⚠️ 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.
{{task}} [[File:Fib_word_fractal.gif|613px||right]]
The [[Fibonacci word]] may be represented as a fractal as described [http://hal.archives-ouvertes.fr/docs/00/36/79/72/PDF/The_Fibonacci_word_fractal.pdf here]:
:For F_wordm start with F_wordCharn=1 :Draw a segment forward :If current F_wordChar is 0 ::Turn left if n is even ::Turn right if n is odd :next n and iterate until end of F_word
;Task: Create and display a fractal similar to [http://hal.archives-ouvertes.fr/docs/00/36/79/72/PDF/The_Fibonacci_word_fractal.pdf Fig 1].
AutoHotkey
Prints F_Word30 currently. Segment length and F_Wordn can be adjusted. {{libheader|GDIP}}Also see the [http://www.autohotkey.com/board/topic/29449-gdi-standard-library-145-by-tic/ Gdip examples].
#NoEnv
SetBatchLines, -1
p := 0.3 ; Segment length (pixels)
F_Word := 30
SysGet, Mon, MonitorWorkArea
W := FibWord(F_Word)
d := 1
x1 := 0
y1 := MonBottom
Width := A_ScreenWidth
Height := A_ScreenHeight
If (!pToken := Gdip_Startup()) {
MsgBox, 48, Gdiplus Error!, Gdiplus failed to start. Please ensure you have Gdiplus on your system.
ExitApp
}
OnExit, Shutdown
Gui, 1: -Caption +E0x80000 +LastFound +AlwaysOnTop +ToolWindow +OwnDialogs
Gui, 1: Show, NA
hwnd1 := WinExist()
hbm := CreateDIBSection(Width, Height)
hdc := CreateCompatibleDC()
obm := SelectObject(hdc, hbm)
G := Gdip_GraphicsFromHDC(hdc)
Gdip_SetSmoothingMode(G, 4)
pPen := Gdip_CreatePen(0xffff0000, 1)
Loop, Parse, W
{
if (d = 0)
x2 := x1 + p, y2 := y1
else if (d = 1 || d = -3)
x2 := x1, y2 := y1 - p
else if (d = 2 || d = -2)
x2 := x1 - p, y2 := y1
else if (d = 3 || d = -1)
x2 := x1, y2 := y1 + p
Gdip_DrawLine(G, pPen, x1, y1, x2, y2)
if (!Mod(A_Index, 1500))
UpdateLayeredWindow(hwnd1, hdc, 0, 0, Width, Height)
if (A_LoopField = 0) {
if (!Mod(A_Index, 2))
d += 1
else
d -= 1
}
x1 := x2, y1 := y2, d := Mod(d, 4)
}
Gdip_DeletePen(pPen)
UpdateLayeredWindow(hwnd1, hdc, 0, 0, Width, Height)
SelectObject(hdc, obm)
DeleteObject(hbm)
DeleteDC(hdc)
Gdip_DeleteGraphics(G)
return
FibWord(n, FW1=1, FW2=0) {
Loop, % n - 2
FW3 := FW2 FW1, FW1 := FW2, FW2 := FW3
return FW3
}
Esc::
Shutdown:
Gdip_DeletePen(pPen)
SelectObject(hdc, obm)
DeleteObject(hbm)
DeleteDC(hdc)
Gdip_DeleteGraphics(G)
Gdip_Shutdown(pToken)
ExitApp
C
Writes an EPS file that has the 26th fractal. This is probably cheating.
#include <stdio.h>
int main(void)
{
puts( "%!PS-Adobe-3.0 EPSF\n"
"%%BoundingBox: -10 -10 400 565\n"
"/a{0 0 moveto 0 .4 translate 0 0 lineto stroke -1 1 scale}def\n"
"/b{a 90 rotate}def");
char i;
for (i = 'c'; i <= 'z'; i++)
printf("/%c{%c %c}def\n", i, i-1, i-2);
puts("0 setlinewidth z showpage\n%%EOF");
return 0;
}
C++
#include <windows.h>
#include <string>
using namespace std;
class myBitmap
{
public:
myBitmap() : pen( NULL ) {}
~myBitmap()
{
DeleteObject( pen );
DeleteDC( hdc );
DeleteObject( bmp );
}
bool create( int w, int h )
{
BITMAPINFO bi;
ZeroMemory( &bi, sizeof( bi ) );
bi.bmiHeader.biSize = sizeof( bi.bmiHeader );
bi.bmiHeader.biBitCount = sizeof( DWORD ) * 8;
bi.bmiHeader.biCompression = BI_RGB;
bi.bmiHeader.biPlanes = 1;
bi.bmiHeader.biWidth = w;
bi.bmiHeader.biHeight = -h;
HDC dc = GetDC( GetConsoleWindow() );
bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 );
if( !bmp ) return false;
hdc = CreateCompatibleDC( dc );
SelectObject( hdc, bmp );
ReleaseDC( GetConsoleWindow(), dc );
width = w; height = h;
clear();
return true;
}
void clear()
{
ZeroMemory( pBits, width * height * sizeof( DWORD ) );
}
void setPenColor( DWORD clr )
{
if( pen ) DeleteObject( pen );
pen = CreatePen( PS_SOLID, 1, clr );
SelectObject( hdc, pen );
}
void saveBitmap( string path )
{
BITMAPFILEHEADER fileheader;
BITMAPINFO infoheader;
BITMAP bitmap;
DWORD* dwpBits;
DWORD wb;
HANDLE file;
GetObject( bmp, sizeof( bitmap ), &bitmap );
dwpBits = new DWORD[bitmap.bmWidth * bitmap.bmHeight];
ZeroMemory( dwpBits, bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ) );
ZeroMemory( &infoheader, sizeof( BITMAPINFO ) );
ZeroMemory( &fileheader, sizeof( BITMAPFILEHEADER ) );
infoheader.bmiHeader.biBitCount = sizeof( DWORD ) * 8;
infoheader.bmiHeader.biCompression = BI_RGB;
infoheader.bmiHeader.biPlanes = 1;
infoheader.bmiHeader.biSize = sizeof( infoheader.bmiHeader );
infoheader.bmiHeader.biHeight = bitmap.bmHeight;
infoheader.bmiHeader.biWidth = bitmap.bmWidth;
infoheader.bmiHeader.biSizeImage = bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD );
fileheader.bfType = 0x4D42;
fileheader.bfOffBits = sizeof( infoheader.bmiHeader ) + sizeof( BITMAPFILEHEADER );
fileheader.bfSize = fileheader.bfOffBits + infoheader.bmiHeader.biSizeImage;
GetDIBits( hdc, bmp, 0, height, ( LPVOID )dwpBits, &infoheader, DIB_RGB_COLORS );
file = CreateFile( path.c_str(), GENERIC_WRITE, 0, NULL, CREATE_ALWAYS, FILE_ATTRIBUTE_NORMAL, NULL );
WriteFile( file, &fileheader, sizeof( BITMAPFILEHEADER ), &wb, NULL );
WriteFile( file, &infoheader.bmiHeader, sizeof( infoheader.bmiHeader ), &wb, NULL );
WriteFile( file, dwpBits, bitmap.bmWidth * bitmap.bmHeight * 4, &wb, NULL );
CloseHandle( file );
delete [] dwpBits;
}
HDC getDC() { return hdc; }
int getWidth() { return width; }
int getHeight() { return height; }
private:
HBITMAP bmp;
HDC hdc;
HPEN pen;
void *pBits;
int width, height;
};
class fiboFractal
{
public:
fiboFractal( int l )
{
bmp.create( 600, 440 );
bmp.setPenColor( 0x00ff00 );
createWord( l ); createFractal();
bmp.saveBitmap( "path_to_save_bitmap" );
}
private:
void createWord( int l )
{
string a = "1", b = "0", c;
l -= 2;
while( l-- )
{ c = b + a; a = b; b = c; }
fWord = c;
}
void createFractal()
{
int n = 1, px = 10, dir,
py = 420, len = 1,
x = 0, y = -len, goingTo = 0;
HDC dc = bmp.getDC();
MoveToEx( dc, px, py, NULL );
for( string::iterator si = fWord.begin(); si != fWord.end(); si++ )
{
px += x; py += y;
LineTo( dc, px, py );
if( !( *si - 48 ) )
{ // odd
if( n & 1 ) dir = 1; // right
else dir = 0; // left
switch( goingTo )
{
case 0: // up
y = 0;
if( dir ){ x = len; goingTo = 1; }
else { x = -len; goingTo = 3; }
break;
case 1: // right
x = 0;
if( dir ) { y = len; goingTo = 2; }
else { y = -len; goingTo = 0; }
break;
case 2: // down
y = 0;
if( dir ) { x = -len; goingTo = 3; }
else { x = len; goingTo = 1; }
break;
case 3: // left
x = 0;
if( dir ) { y = -len; goingTo = 0; }
else { y = len; goingTo = 2; }
}
}
n++;
}
}
string fWord;
myBitmap bmp;
};
int main( int argc, char* argv[] )
{
fiboFractal ff( 23 );
return system( "pause" );
}
D
This uses the turtle module from the Dragon Curve Task, and the module from the Grayscale Image task. {{trans|Python}}
import std.range, grayscale_image, turtle;
void drawFibonacci(Color)(Image!Color img, ref Turtle t,
in string word, in real step) {
foreach (immutable i, immutable c; word) {
t.forward(img, step);
if (c == '0') {
if ((i + 1) % 2 == 0)
t.left(90);
else
t.right(90);
}
}
}
void main() {
auto img = new Image!Gray(1050, 1050);
auto t = Turtle(30, 1010, -90);
const w = recurrence!q{a[n-1] ~ a[n-2]}("1", "0").drop(24).front;
img.drawFibonacci(t, w, 1);
img.savePGM("fibonacci_word_fractal.pgm");
}
It prints the level 25 word as the Python entry.
