to-file file
(format t "P2\n~s\n~s\n~s\n" i-max j-max colour-max)
(each ((j (range 1 j-max)))
(each ((i (range 1 i-max)))
(format *stdout* "~s " (pixel i j)))
(put-line "" *stdout*))))
(plot)
uBasic/4tH
uBasic does not support floating point calculations, so fixed point arithmetic is used, with Value 10000 representing 1.0. The Mandelbrot image is drawn using ASCII characters 1-9 to show number of iterations. Iteration count 10 or more is represented with '@'. To compensate the aspect ratio of
the font, step sizes in x and y directions are different.
For L = C To D Step -G ' Y0 For K = A To B-1 Step F ' X0 V = 0 ' Y U = 0 ' X I = 32 ' Char To Be Displayed For O = 0 To E-1 ' Iteration X = (U/10 * U) / 1000 ' XX Y = (V/10 * V) / 1000 ' YY If (X + Y > 40000) I = 48 + O ' Print Digit 0...9 If (O > 9) ' If Iteration Count > 9, I = 64 ' Print '@' Endif Break Endif Z = X - Y + K ' Temp = XX - YY + X0 V = (U/10 * V) / 500 + L ' Y = 2XY + Y0 U = Z ' X = Temp Next Gosub I ' Ins_char(I) Next Print Next
End ' Translate number to ASCII 32 Print " "; : Return 48 Print "0"; : Return 49 Print "1"; : Return 50 Print "2"; : Return 51 Print "3"; : Return 52 Print "4"; : Return 53 Print "5"; : Return 54 Print "6"; : Return 55 Print "7"; : Return 56 Print "8"; : Return 57 Print "9"; : Return 64 Print "@"; : Return
Output:
```txt
1111111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222211111
1111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222211
1111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222
1111111111111111222222222222222222233333333333333333333333222222222222222222222222222222222222222222222
1111111111111112222222222222333333333333333333333333333333333333322222222222222222222222222222222222222
1111111111111222222222233333333333333333333333344444457655544443333332222222222222222222222222222222222
1111111111112222222233333333333333333333333444444445567@@6665444444333333222222222222222222222222222222
11111111111222222333333333333333333333334444444445555678@@@@7654444443333332222222222222222222222222222
1111111112222223333333333333333333333444444444455556789@@@@98655544444433333332222222222222222222222222
1111111122222333333333333333333333344444444445556668@@@ @@@@76555544444333333322222222222222222222222
1111111122233333333333333333333344444444445566667778@@ @987666555544433333333222222222222222222222
111111122333333333333333333333444444455556@@@@@99@@@@@@ @@@@@@87777@95443333333322222222222222222222
1111112233333333333333333334444455555556678@@ @@ @@@@@@@8544333333333222222222222222222
1111122333333333333333334445555555555666789@@@ @86554433333333322222222222222222
1111123333333333333444466666555556666778@@@@ @@87655443333333332222222222222222
111123333333344444455568@887789@8777788@@@ @@@@65443333333332222222222222222
1111333344444444455556679@@@@@@@@@@@99@@@ @@765444333333333222222222222222
1111334444444455555567789@@ @@@@ @855444333333333222222222222222
11114444444455555668@99@@@ @ @@655444433333333322222222222222
11134555556666677789@@@ @ @86655444433333333322222222222222
111 @@876555444433333333322222222222222
11134555556666677789@@@ @ @86655444433333333322222222222222
11114444444455555668@99@@@ @ @@655444433333333322222222222222
1111334444444455555567789@@ @@@@ @855444333333333222222222222222
1111333344444444455556679@@@@@@@@@@@99@@@ @@765444333333333222222222222222
111123333333344444455568@887789@8777788@@@ @@@@65443333333332222222222222222
1111123333333333333444466666555556666778@@@@ @@87655443333333332222222222222222
1111122333333333333333334445555555555666789@@@ @86554433333333322222222222222222
1111112233333333333333333334444455555556678@@ @@ @@@@@@@8544333333333222222222222222222
111111122333333333333333333333444444455556@@@@@99@@@@@@ @@@@@@87777@95443333333322222222222222222222
1111111122233333333333333333333344444444445566667778@@ @987666555544433333333222222222222222222222
1111111122222333333333333333333333344444444445556668@@@ @@@@76555544444333333322222222222222222222222
1111111112222223333333333333333333333444444444455556789@@@@98655544444433333332222222222222222222222222
11111111111222222333333333333333333333334444444445555678@@@@7654444443333332222222222222222222222222222
1111111111112222222233333333333333333333333444444445567@@6665444444333333222222222222222222222222222222
1111111111111222222222233333333333333333333333344444457655544443333332222222222222222222222222222222222
1111111111111112222222222222333333333333333333333333333333333333322222222222222222222222222222222222222
1111111111111111222222222222222222233333333333333333333333222222222222222222222222222222222222222222222
1111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222
1111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222211
1111111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222211111
0 OK, 0:1726
Vedit macro language
Vedit macro language does not support floating point calculations, so fixed point arithmetic is used, with Value 10000 representing 1.0. The Mandelbrot image is drawn using ASCII characters 1-9 to show number of iterations. Iteration count 10 or more is represented with '@'. To compensate the aspect ratio of the font, step sizes in x and y directions are different.
