⚠️ 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|Fractals}}[[Category:Raster graphics operations]][[Category:Recursion]]{{requires|Graphics}} Generate and draw a fractal tree.
Draw the trunk
At the end of the trunk, split by some angle and draw two branches
Repeat at the end of each branch until a sufficient level of branching is reached
;Related tasks
- [[Pythagoras_tree|Pythagoras Tree]]
AutoHotkey
[http://i.imgur.com/H7iJOde.png Image] - Link, since uploads seem to be disabled currently. {{libheader|GDIP}}
#SingleInstance, Force
#NoEnv
SetBatchLines, -1
; Uncomment if Gdip.ahk is not in your standard library
; #Include, Gdip.ahk
FileOut := A_Desktop "\MyNewFile.png"
TreeColor := 0xff0066ff ; ARGB
TrunkWidth := 10 ; Pixels
TrunkLength := 80 ; Pixels
Angle := 60 ; Degrees
ImageWidth := 670 ; Pixels
ImageHeight := 450 ; Pixels
Branches := 13
Decrease := 0.81
Angle := (Angle * 0.01745329252) / 2
, Points := {}
, Points[1, "Angle"] := 0
, Points[1, "X"] := ImageWidth // 2
, Points[1, "Y"] := ImageHeight - TrunkLength
if (!pToken := Gdip_Startup()) {
MsgBox, 48, Gdiplus error!, Gdiplus failed to start. Please ensure you have Gdiplus on your system.
ExitApp
}
OnExit, Exit
pBitmap := Gdip_CreateBitmap(ImageWidth, ImageHeight)
, G := Gdip_GraphicsFromImage(pBitmap)
, Gdip_SetSmoothingMode(G, 4)
, pBrush := Gdip_BrushCreateSolid(0xff000000)
, Gdip_FillRectangle(G, pBrush, -5, -5, ImageWidth + 10, ImageHeight + 10)
, Gdip_DeleteBrush(pBrush)
, pPen := Gdip_CreatePen(TreeColor, TrunkWidth/Decrease)
, Gdip_DrawLine(G, pPen, Points.1.X, Points.1.Y, Points.1.X, ImageHeight)
, Gdip_DeletePen(pPen)
Loop, % Branches {
NewPoints := {}
pPen := Gdip_CreatePen(TreeColor, TrunkWidth)
for Each, Point in Points {
N1 := A_Index * 2
, N2 := (A_Index * 2) + 1
, NewPoints[N1, "X"] := Point.X + (TrunkLength * Sin(NewPoints[N1, "Angle"] := Point.Angle - Angle))
, NewPoints[N1, "Y"] := Point.Y - (TrunkLength * Cos(NewPoints[N1].Angle))
, NewPoints[N2, "X"] := Point.X + (TrunkLength * Sin(NewPoints[N2, "Angle"] := Point.Angle + Angle))
, NewPoints[N2, "Y"] := Point.Y - (TrunkLength * Cos(NewPoints[N2].Angle))
, Gdip_DrawLine(G, pPen, Point.X, Point.Y, NewPoints[N1].X, NewPoints[N1].Y)
, Gdip_DrawLine(G, pPen, Point.X, Point.Y, NewPoints[N2].X, NewPoints[N2].Y)
}
TrunkWidth *= Decrease
, TrunkLength *= Decrease
, Points := NewPoints
, Gdip_DeletePen(pPen)
}
Gdip_SaveBitmapToFile(pBitmap, FileOut)
, Gdip_DisposeImage(pBitmap)
, Gdip_DeleteGraphics(G)
Run, % FileOut
Exit:
Gdip_Shutdown(pToken)
ExitApp
BASIC
=
BASIC256
= [[File:Fractal tree BASIC-256.png|thumb|right|Asymmetric fractal tree image created by the BASIC-256 script]]
graphsize 300,300
level = 12 : len =63 # initial values
x = 230: y = 285
rotation = pi/2
A1 = pi/27 : A2 = pi/8 # constants which determine shape
C1 = 0.7 : C2 = 0.85
dim xs(level+1) : dim ys(level+1) # stacks
fastgraphics
color black
rect 0,0,graphwidth,graphheight
refresh
color green
gosub tree
refresh
imgsave "Fractal_tree_BASIC-256.png", "PNG"
end
tree:
xs[level] = x : ys[level] = y
gosub putline
if level>0 then
level = level - 1
len = len*C1
rotation = rotation - A1
gosub tree
len = len/C1*C2
rotation = rotation + A1 + A2
gosub tree
rotation = rotation - A2
len = len/C2
level = level + 1
end if
x = xs[level] : y = ys[level]
return
putline:
yn = -sin(rotation)*len + y
xn = cos(rotation)*len + x
line x,y,xn,yn
x = xn : y = yn
return
=
Run BASIC
=
'Fractal Tree - for Run Basic - 29 Apr 2018
'from BASIC256 - http://rosettacode.org/wiki/Fractal_tree#BASIC256
'copy this text and go to http://www.runbasic.com
WindowWidth = 500 'Run Basic max size 800 x 600
WindowHeight = 350