Elixir
{{trans|Ruby}}
defmodule Fibonacci do
def fibonacci_word, do: Stream.unfold({"1","0"}, fn{a,b} -> {a, {b, b<>a}} end)
def word_fractal(n) do
word = fibonacci_word |> Enum.at(n)
walk(to_char_list(word), 1, 0, 0, 0, -1, %{{0,0}=>"S"})
|> print
end
defp walk([], _, _, _, _, _, map), do: map
defp walk([h|t], n, x, y, dx, dy, map) do
map2 = Map.put(map, {x+dx, y+dy}, (if dx==0, do: "|", else: "-"))
|> Map.put({x2=x+2*dx, y2=y+2*dy}, "+")
if h == ?0 do
if rem(n,2)==0, do: walk(t, n+1, x2, y2, dy, -dx, map2),
else: walk(t, n+1, x2, y2, -dy, dx, map2)
else
walk(t, n+1, x2, y2, dx, dy, map2)
end
end
defp print(map) do
xkeys = Map.keys(map) |> Enum.map(fn {x,_} -> x end)
{xmin, xmax} = Enum.min_max(xkeys)
ykeys = Map.keys(map) |> Enum.map(fn {_,y} -> y end)
{ymin, ymax} = Enum.min_max(ykeys)
Enum.each(ymin..ymax, fn y ->
IO.puts Enum.map(xmin..xmax, fn x -> Map.get(map, {x,y}, " ") end)
end)
end
end
Fibonacci.word_fractal(16)
Output is same as Ruby.
=={{header|F_Sharp|F#}}==
We output an SVG or rather an HTML with an embedded SVG
Points to note:
- Rather than using the "usual" Fibonacci catamorphismen ```fsharp Seq.unfold(fun (f1, f2) -> Some(f1, (f2, f2+f1))) ("1", "0") ``` we use the morphism σ: 0 → 01, 1 → 0, starting with a single 1, described in the referenced PDF in the task description.
- The outer dimension of the SVG is computed. For a simplification we compute bounding boxes for fractals with number 3*k+2 only. These are ∩ formed or ⊃ formed. For 3*k and 3*k+1 fractals the bounding box for the next 3*k+2 fractal is taken. (c/f PDF; Theorem 3, Theorem 4)
let sigma s = seq {
for c in s do if c = '1' then yield '0' else yield '0'; yield '1'
}
let rec fibwordIterator s = seq { yield s; yield! fibwordIterator (sigma s) }
let goto (x, y) (dx, dy) c n =
let (dx', dy') =
if c = '0' then
match (dx, dy), n with
| (1,0),0 -> (0,1) | (1,0),1 -> (0,-1)
| (0,1),0 -> (-1,0) | (0,1),1 -> (1,0)
| (-1,0),0 -> (0,-1)| (-1,0),1 -> (0,1)
| (0,-1),0 -> (1,0) | (0,-1),1 -> (-1,0)
| _ -> failwith "not possible (c=0)"
else
(dx, dy)
(x+dx, y+dy), (dx', dy')
// How much longer a line is, compared to its thickness:
let factor = 2
let rec draw (x, y) (dx, dy) n = function
| [] -> ()
| z::zs ->
printf "%d,%d " (factor*(x+dx)) (factor*(y+dy))
let (xyd, d') = goto (x, y) (dx, dy) z n
draw xyd d' (n^^^1) zs
// Seq of (width,height). n-th (n>=0) pair is for fibword fractal f(3*n+2)
let wh = Seq.unfold (fun ((w1,h1,n),(w2,h2)) ->
Some((if n=0 then (w1,h1) else (h1,w1)), ((w2,h2,n^^^1),(2*w2+w1,w2+h2)))) ((1,0,1),(3,1))
[<EntryPoint>]
let main argv =
let n = (if argv.Length > 0 then int (System.UInt16.Parse(argv.[0])) else 23)
let (width,height) = Seq.head <| Seq.skip (n/3) wh
let fibWord = Seq.toList (Seq.item (n-1) <| fibwordIterator ['1'])
let (viewboxWidth, viewboxHeight) = ((factor*(width+1)), (factor*(height+1)))
printf """<!DOCTYPE html>
<html><body><svg height="100%%" width="100%%" viewbox="0 0 %d %d">
<polyline points="0,0 """ viewboxWidth viewboxHeight
draw (0,0) (0,1) 1 <| Seq.toList fibWord
printf """" style="fill:white;stroke:red;stroke-width:1" transform="matrix(1,0,0,-1,1,%d)"/>
Sorry, your browser does not support inline SVG.
</svg></body></html>""" (viewboxHeight-1)
0
{{out}}
Since file upload to the Wiki is not possible, the raw output for F11 is given:
```Factor
USING: accessors arrays combinators fry images images.loader kernel literals make match math math.vectors pair-rocket sequences ; FROM: fry => '[ _ ; IN: rosetta-code.fibonacci-word-fractal ! ### Turtle code =========================================== TUPLE: turtle heading loc ; C: <turtle> turtle : forward ( turtle -- turtle' ) dup heading>> [ v+ ] curry change-loc ; MATCH-VARS: ?a ; CONSTANT: left { { 0 ?a } => [ ?a 0 ] { ?a 0 } => [ 0 ?a neg ] } CONSTANT: right { { 0 ?a } => [ ?a neg 0 ] { ?a 0 } => [ 0 ?a ] } : turn ( turtle left/right -- turtle' ) [ dup heading>> ] dip match-cond 2array >>heading ; inline ! ### Fib word ============================================== : fib-word ( n -- str ) { 1 => [ "1" ] 2 => [ "0" ] [ [ 1 - fib-word ] [ 2 - fib-word ] bi append ] } case ; ! ### Fractal =============================================== : fib-word-fractal ( n -- seq ) [ [ { 0 -1 } { 10 417 } dup , <turtle> ] dip fib-word [ 1 + -rot forward dup loc>> , -rot CHAR: 0 = [ even? [ left turn ] [ right turn ] if ] [ drop ] if drop ] with each-index ] { } make ; ! ### Image ================================================= CONSTANT: w 598 CONSTANT: h 428 : init-img-data ( -- seq ) w h * 4 * [ 255 ] B{ } replicate-as ; : <fib-word-fractal-img> ( -- img ) <image> ${ w h } >>dim BGRA >>component-order ubyte-components >>component-type init-img-data >>bitmap ; : fract>img ( seq -- img' ) [ <fib-word-fractal-img> dup ] dip [ '[ B{ 33 33 33 255 } _ first2 ] dip set-pixel-at ] with each ; : main ( -- ) 23 fib-word-fractal fract>img "fib-word-fractal.png" save-graphic-image ; MAIN: main{{out}} Similar to fig. 1 from the paper and the image at the top of this page.
FreeBASIC
On a Windows 32bit system F_word35 is the biggest that can be drawn.
' version 23-06-2015 ' compile with: fbc -s console "filename".bas Dim As String fw1, fw2, fw3 Dim As Integer a, b, d , i, n , x, y, w, h Dim As Any Ptr img_ptr, scr_ptr ' data for screen/buffer size Data 1, 2, 3, 2, 2, 2, 2, 2, 7, 10, 8, 14 Dim As Integer s(38,2) For i = 3 To 9 Read s(i,1) : Read s(i,2) Next For i = 9 To 38 Step 6 s(i, 1) = s(i -1, 1) +2 : s(i, 2) = s(i -1, 1) + s(i -1, 2) s(i +1, 1) = s(i, 2) +2 : s(i +1, 2) = s(i, 2) s(i +2, 1) = s(i, 1) + s(i, 2) : s(i +2, 2) = s(i, 2) s(i +3, 1) = s(i +1, 1 ) + s(i +2, 1) : s(i +3, 2) = s(i ,2) s(i +4, 1) = s(i +3, 1) : s(i +4, 2) = s(i +3, 1) + 2 s(i +5, 1) = s(i +3, 1) : s(i +5, 2) = s(i +3, 2) + s(i +4, 2) +2 Next ' we need to set screen in order to create image buffer in memory Screen 21 scr_ptr = ScreenPtr() If (scr_ptr = 0) Then Print "Error: graphics screen not initialized." Sleep End -1 End If Do Cls Do Print Print "For wich n do you want the Fibonacci Word fractal (3 to 35)." While Inkey <> "" : fw1 = Inkey : Wend ' empty keyboard buffer Input "Enter or a value smaller then 3 to stop: "; n If n < 3 Then Print : Print "Stopping." Sleep 3000,1 End EndIf If n > 35 then Print : Print "Fractal is to big, unable to create it." Sleep 3000,1 Continue Do End If Loop Until n < 36 fw1 = "1" : fw2 = "0" ' construct the string For i = 3 To n fw3 = fw2 + fw1 Swap fw1, fw2 ' swap pointers of fw1 and fw2 Swap fw2, fw3 ' swap pointers of fw2 and fw3 Next fw1 = "" : fw3 = "" ' free up memory w = s(n, 1) +1 : h = s(n, 2) +1 ' allocate memory for a buffer to hold the image ' use 8 bits to hold the color img_ptr = ImageCreate(w,h,0,8) If img_ptr = 0 Then ' check if we have created a image buffer Print "Failed to create image." Sleep End -1 End If x = 0: y = h -1 : d = 1 ' set starting point and direction flag PSet img_ptr, (x, y) ' set start point For a = 1 To Len(fw2) Select Case As Const d Case 0 x = x + 2 Case 1 y = y - 2 Case 2 x = x - 2 Case 3 y = y + 2 End Select Line img_ptr, -(x, y) b = fw2[a-1] - Asc("0") If b = 0 Then If (a And 1) Then d = d + 3 ' a = odd Else d = d + 1 ' a = even End If d = d And 3 End If Next If n < 24 Then ' size is smaller then screen dispay fractal Cls Put (5, 5),img_ptr, PSet Else Print Print "Fractal is to big for display." End If ' saves fractal as bmp file (8 bit palette) If n > 23 Then h = 80 Draw String (0, h +16), "saving fractal as fibword" + Str(n) + ".bmp." BSave "F_Word" + Str(n) + ".bmp", img_ptr Draw String (0, h +32), "Hit any key to continue." Sleep ImageDestroy(img_ptr) ' free memory holding the image LoopGo
{{libheader|Go Graphics}} {{trans|Kotlin}}
package main import ( "github.com/fogleman/gg" "strings" ) func wordFractal(i int) string { if i < 2 { if i == 1 { return "1" } return "" } var f1 strings.Builder f1.WriteString("1") var f2 strings.Builder f2.WriteString("0") for j := i - 2; j >= 1; j-- { tmp := f2.String() f2.WriteString(f1.String()) f1.Reset() f1.WriteString(tmp) } return f2.String() } func draw(dc *gg.Context, x, y, dx, dy float64, wf string) { for i, c := range wf { dc.DrawLine(x, y, x+dx, y+dy) x += dx y += dy if c == '0' { tx := dx dx = dy if i%2 == 0 { dx = -dy } dy = -tx if i%2 == 0 { dy = tx } } } } func main() { dc := gg.NewContext(450, 620) dc.SetRGB(0, 0, 0) dc.Clear() wf := wordFractal(23) draw(dc, 20, 20, 1, 0, wf) dc.SetRGB(0, 1, 0) dc.SetLineWidth(1) dc.Stroke() dc.SavePNG("fib_wordfractal.png") }{{out}}
Image similar to Java entry except green on black background.=={{header|Icon}} and {{header|Unicon}}== This probably only works in Unicon. It also defaults to showing the factal for F_word25 as larger Fibonacci words quickly exceed the size of window I can display, even with a line segment length of a single pixel.