#1 =-21000 // left edge = -2.1
#2 = 15000 // right edge = 1.5
#3 = 15000 // top edge = 1.5
#4 =-15000 // bottom edge = -1.5
#5 = 200 // max iteration depth
#6 = 350 // x step size
#7 = 750 // y step size
Buf_Switch(Buf_Free)
for (#12 = #3; #12 > #4; #12 -= #7) { // y0
for (#11 = #1; #11 < #2; #11 += #6) { // x0
#22 = 0 // y
#21 = 0 // x
#9 = ' ' // char to be displayed
for (#15 = 0; #15 < #5; #15++) { // iteration
#31 = (#21/10 * #21) / 1000 // x*x
#32 = (#22/10 * #22) / 1000 // y*y
if (#31 + #32 > 40000) {
#9 = '0' + #15 // print digit 0...9
if (#15 > 9) { // if iteration count > 9,
#9 = '@' // print '@'
}
break
}
#33 = #31 - #32 + #11 // temp = x*x - y*y + x0
#22 = (#21/10 * #22) / 500 + #12 // y = 2*x*y + y0
#21 = #33 // x = temp
}
Ins_Char(#9)
}
Ins_Newline
}
BOF
{{out}}
1111111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222211111
1111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222211
1111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222
1111111111111111222222222222222222233333333333333333333333222222222222222222222222222222222222222222222
1111111111111112222222222222333333333333333333333333333333333333322222222222222222222222222222222222222
1111111111111222222222233333333333333333333333344444457655544443333332222222222222222222222222222222222
1111111111112222222233333333333333333333333444444445567@@6665444444333333222222222222222222222222222222
11111111111222222333333333333333333333334444444445555678@@@@7654444443333332222222222222222222222222222
1111111112222223333333333333333333333444444444455556789@@@@98655544444433333332222222222222222222222222
1111111122222333333333333333333333344444444445556668@@@ @@@@76555544444333333322222222222222222222222
1111111122233333333333333333333344444444445566667778@@ @987666555544433333333222222222222222222222
111111122333333333333333333333444444455556@@@@@99@@@@@@ @@@@@@87777@95443333333322222222222222222222
1111112233333333333333333334444455555556678@@ @@ @@@@@@@8544333333333222222222222222222
1111122333333333333333334445555555555666789@@@ @86554433333333322222222222222222
1111123333333333333444466666555556666778@@@@ @@87655443333333332222222222222222
111123333333344444455568@887789@8777788@@@ @@@@65443333333332222222222222222
1111333344444444455556679@@@@@@@@@@@99@@@ @@765444333333333222222222222222
1111334444444455555567789@@ @@@@ @855444333333333222222222222222
11114444444455555668@99@@@ @ @@655444433333333322222222222222
11134555556666677789@@@ @ @86655444433333333322222222222222
111 @@876555444433333333322222222222222
11134555556666677789@@@ @ @86655444433333333322222222222222
11114444444455555668@99@@@ @ @@655444433333333322222222222222
1111334444444455555567789@@ @@@@ @855444333333333222222222222222
1111333344444444455556679@@@@@@@@@@@99@@@ @@765444333333333222222222222222
111123333333344444455568@887789@8777788@@@ @@@@65443333333332222222222222222
1111123333333333333444466666555556666778@@@@ @@87655443333333332222222222222222
1111122333333333333333334445555555555666789@@@ @86554433333333322222222222222222
1111112233333333333333333334444455555556678@@ @@ @@@@@@@8544333333333222222222222222222
111111122333333333333333333333444444455556@@@@@99@@@@@@ @@@@@@87777@95443333333322222222222222222222