c = 255 '255 for white '0 for black
graphic #w, WindowWidth, WindowHeight
#w cls("black") 'black background color
#w color(c,c,c) 'changes color to white
level = 10 ' initial values
leng = 50
x = 230: y = 325 ' initial values x = 230: y = 285
pi = 3.1415
rotation = 3.1415/2
'A1 = pi/27 : A2 = pi/8 ' constants which determine shape
'C1 = 0.7 : C2 = 0.85 ' tree is drifted left
A1 = pi/9 : A2 = pi/9 ' constants which determine shape
C1 = 0.85 : C2 = 0.85 ' Symmetrical Tree
dim xs(level+1) : dim ys(level+1) ' stacks
print : print "Welcome to the Run BASIC Fractal Tree Program"
#w color("green") 'color green
gosub [tree]
render #w
' imgsave "Fractal_tree_BASIC-256.png", "PNG"
Print "Thank you and goodbye"
end
[tree]
xs(level) = x : ys(level) = y
gosub [putline]
if level>0 then
level = level - 1
leng = leng*C1
rotation = rotation - A1
gosub [tree]
leng = leng/C1*C2
rotation = rotation + A1 + A2
gosub [tree]
rotation = rotation - A2
leng = leng/C2
level = level + 1
end if
x = xs(level) : y = ys(level)
return
[putline]
yn = -1*sin(rotation)*leng + y
xn = cos(rotation)*leng + x
#w line(x,y,xn,yn)
x = xn : y = yn
return
'end of code
End
=
BBC BASIC
= {{Out}}[[Image:fractal_tree_bbc.gif|right]]
{{works with|BBC BASIC for Windows}}
Spread = 25
Scale = 0.76
SizeX% = 400
SizeY% = 300
Depth% = 10
VDU 23,22,SizeX%;SizeY%;8,16,16,128
PROCbranch(SizeX%, 0, SizeY%/2, 90, Depth%)
END
DEF PROCbranch(x1, y1, size, angle, depth%)
LOCAL x2, y2
x2 = x1 + size * COSRAD(angle)
y2 = y1 + size * SINRAD(angle)
VDU 23,23,depth%;0;0;0;
LINE x1, y1, x2, y2
IF depth% > 0 THEN
PROCbranch(x2, y2, size * Scale, angle - Spread, depth% - 1)
PROCbranch(x2, y2, size * Scale, angle + Spread, depth% - 1)
ENDIF
ENDPROC
==={{header|IS-BASIC}}===
## C
{{libheader|SDL}}
{{libheader|SGE}} or {{libheader|cairo}}
```c
#include <SDL/SDL.h>
#ifdef WITH_CAIRO
#include <cairo.h>
#else
#include <SDL/sge.h>
#endif
#include <cairo.h>
#include <stdlib.h>
#include <time.h>
#include <math.h>
#ifdef WITH_CAIRO
#define PI 3.1415926535
#endif
#define SIZE 800 // determines size of window
#define SCALE 5 // determines how quickly branches shrink (higher value means faster shrinking)
#define BRANCHES 14 // number of branches
#define ROTATION_SCALE 0.75 // determines how slowly the angle between branches shrinks (higher value means slower shrinking)
#define INITIAL_LENGTH 50 // length of first branch
double rand_fl(){
return (double)rand() / (double)RAND_MAX;
}
void draw_tree(SDL_Surface * surface, double offsetx, double offsety,
double directionx, double directiony, double size,
double rotation, int depth) {
#ifdef WITH_CAIRO
cairo_surface_t *surf = cairo_image_surface_create_for_data( surface->pixels,
CAIRO_FORMAT_RGB24,
surface->w, surface->h,
surface->pitch );
cairo_t *ct = cairo_create(surf);
cairo_set_line_width(ct, 1);
cairo_set_source_rgba(ct, 0,0,0,1);
cairo_move_to(ct, (int)offsetx, (int)offsety);
cairo_line_to(ct, (int)(offsetx + directionx * size), (int)(offsety + directiony * size));
cairo_stroke(ct);
#else
sge_AALine(surface,
(int)offsetx, (int)offsety,
(int)(offsetx + directionx * size), (int)(offsety + directiony * size),
SDL_MapRGB(surface->format, 0, 0, 0));
#endif
if (depth > 0){
// draw left branch
draw_tree(surface,
offsetx + directionx * size,
offsety + directiony * size,
directionx * cos(rotation) + directiony * sin(rotation),
directionx * -sin(rotation) + directiony * cos(rotation),
size * rand_fl() / SCALE + size * (SCALE - 1) / SCALE,
rotation * ROTATION_SCALE,
depth - 1);
// draw right branch
draw_tree(surface,
offsetx + directionx * size,
offsety + directiony * size,
directionx * cos(-rotation) + directiony * sin(-rotation),