global width, height procedure main(A) n := integer(A[1]) | 25 # F_word to use sl := integer(A[2]) | 1 # Segment length width := integer(A[3]) | 1050 # Width of plot area height := integer(A[4]) | 1050 # Height of plot area w := fword(n) drawFractal(n,w,sl) end procedure fword(n) static fcache initial fcache := table() /fcache[n] := case n of { 1: "1" 2: "0" default: fword(n-1)||fword(n-2) } return fcache[n] end record loc(x,y) procedure drawFractal(n,w,sl) static lTurn, rTurn initial { every (lTurn|rTurn) := table() lTurn["north"] := "west"; lTurn["west"] := "south" lTurn["south"] := "east"; lTurn["east"] := "north" rTurn["north"] := "east"; rTurn["east"] := "south" rTurn["south"] := "west"; rTurn["west"] := "north" } wparms := ["FibFractal "||n,"g","bg=white","canvas=normal", "fg=black","size="||width||","||height,"dx=10","dy=10"] &window := open!wparms | stop("Unable to open window") p := loc(10,10) d := "north" every i := 1 to *w do { p := draw(p,d,sl) if w[i] == "0" then d := if i%2 = 0 then lTurn[d] else rTurn[d] } until Event() == &lpress WriteImage("FibFract"||n||".png") close(&window) end procedure draw(p,d,sl) if d == "north" then p1 := loc(p.x,p.y+sl) else if d == "south" then p1 := loc(p.x,p.y-sl) else if d == "east" then p1 := loc(p.x+sl,p.y) else p1 := loc(p.x-sl,p.y) DrawLine(p.x,p.y, p1.x,p1.y) return p1 endJ
Plotting the fractal as a parametric equation, this looks reasonably nice:
require 'plot' plot }:+/\ 0,*/\(^~ 0j_1 0j1 $~ #)'0'=_1{::F_Words 20Note that we need the definition of F_Words from the [[Fibonacci_word#J|Fibonacci word]] page:
F_Words=: (,<@;@:{~&_1 _2)@]^:(2-~[)&('1';'0')However, image uploads are currently disabled, and rendering images of this sort as wikitext gets bulky.
Instead, I'll just describe the algorithm:
This draws a discrete parametric curve. Right turn is 0j_1, left turn is 0j1 (negative and positive square roots of negative 1), straight ahead is 1. So: build a list of alternating 0j_1 and 0j1 and raise them to the first power for the 0s in the fibonacci word list and raise them to the 0th power for the 1s in that list. Then compute the running product, shift a 0 onto the front of the list of products and compute the running sum. (Of course, this would translate to a rather simple loop, also, once you see the pattern.)
Java
[[File:fib_word_fractal_java.gif|300px|thumb|right]] {{works with|Java|8}}
import java.awt.*; import javax.swing.*; public class FibonacciWordFractal extends JPanel { String wordFractal; FibonacciWordFractal(int n) { setPreferredSize(new Dimension(450, 620)); setBackground(Color.white); wordFractal = wordFractal(n); } public String wordFractal(int n) { if (n < 2) return n == 1 ? "1" : ""; // we should really reserve fib n space here StringBuilder f1 = new StringBuilder("1"); StringBuilder f2 = new StringBuilder("0"); for (n = n - 2; n > 0; n--) { String tmp = f2.toString(); f2.append(f1); f1.setLength(0); f1.append(tmp); } return f2.toString(); } void drawWordFractal(Graphics2D g, int x, int y, int dx, int dy) { for (int n = 0; n < wordFractal.length(); n++) { g.drawLine(x, y, x + dx, y + dy); x += dx; y += dy; if (wordFractal.charAt(n) == '0') { int tx = dx; dx = (n % 2 == 0) ? -dy : dy; dy = (n % 2 == 0) ? tx : -tx; } } } @Override public void paintComponent(Graphics gg) { super.paintComponent(gg); Graphics2D g = (Graphics2D) gg; g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON); drawWordFractal(g, 20, 20, 1, 0); } public static void main(String[] args) { SwingUtilities.invokeLater(() -> { JFrame f = new JFrame(); f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); f.setTitle("Fibonacci Word Fractal"); f.setResizable(false); f.add(new FibonacciWordFractal(23), BorderLayout.CENTER); f.pack(); f.setLocationRelativeTo(null); f.setVisible(true); }); } }JavaScript
{{trans|PARI/GP}}
[[File:FiboWFractal2.png|200px|right|thumb|Output FiboWFractal2.png]] [[File:FiboWFractal1.png|200px|right|thumb|Output FiboWFractal1.png]]
// Plot Fibonacci word/fractal // FiboWFractal.js - 6/27/16 aev function pFibowFractal(n,len,canvasId,color) { // DCLs var canvas = document.getElementById(canvasId); var ctx = canvas.getContext("2d"); var w = canvas.width; var h = canvas.height; var fwv,fwe,fn,tx,x=10,y=10,dx=len,dy=0,nr; // Cleaning canvas, setting plotting color, etc ctx.fillStyle="white"; ctx.fillRect(0,0,w,h); ctx.beginPath(); ctx.moveTo(x,y); fwv=fibword(n); fn=fwv.length; // MAIN LOOP for(var i=0; i<fn; i++) { ctx.lineTo(x+dx,y+dy); fwe=fwv[i]; if(fwe=="0") {tx=dx; nr=i%2; if(nr==0) {dx=-dy;dy=tx} else {dx=dy;dy=-tx}}; x+=dx; y+=dy; }//fend i ctx.strokeStyle = color; ctx.stroke(); }//func end // Create and return Fibonacci word function fibword(n) { var f1="1",f2="0",fw,fwn,n2,i; if (n<5) {n=5}; n2=n+2; for (i=0; i<n2; i++) {fw=f2+f1;f1=f2;f2=fw}; return(fw) }'''Executing:'''
<!-- FiboWFractal2.html --> <html> <head> <title>Fibonacci word/fractal</title> <script src="FiboWFractal.js"></script> </head> <body onload="pFibowFractal(31,2,'canvid','red')"> <h3>Fibonacci word/fractal: n=31, len=2</h3> <canvas id="canvid" width="850" height="1150" style="border: 2px inset;"></canvas> </body> </html> <!-- FiboWFractal1.html --> <html> <head> <title>Fibonacci word/fractal</title> <script src="FiboWFractal.js"></script> </head> <body onload="pFibowFractal(31,1,'canvid','navy')"> <h3>Fibonacci word/fractal: n=31, len=1</h3> <canvas id="canvid" width="1400" height="1030" style="border: 2px inset;"></canvas> </body> </html>{{Output}}
Page with FiboWFractal2.png Page with FiboWFractal1.pngJulia
{{works with|Julia|0.6}}
using Luxor, Colors function fwfractal!(word::AbstractString, t::Turtle) left = 90 right = -90 for (n, c) in enumerate(word) Forward(t) if c == '0' Turn(t, ifelse(iseven(n), left, right)) end end return t end word = last(fiboword(25)) touch("data/fibonaccifractal.png") Drawing(800, 800, "data/fibonaccifractal.png"); background(colorant"white") t = Turtle(100, 300) fwfractal!(word, t) finish() preview()Kotlin
{{trans|Java}}
// version 1.1.2 import java.awt.* import javax.swing.* class FibonacciWordFractal(n: Int) : JPanel() { private val wordFractal: String init { preferredSize = Dimension(450, 620) background = Color.black wordFractal = wordFractal(n) } fun wordFractal(i: Int): String { if (i < 2) return if (i == 1) "1" else "" val f1 = StringBuilder("1") val f2 = StringBuilder("0") for (j in i - 2 downTo 1) { val tmp = f2.toString() f2.append(f1) f1.setLength(0) f1.append(tmp) } return f2.toString() } private fun drawWordFractal(g: Graphics2D, x: Int, y: Int, dx: Int, dy: Int) { var x2 = x var y2 = y var dx2 = dx var dy2 = dy for (i in 0 until wordFractal.length) { g.drawLine(x2, y2, x2 + dx2, y2 + dy2) x2 += dx2 y2 += dy2 if (wordFractal[i] == '0') { val tx = dx2 dx2 = if (i % 2 == 0) -dy2 else dy2 dy2 = if (i % 2 == 0) tx else -tx } } } override fun paintComponent(gg: Graphics) { super.paintComponent(gg) val g = gg as Graphics2D g.color = Color.green g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON) drawWordFractal(g, 20, 20, 1, 0) } } fun main(args: Array<String>) { SwingUtilities.invokeLater { val f = JFrame() with(f) { defaultCloseOperation = JFrame.EXIT_ON_CLOSE title = "Fibonacci Word Fractal" isResizable = false add(FibonacciWordFractal(23), BorderLayout.CENTER) pack() setLocationRelativeTo(null) isVisible = true } } }Logo