1111111122233333333333333333333344444444445566667778@@ @987666555544433333333222222222222222222222
1111111122222333333333333333333333344444444445556668@@@ @@@@76555544444333333322222222222222222222222
1111111112222223333333333333333333333444444444455556789@@@@98655544444433333332222222222222222222222222
11111111111222222333333333333333333333334444444445555678@@@@7654444443333332222222222222222222222222222
1111111111112222222233333333333333333333333444444445567@@6665444444333333222222222222222222222222222222
1111111111111222222222233333333333333333333333344444457655544443333332222222222222222222222222222222222
1111111111111112222222222222333333333333333333333333333333333333322222222222222222222222222222222222222
1111111111111111222222222222222222233333333333333333333333222222222222222222222222222222222222222222222
1111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222
1111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222211
XPL0
include c:\cxpl\codes; \intrinsic 'code' declarations
int X, Y, \screen coordinates of current point
Cnt; \iteration counter
real Cx, Cy, \coordinates scaled to +/-2 range
Zx, Zy, \complex accumulator
Temp; \temporary scratch
[SetVid($112); \set 640x480x24 graphics mode
for Y:= 0 to 480-1 do \for all points on the screen...
for X:= 0 to 640-1 do
[Cx:= (float(X)/640.0 - 0.5) * 4.0; \range: -2.0 to +2.0
Cy:= (float(Y-240)/240.0) * 1.5; \range: -1.5 to +1.5
Cnt:= 0; Zx:= 0.0; Zy:= 0.0; \initialize
loop [if Zx*Zx + Zy*Zy > 2.0 then \Z heads toward infinity
[Point(X, Y, Cnt<<21+Cnt<<10+Cnt<<3); \set color of pixel to
quit; \ rate it approached infinity
]; \move on to next point
Temp:= Zx*Zy;
Zx:= Zx*Zx - Zy*Zy + Cx; \calculate next iteration of Z
Zy:= 2.0*Temp + Cy;
Cnt:= Cnt+1; \count number of iterations
if Cnt >= 1000 then quit; \assume point is in Mandelbrot
]; \ set and leave it colored black
];
X:= ChIn(1); \wait for keystroke
SetVid($03); \restore normal text display
]
{{out}} [[File:MandelXPL0.png]]
XSLT
The fact that you can create an image of the Mandelbrot Set with XSLT is sometimes under-appreciated. However, it has been discussed extensively [http://thedailywtf.com/Articles/Stupid-Coding-Tricks-XSLT-Mandelbrot.aspx on the internet] so is best reproduced here, and the code can be executed directly in your browser at that site.
{{omit from|M4}}
<?xml version="1.0" encoding="UTF-8"?> <xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform"> <!-- XSLT Mandelbrot - written by Joel Yliluoma 2007, http://iki.fi/bisqwit/ --> <xsl:output method="html" indent="no" doctype-public="-//W3C//DTD HTML 4.01//EN" doctype-system="http://www.w3.org/TR/REC-html40/strict.dtd" /> <xsl:template match="/fractal"> <html> <head> <title>XSLT fractal</title> <style type="text/css"> body { color:#55F; background:#000 } pre { font-family:monospace; font-size:7px } pre span { background:<xsl:value-of select="background" /> } </style> </head> <body> <div style="position:absolute;top:20px;left:20em"> Copyright © 1992,2007 Joel Yliluoma (<a href="http://iki.fi/bisqwit/">http://iki.fi/bisqwit/</a>) </div> <h1 style="margin:0px">XSLT fractal</h1> ```txt <xsl:call-template name="bisqwit-mandelbrot" />