directionx * -sin(-rotation) + directiony * cos(-rotation),
size * rand_fl() / SCALE + size * (SCALE - 1) / SCALE,
rotation * ROTATION_SCALE,
depth - 1);
}
}
void render(SDL_Surface * surface){
SDL_FillRect(surface, NULL, SDL_MapRGB(surface->format, 255, 255, 255));
draw_tree(surface,
surface->w / 2.0,
surface->h - 10.0,
0.0, -1.0,
INITIAL_LENGTH,
PI / 8,
BRANCHES);
SDL_UpdateRect(surface, 0, 0, 0, 0);
}
int main(){
SDL_Surface * screen;
SDL_Event evt;
SDL_Init(SDL_INIT_VIDEO);
srand((unsigned)time(NULL));
screen = SDL_SetVideoMode(SIZE, SIZE, 32, SDL_HWSURFACE);
render(screen);
while(1){
if (SDL_PollEvent(&evt)){
if(evt.type == SDL_QUIT) break;
}
SDL_Delay(1);
}
SDL_Quit();
return 0;
}
C++
[[File:fracTree_cpp.png|320px]]
#include <windows.h>
#include <string>
#include <math.h>
//--------------------------------------------------------------------------------------------------
using namespace std;
//--------------------------------------------------------------------------------------------------
const float PI = 3.1415926536f;
//--------------------------------------------------------------------------------------------------
class myBitmap
{
public:
myBitmap() : pen( NULL ) {}
~myBitmap()
{
DeleteObject( pen );
DeleteDC( hdc );
DeleteObject( bmp );
}
bool create( int w, int h )
{
BITMAPINFO bi;
void *pBits;
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;
return true;
}
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;
int width, height;
};
//--------------------------------------------------------------------------------------------------
class vector2
{
public:
vector2() { x = y = 0; }
vector2( int a, int b ) { x = a; y = b; }
void set( int a, int b ) { x = a; y = b; }
void rotate( float angle_r )
{
float _x = static_cast<float>( x ),
_y = static_cast<float>( y ),
s = sinf( angle_r ),
c = cosf( angle_r ),
a = _x * c - _y * s,
b = _x * s + _y * c;
x = static_cast<int>( a );
y = static_cast<int>( b );
}
int x, y;
};
//--------------------------------------------------------------------------------------------------
class fractalTree
{
public:
fractalTree() { _ang = DegToRadian( 24.0f ); }
float DegToRadian( float degree ) { return degree * ( PI / 180.0f ); }
void create( myBitmap* bmp )
{
_bmp = bmp;
float line_len = 130.0f;
vector2 sp( _bmp->getWidth() / 2, _bmp->getHeight() - 1 );
MoveToEx( _bmp->getDC(), sp.x, sp.y, NULL );
sp.y -= static_cast<int>( line_len );
LineTo( _bmp->getDC(), sp.x, sp.y);
drawRL( &sp, line_len, 0, true );
drawRL( &sp, line_len, 0, false );
}
private:
void drawRL( vector2* sp, float line_len, float a, bool rg )
{
line_len *= .75f;
if( line_len < 2.0f ) return;
MoveToEx( _bmp->getDC(), sp->x, sp->y, NULL );
vector2 r( 0, static_cast<int>( line_len ) );
if( rg ) a -= _ang;
else a += _ang;
r.rotate( a );
r.x += sp->x; r.y = sp->y - r.y;
LineTo( _bmp->getDC(), r.x, r.y );
drawRL( &r, line_len, a, true );
drawRL( &r, line_len, a, false );
}
myBitmap* _bmp;
float _ang;
};
//--------------------------------------------------------------------------------------------------
int main( int argc, char* argv[] )
{
ShowWindow( GetConsoleWindow(), SW_MAXIMIZE );
myBitmap bmp;
bmp.create( 640, 512 );
bmp.setPenColor( RGB( 255, 255, 0 ) );
fractalTree tree;
tree.create( &bmp );
BitBlt( GetDC( GetConsoleWindow() ), 0, 20, 648, 512, bmp.getDC(), 0, 0, SRCCOPY );
bmp.saveBitmap( "f://rc//fracTree.bmp" );
system( "pause" );
return 0;
}
//--------------------------------------------------------------------------------------------------
Ceylon
{{trans|Java}} {{libheader|Swing}} {{libheader|AWT}} Be sure to import java.desktop and ceylon.numeric in your module.ceylon file.