fibonacci.word.fractalcan draw any number of line segments. A Fibonacci number shows the self-similar nature of the fractal. The Fibonacci word values which control the turns are generated here by some bit-twiddling iteration.{{works with|UCB Logo}}
; Return the low 1-bits of :n ; For example if n = binary 10110111 = 183 ; then return binary 111 = 7 to low.ones :n output ashift (bitxor :n (:n+1)) -1 end ; :fibbinary should be a fibbinary value ; return the next larger fibbinary value to fibbinary.next :fibbinary localmake "filled bitor :fibbinary (ashift :fibbinary -1) localmake "mask low.ones :filled output (bitor :fibbinary :mask) + 1 end to fibonacci.word.fractal :steps localmake "step.length 5 ; length of each step localmake "fibbinary 0 repeat :steps [ forward :step.length if (bitand 1 :fibbinary) = 0 [ ifelse (bitand repcount 1) = 1 [right 90] [left 90] ] make "fibbinary fibbinary.next :fibbinary ] end setheading 0 ; initial line North fibonacci.word.fractal 377Lua
Needs LÖVE 2D Engine
RIGHT, LEFT, UP, DOWN = 1, 2, 4, 8 function drawFractals( w ) love.graphics.setCanvas( canvas ) love.graphics.clear() love.graphics.setColor( 255, 255, 255 ) local dir, facing, lineLen, px, py, c = RIGHT, UP, 1, 10, love.graphics.getHeight() - 20, 1 local x, y = 0, -lineLen local pts = {} table.insert( pts, px + .5 ); table.insert( pts, py + .5 ) for i = 1, #w do px = px + x; table.insert( pts, px + .5 ) py = py + y; table.insert( pts, py + .5 ) if w:sub( i, i ) == "0" then if c % 2 == 1 then dir = RIGHT else dir = LEFT end if facing == UP then if dir == RIGHT then x = lineLen; facing = RIGHT else x = -lineLen; facing = LEFT end; y = 0 elseif facing == RIGHT then if dir == RIGHT then y = lineLen; facing = DOWN else y = -lineLen; facing = UP end; x = 0 elseif facing == DOWN then if dir == RIGHT then x = -lineLen; facing = LEFT else x = lineLen; facing = RIGHT end; y = 0 elseif facing == LEFT then if dir == RIGHT then y = -lineLen; facing = UP else y = lineLen; facing = DOWN end; x = 0 end end c = c + 1 end love.graphics.line( pts ) love.graphics.setCanvas() end function createWord( wordLen ) local a, b, w = "1", "0" repeat w = b .. a; a = b; b = w; wordLen = wordLen - 1 until wordLen == 0 return w end function love.load() wid, hei = love.graphics.getWidth(), love.graphics.getHeight() canvas = love.graphics.newCanvas( wid, hei ) drawFractals( createWord( 21 ) ) end function love.draw() love.graphics.draw( canvas ) end=={{header|Mathematica}} / {{header|Wolfram Language}}==
(*note, this usage of Module allows us to memoize FibonacciWord without exposing it to the global scope*) Module[{FibonacciWord, step}, FibonacciWord[1] = "1"; FibonacciWord[2] = "0"; FibonacciWord[n_Integer?(# > 2 &)] := (FibonacciWord[n] = FibonacciWord[n - 1] <> FibonacciWord[n - 2]); step["0", {_?EvenQ}] = N@RotationTransform[Pi/2]; step["0", {_?OddQ}] = N@RotationTransform[-Pi/2]; step[___] = Identity; FibonacciFractal[n_] := Module[{steps, dirs}, steps = MapIndexed[step, Characters[FibonacciWord[n]]]; dirs = ComposeList[steps, {0, 1}]; Graphics[Line[FoldList[Plus, {0, 0}, dirs]]]]];PARI/GP
Version #1.
In this version only function plotfibofract() was translated from C++, plus upgraded to plot different kind/size of Fibonacci word/fractals.
[[File:Fibofrac1.png|200px|right|thumb|Output Fibofrac1.png]] [[File:Fibofrac2.png|200px|right|thumb|Output Fibofrac2.png]]
{{trans|C++}}
{{Works with|PARI/GP|2.7.4 and above}}
\\ Fibonacci word/fractals \\ 4/25/16 aev fibword(n)={ my(f1="1",f2="0",fw,fwn,n2); if(n<=4, n=5);n2=n-2; for(i=1,n2, fw=Str(f2,f1); f1=f2;f2=fw;); fwn=#fw; fw=Vecsmall(fw); for(i=1,fwn,fw[i]-=48); return(fw); } nextdir(n,d)={ my(dir=-1); if(d==0, if(n%2==0, dir=0,dir=1)); \\0-left,1-right return(dir); } plotfibofract(n,sz,len)={ my(fwv,fn,dr,px=10,py=420,x=0,y=-len,g2=0, ttl="Fibonacci word/fractal: n="); plotinit(0); plotcolor(0,6); \\green plotscale(0, -sz,sz, -sz,sz); plotmove(0, px,py); fwv=fibword(n); fn=#fwv; for(i=1,fn, plotrline(0,x,y); dr=nextdir(i,fwv[i]); if(dr==-1, next); \\up if(g2==0, y=0; if(dr, x=len;g2=1, x=-len;g2=3); next); \\right if(g2==1, x=0; if(dr, y=len;g2=2, y=-len;g2=0); next); \\down if(g2==2, y=0; if(dr, x=-len;g2=3, x=len;g2=1); next); \\left if(g2==3, x=0; if(dr, y=-len;g2=0, y=len;g2=2); next); );\\fend i plotdraw([0,-sz,-sz]); print(" *** ",ttl,n," sz=",sz," len=",len," fw-len=",fn); } {\\ Executing: plotfibofract(11,430,20); \\ Fibofrac1.png plotfibofract(21,430,2); \\ Fibofrac2.png }{{Output}}
> plotfibofract(11,430,20); \\ Fibofrac1.png *** Fibonacci word/fractal: n=11 sz=430 len=20 fw-len=89 > plotfibofract(21,430,2); \\ Fibofrac2.png *** Fibonacci word/fractal: n=21 sz=430 len=2 fw-len=10946Version #2.
In this version only function plotfibofract1() was translated from Java, plus upgraded to plot different kind/size of Fibonacci word/fractals.
[[File:Fibofrac3.png|200px|right|thumb|Output Fibofrac3.png]] [[File:Fibofrac4.png|200px|right|thumb|Output Fibofrac4.png]]
{{trans|Java}}
{{Works with|PARI/GP|2.7.4 and above}}
\\ Fibonacci word/fractals 2nd version \\ 4/26/16 aev fibword(n)={ my(f1="1",f2="0",fw,fwn,n2); \\check n2 in v2 ADD it!! if(n<=4, n=5); n2=n-2; for(i=1,n2, fw=Str(f2,f1); f1=f2;f2=fw;); fwn=#fw; fw=Vecsmall(fw); for(i=1,fwn,fw[i]-=48); return(fw); } plotfibofract1(n,sz,len)={ my(fwv,fn,dx=len,dy=0,nr,ttl="Fibonacci word/fractal, n="); plotinit(0); plotcolor(0,5); \\red plotscale(0, -sz,sz, -sz,sz); plotmove(0, 0,0); fwv=fibword(n); fn=#fwv; for(i=1,fn, plotrline(0,dx,dy); if(fwv[i]==0, tx=dx; nr=i%2; if(!nr,dx=-dy;dy=tx, dx=dy;dy=-tx)); );\\fend i plotdraw([0,0,0]); print(" *** ",ttl,n," sz=",sz," len=",len," fw-len=",fn); } {\\ Executing: plotfibofract1(17,500,6); \\ Fibofrac3.png plotfibofract1(21,600,1); \\ Fibofrac4.png }{{Output}}
> plotfibofract1(17,500,6); \\ Fibofrac3.png *** Fibonacci word/fractal: n=17 sz=500 len=6 fw-len=1597 > plotfibofract1(21,600,1); \\ Fibofrac4.png *** Fibonacci word/fractal: n=21 sz=600 len=1 fw-len=10946Perl
Creates file fword.png containing the Fibonacci Fractal.
use strict; use warnings; use GD; my @fword = ( undef, 1, 0 ); sub fword { my $n = shift; return $fword[$n] if $n<3; return $fword[$n] //= fword($n-1).fword($n-2); } my $size = 3000; my $im = new GD::Image($size,$size); my $white = $im->colorAllocate(255,255,255); my $black = $im->colorAllocate(0,0,0); $im->transparent($white); $im->interlaced('true'); my @pos = (0,0); my @dir = (0,5); my @steps = split //, fword 23; my $i = 1; for( @steps ) { my @next = ( $pos[0]+$dir[0], $pos[1]+$dir[1] ); $im->line( @pos, @next, $black ); @dir = ( $dir[1], -$dir[0] ) if 0==$_ && 1==$i%2; # odd @dir = ( -$dir[1], $dir[0] ) if 0==$_ && 0==$i%2; # even $i++; @pos = @next; } open my $out, ">", "fword.png" or die "Cannot open output file.\n"; binmode $out; print $out $im->png; close $out;Perl 6
constant @fib-word = '1', '0', { $^b ~ $^a } ... *; sub MAIN($m = 17, $scale = 3) { (my %world){0}{0} = 1; my $loc = 0+0i; my $dir = i; my $n = 1; for @fib-word[$m].comb { when '0' { step; if $n %% 2 { turn-left } else { turn-right; } } $n++; } braille-graphics %world; sub step { for ^$scale { $loc += $dir; %world{$loc.im}{$loc.re} = 1; } } sub turn-left { $dir *= i; } sub turn-right { $dir *= -i; } } sub braille-graphics (%a) { my ($ylo, $yhi, $xlo, $xhi); for %a.keys -> $y { $ylo min= +$y; $yhi max= +$y; for %a{$y}.keys -> $x { $xlo min= +$x; $xhi max= +$x; } } for $ylo, $ylo + 4 ...^ * > $yhi -> \y { for $xlo, $xlo + 2 ...^ * > $xhi -> \x { my $cell = 0x2800; $cell += 1 if %a{y + 0}{x + 0}; $cell += 2 if %a{y + 1}{x + 0}; $cell += 4 if %a{y + 2}{x + 0}; $cell += 8 if %a{y + 0}{x + 1}; $cell += 16 if %a{y + 1}{x + 1}; $cell += 32 if %a{y + 2}{x + 1}; $cell += 64 if %a{y + 3}{x + 0}; $cell += 128 if %a{y + 3}{x + 1}; print chr($cell); } print "\n"; } }{{out}}
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⣸⠉⣇⣀⠀⣀⣸⠉⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⡖⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡁⠀⠀⠀⢈⣉⡁⢈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠧⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⢹⣀⡀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡄⢠⠤⡄⠀⠀⠀⢠⠤⡄⢠⠤⠇⠸⠤⡄⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⡖⠚⠀⠓⠚⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡏⢹⣀⡀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⢹⣀⡀⢀⣀⡏⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠤⡄⢠⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠒⡆⢰⠒⠃⠘⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⣉⠀⣉⣉⠀⠀⠀⠀⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⠤⠇⠸⠤⡄⢠⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠒⠃⠘⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⣇⣸⠉⠁⠈⠉⣇⣸⠉⣇⣀⠀⣀⣸⠉⣇⣸⠉⠁⠈⠉⣇⣸⠉⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠉⣇⣸⠉⠁⠈⠉⣇⣸⠉⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠧⢤⠀⡤⢤⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⠀⡤⢤⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⠃⠀⠀⠀⠘⠒⠃⠘⠒⡆⢰⠒⠃⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃⠘⠒⡆⢰⠒⠃⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⣸⠉⣇⣀⠀⣀⣸⠉⣇⣸⠉⠁⠈⠉⣇⣸⠉⣇⣀⠀⣀⣸⠉⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠉⣇⣀⠀⣀⣸⠉⣇⣸⠉⠁⠈⠉⣇⣸⠉⣇⣀⠀⣀⣸⠉⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⠀⡤⠼⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⡖⢲⠀⠀⠀⠀⡖⢲⠀⡖⠚⠀⠓⢲⠀⡖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⡖⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡁⠀⠀⠀⢈⣉⡁⢈⣉⡇⢸⣉⡁⢈⣉⡁⠀⠀⠀⢈⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡁⠀⠀⠀⢈⣉⡁⢈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠧⠼⠀⠀⠀⠀⠧⠼⠀⠧⢤⠀⡤⠼⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠧⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠀⠓⢲⠀⡖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣀⡏⠉⠀⠉⢹⣀⡏⢹⣀⡀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡄⢠⠤⡄⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⠀⢠⠤⡄⢠⠤⠇⠸⠤⡄⢠⠤⡄⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠀⠓⢲⠀⡖⠚⠀⠓⠚⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⣏⣉⠀⣀⣀⠀⠀⠀⠀⣀⣀⠀⣉⣹⠀⣏⣉⠀⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⣏⣉⠀⣀⣀⠀⠀⠀⠀⣀⣀⠀⣉⣹⠀⣏⣉⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠀⠀⠀⠸⠤⠇⠸⠤⡄⢠⠤⠇⠸⠤⠇⠀⠀⠀⠸⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠀⠀⠀⠸⠤⠇⠸⠤⡄⢠⠤⠇⠸⠤⠇⠀⠀⠀⠸⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⡆⢰⠒⠃⠘⠒⡆⢰⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⡆⢰⠒⠃⠘⠒⡆⢰⠒⡆⠀⠀⠀⢰⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣉⠀⠀⠀⠀⣉⣉⠀⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣉⠀⠀⠀⠀⣉⣉⠀⣉⣹⠀⣏⣉⠀⣉⣉⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠸⠤⡄⢠⠤⠇⠸⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠸⠤⡄⢠⠤⠇⠸⠤⠇⠀⠀⠀⠸⠤⠇⠸⠤⡄⢠⠤⠇⠸⠤⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⡆⢰⠒⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⣸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⣸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⣸⠉⠁⠈⠉⣇⣸⠉⣇⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⡤⢤⠀⡤⠼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⡆⢰⠒⠃⠘⠒⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢈⣉⡇⢸⣉⡁⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢈⣉⡇⢸⣉⡁⢀⣀⡀⠀⠀⠀⢀⣀⡀⢈⣉⡇⢸⣉⡁⢈⣉⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⠼⠀⠀⠀⠀⠧⠼⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⠼⠀⠀⠀⠀⠧⠼⠀⠧⢤⠀⡤⠼⠀⠧⠼⠀⠀⠀⠀⠧⠼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⢲⠀⠀⠀⠀⡖⢲⠀⡖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⢲⠀⠀⠀⠀⡖⢲⠀⡖⠚⠀⠓⢲⠀⡖⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢈⣉⡁⢈⣉⡇⢸⣉⡁⢈⣉⡁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢈⣉⡁⢈⣉⡇⢸⣉⡁⢈⣉⡁⠀⠀⠀⢈⣉⡁⢈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠧⠼⠀⠀⠀⠀⠧⠼⠀⠧⢤⠀⡤⠼⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠧⠼⠀⠀⠀⠀⠧⠼⠀⠧⢤⠀⡤⠼⠀⠧⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠀⠓⢲⠀⡖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣀⡏⠉⠀⠉⢹⣀⡏⢹⣀⡀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡄⢠⠤⡄⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⠀⢠⠤⡄⢠⠤⠇⠸⠤⡄⢠⠤⡄⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠀⠓⢲⠀⡖⠚⠀⠓⠚⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⣏⣉⠀⣀⣀⠀⠀⠀⠀⣀⣀⠀⣉⣹⠀⣏⣉⠀⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⣏⣉⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠀⠀⠀⠸⠤⠇⠸⠤⡄⢠⠤⠇⠸⠤⠇⠀⠀⠀⠸⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠀⠀⠀⠸⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⡆⠀⠀⠀⢰⠒⡆⢰⠒⠃⠘⠒⡆⢰⠒⡆⠀⠀⠀⢰⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⡆⠀⠀⠀⢰⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⣏⣉⠀⠉⠉⠀⠀⠀⠀⠉⠉⠀⣉⣹⠀⣏⣉⠀⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⣏⣉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠧⢤⠀⡤⢤⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⠀⡤⠼⠀⠧⢤⠀⡤⢤⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⠃⠀⠀⠀⠘⠒⠃⠘⠒⡆⢰⠒⠃⠘⠒⠃⠀⠀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃⠀⠀⠀⠘⠒⠃⠘⠒⡆⢰⠒⠃⠘⠒⠃⠀⠀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⣸⠉⣇⣀⠀⣀⣸⠉⣇⣸⠉⠁⠈⠉⣇⣸⠉⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠉⣇⣸⠉⠁⠈⠉⣇⣸⠉⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠧⢤⠀⡤⢤⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⠀⡤⢤⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠒⠃⠘⠒⡆⢰⠒⠃⠘⠒⠃⠀⠀⠀⠘⠒⠃⠘⠒⡆⢰⠒⠃⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃⠘⠒⡆⢰⠒⠃⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⡀⢈⣉⡇⢸⣉⡁⢈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⡁⢈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⡁⢈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡤⠼⠀⠧⠼⠀⠀⠀⠀⠧⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠓⢲⠀⡖⢲⠀⠀⠀⠀⡖⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠁⢈⣉⡇⢸⣉⡁⢈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⡁⢈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠤⡄⢠⠤⠇⠸⠤⡄⢠⠤⡄⠀⠀⠀⢠⠤⡄⢠⠤⠇⠸⠤⡄⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠓⠚⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⡖⠚⠀⠓⠚⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⢹⣀⡀⢀⣀⡏⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡄⢠⠤⡄⠀⠀⠀⢠⠤⡄⢠⠤⠇⠸⠤⡄⢠⠤⡄⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⡖⠚⠀⠓⠚⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⣏⣉⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠀⠀⠀⠸⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⡆⠀⠀⠀⢰⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⣏⣉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⠃⠀⠀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⣸⠉⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃Phix
Output matches Fig 1 (at the top of the page) {{libheader|pGUI}}
-- -- demo\rosetta\FibonacciFractal.exw -- include pGUI.e Ihandle dlg, canvas cdCanvas cddbuffer, cdcanvas procedure drawFibonacci(integer x, y, dx, dy, n) string prev = "1", word = "0" for i=3 to n do {prev,word} = {word,word&prev} end for for i=1 to length(word) do cdCanvasLine(cddbuffer, x, y, x+dx, y+dy) x += dx y += dy if word[i]=='0' then {dx,dy} = iff(remainder(i,2)?{dy,-dx}:{-dy,dx}) end if end for end procedure function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/) cdCanvasActivate(cddbuffer) cdCanvasClear(cddbuffer) drawFibonacci(20, 20, 0, 1, 23) cdCanvasFlush(cddbuffer) return IUP_DEFAULT end function function map_cb(Ihandle ih) cdcanvas = cdCreateCanvas(CD_IUP, ih) cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas) cdCanvasSetBackground(cddbuffer, CD_WHITE) cdCanvasSetForeground(cddbuffer, CD_GREEN) return IUP_DEFAULT end function function esc_close(Ihandle /*ih*/, atom c) if c=K_ESC then return IUP_CLOSE end if return IUP_CONTINUE end function procedure main() IupOpen() canvas = IupCanvas(NULL) IupSetAttribute(canvas, "RASTERSIZE", "620x450") IupSetCallback(canvas, "MAP_CB", Icallback("map_cb")) dlg = IupDialog(canvas, "RESIZE=NO") IupSetAttribute(dlg, "TITLE", "Fibonacci Fractal") IupSetCallback(dlg, "K_ANY", Icallback("esc_close")) IupSetCallback(canvas, "ACTION", Icallback("redraw_cb")) IupMap(dlg) IupShowXY(dlg,IUP_CENTER,IUP_CENTER) IupMainLoop() IupClose() end procedure main()Python
{{trans|Unicon}} Note that for Python 3, [http://docs.python.org/py3k/library/functools.html#functools.lru_cache functools.lru_cache] could be used instead of the memoize decorator below.
from functools import wraps from turtle import * def memoize(obj): cache = obj.cache = {} @wraps(obj) def memoizer(*args, **kwargs): key = str(args) + str(kwargs) if key not in cache: cache[key] = obj(*args, **kwargs) return cache[key] return memoizer @memoize def fibonacci_word(n): assert n > 0 if n == 1: return "1" if n == 2: return "0" return fibonacci_word(n - 1) + fibonacci_word(n - 2) def draw_fractal(word, step): for i, c in enumerate(word, 1): forward(step) if c == "0": if i % 2 == 0: left(90) else: right(90) def main(): n = 25 # Fibonacci Word to use. step = 1 # Segment length. width = 1050 # Width of plot area. height = 1050 # Height of plot area. w = fibonacci_word(n) setup(width=width, height=height) speed(0) setheading(90) left(90) penup() forward(500) right(90) backward(500) pendown() tracer(10000) hideturtle() draw_fractal(w, step) # Save Poscript image. getscreen().getcanvas().postscript(file="fibonacci_word_fractal.eps") exitonclick() if __name__ == '__main__': main()The output image is probably the same.
R
{{trans|PARI/GP}} {{Works with|R|3.3.1 and above}} [[File:FiboFractR23.png|right|thumb|Output FiboFractR23.png]] [[File:FiboFractR25.png|right|thumb|Output FiboFractR25.png]]
## Fibonacci word/fractal 2/20/17 aev ## Create Fibonacci word order n fibow <- function(n) { t2="0"; t1="01"; t=""; if(n<2) {n=2} for (i in 2:n) {t=paste0(t1,t2); t2=t1; t1=t} return(t) } ## Plot Fibonacci word/fractal: ## n - word order, w - width, h - height, d - segment size, clr - color. pfibofractal <- function(n, w, h, d, clr) { dx=d; x=y=x2=y2=tx=dy=nr=0; if(n<2) {n=2} fw=fibow(n); nf=nchar(fw); pf = paste0("FiboFractR", n, ".png"); ttl=paste0("Fibonacci word/fractal, n=",n); cat(ttl,"nf=", nf, "pf=", pf,"\n"); plot(NA, xlim=c(0,w), ylim=c(-h,0), xlab="", ylab="", main=ttl) for (i in 1:nf) { fwi=substr(fw, i, i); x2=x+dx; y2=y+dy; segments(x, y, x2, y2, col=clr); x=x2; y=y2; if(fwi=="0") {tx=dx; nr=i%%2; if(nr==0) {dx=-dy;dy=tx} else {dx=dy;dy=-tx}} } dev.copy(png, filename=pf, width=w, height=h); # plot to png-file dev.off(); graphics.off(); # Cleaning } ## Executing: pfibofractal(23, 1000, 1000, 1, "navy") pfibofractal(25, 2300, 1000, 1, "red"){{Output}}
> pfibofractal(23, 1000, 1000, 1, "navy") Fibonacci word/fractal, n=23 nf= 75025 pf= FiboFractR23.png > pfibofractal(25, 2300, 1000, 1, "red") Fibonacci word/fractal, n=25 nf= 196418 pf= FiboFractR25.pngREXX
Programming note: the starting point ('''.''') and the ending point ('''∙''') are also shown to help visually identify the end points.
About half of the REXX program is dedicated to plotting the appropriate characters.
The output of this REXX program is written to the screen as well as a disk file.
/*REXX program generates a Fibonacci word, then displays the fractal curve. */ parse arg ord . /*obtain optional arguments from the CL*/ if ord=='' then ord=23 /*Not specified? Then use the default*/ s=FibWord(ord) /*obtain the order of Fibonacci word.*/ x=0; maxX=0; dx=0; b=' '; @.=b; xp=0 y=0; maxY=0; dy=1; @.0.0=.; yp=0 do n=1 for length(s); x=x+dx; y=y+dy /*advance the plot for the next point. */ maxX=max(maxX,x); maxY=max(maxY,y) /*set the maximums for displaying plot.*/ c='│'; if dx\==0 then c="─"; if n==1 then c='┌' /*is this the first plot?*/ @.x.y=c /*assign a plotting character for curve*/ if @(xp-1,yp)\==b then if @(xp,yp-1)\==b then call @ xp,yp,'┐' /*fix─up a corner.*/ if @(xp-1,yp)\==b then if @(xp,yp+1)\==b then call @ xp,yp,'┘' /* " " " */ if @(xp+1,yp)\==b then if @(xp,yp+1)\==b then call @ xp,yp,'└' /* " " " */ if @(xp+1,yp)\==b then if @(xp,yp-1)\==b then call @ xp,yp,'┌' /* " " " */ xp=x; yp=y; z=substr(s,n,1) /*save old x,y; assign plot character.*/ if z==1 then iterate /*Is Z equal to unity? Then ignore it.*/ ox=dx; oy=dy; dx=0; dy=0 /*save DX,DY as the old versions. */ d=-n//2; if d==0 then d=1 /*determine the sign for the chirality.*/ if oy\==0 then dx=-sign(oy)*d /*Going north|south? Go east|west */ if ox\==0 then dy= sign(ox)*d /* " east|west? " south|north */ end /*n*/ call @ x, y, '∙' /*set the last point that was plotted. */ do r=maxY to 0 by -1; _= /*show single row at a time, top first.*/ do c=0 to maxX; _=_ || @.c.r; end /*c*/; _=strip(_, 'T') /*build a line.*/ if _=='' then iterate /*if the line is blank, then ignore it.*/ say _; call lineout "FIBFRACT.OUT", _ /*display the line; also write to disk.*/ end /*r*/ /* [↑] only display the non-blank rows*/ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ @: parse arg xx,yy,p; if arg(3)=='' then return @.xx.yy; @.xx.yy=p; return /*──────────────────────────────────────────────────────────────────────────────────────*/ FibWord: procedure; parse arg x; !.=0; !.1=1 /*obtain the order of Fibonacci word. */ do k=3 to x; k1=k-1; k2=k-2 /*generate the Kth " " */ !.k=!.k1 || !.k2 /*construct the next " " */ end /*k*/ /* [↑] generate a " " */ return !.x /*return the Xth " " */'''output''' when using the input: 17
(The output is shown 1/2 size.)
┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ │ └─┘ │ │ └─┘ │ │ └─┘ │ │ └─┘ │ │ └─┘ │ │ └─┘ │ │ └─┘ │ │ └─┘ │ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ │ │ ┌─┐ │ │ │ │ ┌─┐ │ │ │ │ ┌─┐ │ │ │ │ ┌─┐ │ │ ┌┘ └─┘ └─┘ └┐ ┌┘ └─┘ └─┘ └┐ ┌┘ └─┘ └─┘ └┐ ┌┘ └─┘ └─┘ └┐ │ ┌─┐ ┌─┐ │ │ ┌─┐ ┌─┐ │ │ ┌─┐ ┌─┐ │ │ ┌─┐ ┌─┐ │ └─┘ │ │ └─┘ └─┘ │ │ └─┘ └─┘ │ │ └─┘ └─┘ │ │ └─┘ ┌┘ └┐ ┌─┐ ┌─┐ ┌┘ └┐ ┌┘ └┐ ┌─┐ ┌─┐ ┌┘ └┐ │ │ │ └─┘ │ │ │ │ │ │ └─┘ │ │ │ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ │ │ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ │ └┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌┘ └┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌┘ │ │ └─┘ │ │ └─┘ │ │ │ │ └─┘ │ │ └─┘ │ │ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ │ ┌─┐ │ │ │ │ ┌─┐ │ │ ┌─┐ │ │ │ │ ┌─┐ │ └─┘ └─┘ └┐ ┌┘ └─┘ └─┘ └─┘ └─┘ └┐ ┌┘ └─┘ └─┘ ┌─┐ │ │ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ │ │ ┌─┐ │ └─┘ └─┘ │ │ └─┘ │ │ └─┘ │ │ └─┘ └─┘ │ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ │ │ │ │ ┌─┐ │ │ │ │ ┌┘ └┐ ┌┘ └─┘ └─┘ └┐ ┌┘ └┐ │ ┌─┐ ┌─┐ │ │ ┌─┐ ┌─┐ │ │ ┌─┐ ┌─┐ │ └─┘ │ │ └─┘ └─┘ │ │ └─┘ └─┘ │ │ └─┘ ┌─┐ ┌─┐ ┌┘ └┐ ┌─┐ ┌─┐ ┌┘ └┐ ┌─┐ ┌─┐ ┌┘ └┐ ┌─┐ ┌─┐ │ └─┘ │ │ │ │ └─┘ │ │ │ │ └─┘ │ │ │ │ └─┘ │ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └┐ │ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ │ └─┘ │ │ └─┘ │ │ └─┘ │ │ └─┘ │ │ └─┘ │ │ └─┘ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ │ │ │ ┌─┐ │ │ │ │ ┌─┐ │ │ │ └┐ ┌┘ └─┘ └─┘ └┐ ┌┘ └─┘ └─┘ └┐ ┌┘ ┌─┐ │ │ ┌─┐ ┌─┐ │ │ ┌─┐ ┌─┐ │ │ ┌─┐ │ └─┘ └─┘ │ │ └─┘ └─┘ │ │ └─┘ └─┘ │ └┐ ┌─┐ ┌─┐ ┌┘ └┐ ┌┘ └┐ ┌─┐ ┌─┐ ┌┘ │ │ └─┘ │ │ │ │ │ │ └─┘ │ │ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ └─┘ └─┘ └─┘ └─┘ └─┘ │ │ └─┘ └─┘ └─┘ └─┘ └─┘ ┌─┐ ┌─┐ ┌┘ └┐ ┌─┐ ┌─┐ │ └─┘ │ │ │ │ └─┘ │ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌┘ └─┘ └─┘ └─┘ └─┘ └┐ │ ┌─┐ ┌─┐ │ └─┘ │ │ └─┘ ┌┘ └┐ │ │ └┐ ┌┘ ┌─┐ │ │ ┌─┐ │ └─┘ └─┘ │ └┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌┘ │ │ └─┘ │ │ └─┘ │ │ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ │ ┌─┐ │ │ │ │ ┌─┐ │ └─┘ └─┘ └┐ ┌┘ └─┘ └─┘ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ │ │ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ │ └─┘ │ │ └─┘ │ │ └─┘ └─┘ │ │ └─┘ │ │ └─┘ │ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ │ │ ┌─┐ │ │ │ │ │ │ ┌─┐ │ │ ┌┘ └─┘ └─┘ └┐ ┌┘ └┐ ┌┘ └─┘ └─┘ └┐ │ ┌─┐ ┌─┐ │ │ ┌─┐ ┌─┐ │ │ ┌─┐ ┌─┐ │ └─┘ │ │ └─┘ └─┘ │ │ └─┘ └─┘ │ │ └─┘ ┌┘ └┐ ┌─┐ ┌─┐ ┌┘ └┐ ┌─┐ ┌─┐ ┌┘ └┐ │ │ │ └─┘ │ │ │ │ └─┘ │ │ │ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ . └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └∙ ``` The '''output''' of this REXX program for this Rosetta Code task requirements can be seen here ───► [[Fibonacci word/fractal/FIBFRACT.REX]]. ## Racket Prime candidate for Turtle Graphics. I've used a '''values-turtle''', which means you don't get the joy of seeing the turltle bimble around the screen. But it allows the size of the image to be set (useful if you want to push the n much higher than 23 or so! We use '''word-order''' 23, which gives a classic n shape (inverted horseshoe). Save the (first) implementation of [[Fibonacci word]] to '''Fibonacci-word.rkt'''; since we do not ''generate'' the words here. ```racket #lang racket (require "Fibonacci-word.rkt") (require graphics/value-turtles) (define word-order 23) ; is a 3k+2 fractal, shaped like an n (define height 420) (define width 600) (define the-word (parameterize ((f-word-max-length #f)) (F-Word word-order))) (for/fold ((T (turtles width height 0 height ; in BL corner (/ pi -2)))) ; point north ((i (in-naturals)) (j (in-string (f-word-str the-word)))) (match* (i j) ((_ #\1) (draw 1 T)) (((? even?) #\0) (turn -90 (draw 1 T))) ((_ #\0) (turn 90 (draw 1 T))))) ``` ## Ruby ```ruby def fibonacci_word(n) words = ["1", "0"] (n-1).times{ words << words[-1] + words[-2] } words[n] end def print_fractal(word) area = Hash.new(" ") x = y = 0 dx, dy = 0, -1 area[[x,y]] = "S" word.each_char.with_index(1) do |c,n| area[[x+dx, y+dy]] = dx.zero? ? "|" : "-" x, y = x+2*dx, y+2*dy area[[x, y]] = "+" dx,dy = n.even? ? [dy,-dx] : [-dy,dx] if c=="0" end (xmin, xmax), (ymin, ymax) = area.keys.transpose.map(&:minmax) for y in ymin..ymax puts (xmin..xmax).map{|x| area[[x,y]]}.join end end word = fibonacci_word(16) print_fractal(word) ``` {{out}}+-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + +-+-+ + + +-+-+ + + +-+-+ + + +-+-+ + + +-+-+ + + +-+-+ + + +-+-+ + + +-+-+ + | | | | | | | | | | | | | | | | +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ | | | | | | | | | | | | | | | | + + +-+-+ + + + + +-+-+ + + + + +-+-+ + + + + +-+-+ + + | | | | | | | | | | | | | | | | | | | | | | | | +-+ +-+-+ +-+-+ +-+ +-+ +-+-+ +-+-+ +-+ +-+ +-+-+ +-+-+ +-+ +-+ +-+-+ +-+-+ +-+ | | | | | | | | + +-+-+ +-+-+ + + +-+-+ +-+-+ + + +-+-+ +-+-+ + + +-+-+ +-+-+ + | | | | | | | | | | | | | | | | | | | | | | | | +-+-+ + + +-+-+ +-+-+ + + +-+-+ +-+-+ + + +-+-+ +-+-+ + + +-+-+ | | | | | | | | +-+ +-+ +-+-+ +-+-+ +-+ +-+ +-+ +-+ +-+-+ +-+-+ +-+ +-+ | | | | | | | | | | | | | | | | + + + +-+-+ + + + + + + +-+-+ + + + | | | | | | | | | | | | +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ | | | | | | | | | | | | +-+-+ + + +-+-+ + + +-+-+ + + +-+-+ +-+-+ + + +-+-+ + + +-+-+ + + +-+-+ | | | | | | | | | | | | | | | | | | | | | | | | | | | | + +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ + + +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ + | | | | +-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+ +-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+ | | | | | | | | | | | | | | | | | | | | + + +-+-+ + + +-+-+ + + + + +-+-+ + + +-+-+ + + | | | | | | | | | | | | +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ | | | | | | | | | | | | + +-+-+ + + + + +-+-+ + + +-+-+ + + + + +-+-+ + | | | | | | | | | | | | | | | | | | | | +-+-+ +-+-+ +-+ +-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+ +-+ +-+-+ +-+-+ | | | | +-+-+ + + +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ + + +-+-+ | | | | | | | | | | | | | | | | | | | | + +-+-+ +-+-+ + + +-+-+ + + +-+-+ + + +-+-+ +-+-+ + | | | | | | | | +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ | | | | | | | | + + + + +-+-+ + + + + | | | | | | | | | | +-+ +-+ +-+ +-+-+ +-+-+ +-+ +-+ +-+ | | | | | | + +-+-+ +-+-+ + + +-+-+ +-+-+ + + +-+-+ +-+-+ + | | | | | | | | | | | | | | | | | | +-+-+ + + +-+-+ +-+-+ + + +-+-+ +-+-+ + + +-+-+ | | | | | | +-+-+ +-+-+ +-+ +-+ +-+-+ +-+-+ +-+ +-+ +-+-+ +-+-+ +-+ +-+ +-+-+ +-+-+ | | | | | | | | | | | | | | | | | | | | | | + +-+-+ + + + + +-+-+ + + + + +-+-+ + + + + +-+-+ + | | | | | | | | | | | | | | +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ | | | | | | | | | | | | | | + + +-+-+ + + +-+-+ + + +-+-+ + + +-+-+ + + +-+-+ + + +-+-+ + + | | | | | | | | | | | | | | | | | | | | | | | | | | +-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+ | | + +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ + | | | | | | | | | | | | | | | | | | | | | | +-+-+ + + +-+-+ + + +-+-+ + + +-+-+ + + +-+-+ + + +-+-+ | | | | | | | | | | +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ | | | | | | | | | | + + + +-+-+ + + + + +-+-+ + + + | | | | | | | | | | | | | | +-+ +-+ +-+-+ +-+-+ +-+ +-+ +-+-+ +-+-+ +-+ +-+ | | | | | | +-+-+ + + +-+-+ +-+-+ + + +-+-+ +-+-+ + + +-+-+ | | | | | | | | | | | | | | | | | | + +-+-+ +-+-+ + + +-+-+ +-+-+ + + +-+-+ +-+-+ + | | | | | | +-+ +-+-+ +-+-+ +-+ +-+ +-+ +-+ +-+-+ +-+-+ +-+ | | | | | | | | | | | | | | + + +-+-+ + + + + + + +-+-+ + + | | | | | | | | | | +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ | | | | | | | | | | + +-+-+ + + +-+-+ + + +-+-+ +-+-+ + + +-+-+ + + +-+-+ + | | | | | | | | | | | | | | | | | | | | | | +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ + + +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ | | +-+-+ +-+-+ +-+ +-+ +-+-+ +-+-+ | | | | | | | | | | + +-+-+ + + + + +-+-+ + | | | | | | +-+ +-+ +-+ +-+ +-+ +-+ | | | | | | + + +-+-+ + + +-+-+ + + | | | | | | | | | | +-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+ | | + +-+-+ +-+-+ + | | | | | | +-+-+ + + +-+-+ | | +-+ +-+ | | + + | | +-+ +-+ | | +-+-+ + + +-+-+ | | | | | | + +-+-+ +-+-+ + | | +-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+ | | | | | | | | | | + + +-+-+ + + +-+-+ + + | | | | | | +-+ +-+ +-+ +-+ +-+ +-+ | | | | | | + +-+-+ + + + + +-+-+ + | | | | | | | | | | +-+-+ +-+-+ +-+ +-+ +-+-+ +-+-+ | | +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ + + +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ | | | | | | | | | | | | | | | | | | | | | | + +-+-+ + + +-+-+ + + +-+-+ +-+-+ + + +-+-+ + + +-+-+ + | | | | | | | | | | +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ | | | | | | | | | | + + +-+-+ + + + + + + +-+-+ + + | | | | | | | | | | | | | | +-+ +-+-+ +-+-+ +-+ +-+ +-+ +-+ +-+-+ +-+-+ +-+ | | | | | | + +-+-+ +-+-+ + + +-+-+ +-+-+ + + +-+-+ +-+-+ + | | | | | | | | | | | | | | | | | | +-+-+ + + +-+-+ +-+-+ + + +-+-+ +-+-+ + + +-+-+ | | | | | | +-+ +-+ +-+-+ +-+-+ +-+ +-+ +-+-+ +-+-+ +-+ +-+ | | | | | | | | | | | | | | + + + +-+-+ + + + + +-+-+ + + + | | | | | | | | | | +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ | | | | | | | | | | +-+-+ + + +-+-+ + + +-+-+ + + +-+-+ + + +-+-+ + + +-+-+ | | | | | | | | | | | | | | | | | | | | | | S +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+ ``` ## Scala '''Note:''' will be computing an SVG image - not very efficient, but very cool. worked for me in the scala REPL with ''-J-Xmx2g'' argument. ```scala def fibIt = Iterator.iterate(("1","0")){case (f1,f2) => (f2,f1+f2)}.map(_._1) def turnLeft(c: Char): Char = c match { case 'R' => 'U' case 'U' => 'L' case 'L' => 'D' case 'D' => 'R' } def turnRight(c: Char): Char = c match { case 'R' => 'D' case 'D' => 'L' case 'L' => 'U' case 'U' => 'R' } def directions(xss: List[(Char,Char)], current: Char = 'R'): List[Char] = xss match { case Nil => current :: Nil case x :: xs => x._1 match { case '1' => current :: directions(xs, current) case '0' => x._2 match { case 'E' => current :: directions(xs, turnLeft(current)) case 'O' => current :: directions(xs, turnRight(current)) } } } def buildIt(xss: List[Char], old: Char = 'X', count: Int = 1): List[String] = xss match { case Nil => s"$old$count" :: Nil case x :: xs if x == old => buildIt(xs,old,count+1) case x :: xs => s"$old$count" :: buildIt(xs,x) } def convertToLine(s: String, c: Int): String = (s.head, s.tail) match { case ('R',n) => s"l ${c * n.toInt} 0" case ('U',n) => s"l 0 ${-c * n.toInt}" case ('L',n) => s"l ${-c * n.toInt} 0" case ('D',n) => s"l 0 ${c * n.toInt}" } def drawSVG(xStart: Int, yStart: Int, width: Int, height: Int, fibWord: String, lineMultiplier: Int, color: String): String = { val xs = fibWord.zipWithIndex.map{case (c,i) => (c, if(c == '1') '_' else i % 2 match{case 0 => 'E'; case 1 => 'O'})}.toList val fractalPath = buildIt(directions(xs)).tail.map(convertToLine(_,lineMultiplier)) s"""""" } drawSVG(0,25,550,530,fibIt.drop(18).next,3,"000") ``` {{out}} [https://www.dropbox.com/s/vb4cu4fvq2f6cvz/fibfract.svg?dl=0 output string saved as an SVG file] - BTW, would appreciate help on getting the image to display here nicely. couldn't figure out how to do that... ## Scilab This script uses Scilab's [[Fibonacci_word#Iterative_method|iterative solution]] to generate Fibonacci words, and the interpreting the words to generate the fractal is similar to [[Langton's_ant#Scilab|Langton's ant]]. The result is displayed in a graphic window.final_length = 37; word_n = ''; word_n_1 = ''; word_n_2 = ''; for i = 1:final_length if i == 1 then word_n = '1'; elseif i == 2 word_n = '0'; elseif i == 3 word_n = '01'; word_n_1 = '0'; else word_n_2 = word_n_1; word_n_1 = word_n; word_n = word_n_1 + word_n_2; end end word = strsplit(word_n); fractal_size = sum(word' == '0'); fractal = zeros(1+fractal_size,2); direction_vectors = [1,0; 0,-1; -1,0; 0,1]; direction = direction_vectors(4,:); direction_name = 'N'; for j = 1:length(word_n); fractal(j+1,:) = fractal(j,:) + direction; if word(j) == '0' then if pmodulo(j,2) then //right select direction_name case 'N' then direction = direction_vectors(1,:); direction_name = 'E'; case 'E' then direction = direction_vectors(2,:); direction_name = 'S'; case 'S' then direction = direction_vectors(3,:); direction_name = 'W'; case 'W' then direction = direction_vectors(4,:); direction_name = 'N'; end else //left select direction_name case 'N' then direction = direction_vectors(3,:); direction_name = 'W'; case 'W' then direction = direction_vectors(2,:); direction_name = 'S'; case 'S' then direction = direction_vectors(1,:); direction_name = 'E'; case 'E' then direction = direction_vectors(4,:); direction_name = 'N'; end end end end scf(0); clf(); plot2d(fractal(:,1),fractal(:,2)); set(gca(),'isoview','on'); ``` ## Sidef {{trans|Perl 6}} ```ruby var(m=17, scale=3) = ARGV.map{.to_i}... (var world = Hash.new){0}{0} = 1 var loc = 0 var dir = 1i var fib = ['1', '0'] func fib_word(n) { fib[n] \\= (fib_word(n-1) + fib_word(n-2)) } func step { scale.times { loc += dir world{loc.im}{loc.re} = 1 } } func turn_left { dir *= 1i } func turn_right { dir *= -1i } var n = 1 fib_word(m).each { |c| if (c == '0') { step() n % 2 == 0 ? turn_left() : turn_right() } else { n++ } } func braille_graphics(a) { var (xlo, xhi, ylo, yhi) = ([Inf, -Inf]*2)... a.each_key { |y| ylo.min!(y.to_i) yhi.max!(y.to_i) a{y}.each_key { |x| xlo.min!(x.to_i) xhi.max!(x.to_i) } } for y in (ylo..yhi `by` 4) { for x in (xlo..xhi `by` 2) { var cell = 0x2800 a{y+0}{x+0} && (cell += 1) a{y+1}{x+0} && (cell += 2) a{y+2}{x+0} && (cell += 4) a{y+0}{x+1} && (cell += 8) a{y+1}{x+1} && (cell += 16) a{y+2}{x+1} && (cell += 32) a{y+3}{x+0} && (cell += 64) a{y+3}{x+1} && (cell += 128) print cell.chr } print "\n" } } braille_graphics(world) ``` {{out}} ```txt $ sidef fib_word_fractal.sf 12 3 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⣸⠉⣇⣀⠀⣀⣸⠉⣇⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⡖⢲⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡁⠀⠀⠀⢈⣉⡁⢈⣉⡇ ⠀⠀⠀⡤⠼⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠧⠼⠀⠀ ⠀⠀⠀⠓⢲⠀⡖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀ ⠉⢹⣀⡏⠉⠀⠉⢹⣀⡏⢹⣀⡀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⢠⠤⠇⠸⠤⡄⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡖⠚⠀⠓⠚⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢹⣀⡏⢹⣀⡀⢀⣀⡏⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ``` ## Tcl {{libheader|Tk}} ```tcl package require Tk # OK, this stripped down version doesn't work for n<2… proc fibword {n} { set fw {1 0} while {[llength $fw] < $n} { lappend fw [lindex $fw end][lindex $fw end-1] } return [lindex $fw end] } proc drawFW {canv fw {w {[$canv cget -width]}} {h {[$canv cget -height]}}} { set w [subst $w] set h [subst $h] # Generate the coordinate list using line segments of unit length set d 3; # Match the orientation in the sample paper set eo [set x [set y 0]] set coords [list $x $y] foreach c [split $fw ""] { switch $d { 0 {lappend coords [incr x] $y} 1 {lappend coords $x [incr y]} 2 {lappend coords [incr x -1] $y} 3 {lappend coords $x [incr y -1]} } if {$c == 0} { set d [expr {($d + ($eo ? -1 : 1)) % 4}] } set eo [expr {!$eo}] } # Draw, and rescale to fit in canvas set id [$canv create line $coords] lassign [$canv bbox $id] x1 y1 x2 y2 set sf [expr {min(($w-20.) / ($y2-$y1), ($h-20.) / ($x2-$x1))}] $canv move $id [expr {-$x1}] [expr {-$y1}] $canv scale $id 0 0 $sf $sf $canv move $id 10 10 # Return the item ID to allow user reconfiguration return $id } pack [canvas .c -width 500 -height 500] drawFW .c [fibword 23] ``` ## zkl Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl {{trans|D}} [[File:Fibonacci word fractal.zkl.jpg|250px|thumb|right]] ```zkl fcn drawFibonacci(img,x,y,word){ // word is "01001010...", 75025 characters dx:=0; dy:=1; // turtle direction foreach i,c in ([1..].zip(word)){ // Walker.zip(list)-->Walker of zipped list a:=x; b:=y; x+=dx; y+=dy; img.line(a,b, x,y, 0x00ff00); if (c=="0"){ dxy:=dx+dy; if(i.isEven){ dx=(dx - dxy)%2; dy=(dxy - dy)%2; }// turn left else { dx=(dxy - dx)%2; dy=(dy - dxy)%2; }// turn right } } } img:=PPM(1050,1050); fibWord:=L("1","0"); do(23){ fibWord.append(fibWord[-1] + fibWord[-2]); } drawFibonacci(img,20,20,fibWord[-1]); img.write(File("foo.ppm","wb")); ```