import javax.swing {
JFrame { exitOnClose }
}
import java.awt {
Color { white, black },
Graphics
}
import ceylon.numeric.float {
cos,
toRadians,
sin
}
shared void run() {
value fractalTree = object extends JFrame("fractal tree") {
background = black;
setBounds(100, 100, 800, 600);
resizable = false;
defaultCloseOperation = exitOnClose;
shared actual void paint(Graphics g) {
void drawTree(Integer x1, Integer y1, Float angle, Integer depth) {
if (depth <= 0) {
return;
}
value x2 = x1 + (cos(toRadians(angle)) * depth * 10.0).integer;
value y2 = y1 + (sin(toRadians(angle)) * depth * 10.0).integer;
g.drawLine(x1, y1, x2, y2);
drawTree(x2, y2, angle - 20, depth - 1);
drawTree(x2, y2, angle + 20, depth - 1);
}
g.color = white;
drawTree(400, 500, -90.0, 9);
}
};
fractalTree.visible = true;
}
Clojure
{{trans|Java}} {{libheader|Swing}} {{libheader|AWT}}
(import '[java.awt Color Graphics]
'javax.swing.JFrame)
(defn deg-to-radian [deg] (* deg Math/PI 1/180))
(defn cos-deg [angle] (Math/cos (deg-to-radian angle)))
(defn sin-deg [angle] (Math/sin (deg-to-radian angle)))
(defn draw-tree [^Graphics g, x y angle depth]
(when (pos? depth)
(let [x2 (+ x (int (* depth 10 (cos-deg angle))))
y2 (+ y (int (* depth 10 (sin-deg angle))))]
(.drawLine g x y x2 y2)
(draw-tree g x2 y2 (- angle 20) (dec depth))
(recur g x2 y2 (+ angle 20) (dec depth)))))
(defn fractal-tree [depth]
(doto (proxy [JFrame] []
(paint [g]
(.setColor g Color/BLACK)
(draw-tree g 400 500 -90 depth)))
(.setBounds 100 100 800 600)
(.setResizable false)
(.setDefaultCloseOperation JFrame/DISPOSE_ON_CLOSE)
(.show)))
(fractal-tree 9)
Common Lisp
{{libheader|lispbuilder-sdl}} {{trans|Clojure}}
;; (require :lispbuilder-sdl)
(defun deg-to-radian (deg)
"converts degrees to radians"
(* deg pi 1/180))
(defun cos-deg (angle)
"returns cosin of the angle expressed in degress"
(cos (deg-to-radian angle)))
(defun sin-deg (angle)
"returns sin of the angle expressed in degress"
(sin (deg-to-radian angle)))
(defun draw-tree (surface x y angle depth)
"draws a branch of the tree on the sdl-surface"
(when (plusp depth)
(let ((x2 (+ x (round (* depth 10 (cos-deg angle)))))
(y2 (+ y (round (* depth 10 (sin-deg angle))))))
(sdl:draw-line-* x y x2 y2 :surface surface :color sdl:*green*)
(draw-tree surface x2 y2 (- angle 20) (1- depth))
(draw-tree surface x2 y2 (+ angle 20) (1- depth)))))
(defun fractal-tree (depth)
"shows a window with a fractal tree"
(sdl:with-init ()
(sdl:window 800 600 :title-caption "fractal-tree")
(sdl:clear-display sdl:*black*)
(draw-tree sdl:*default-surface* 400 500 -90 depth)
(sdl:update-display)
(sdl:with-events ()
(:video-expose-event ()
(sdl:update-display))
(:quit-event ()
t))))
(fractal-tree 9)
D
SVG Version
{{trans|Perl 6}}
import std.stdio, std.math;
enum width = 1000, height = 1000; // Image dimension.
enum length = 400; // Trunk size.
enum scale = 6.0 / 10; // Branch scale relative to trunk.
void tree(in double x, in double y, in double length, in double angle) {
if (length < 1)
return;
immutable x2 = x + length * angle.cos;
immutable y2 = y + length * angle.sin;
writefln("<line x1='%f' y1='%f' x2='%f' y2='%f' " ~
"style='stroke:black;stroke-width:1'/>", x, y, x2, y2);
tree(x2, y2, length * scale, angle + PI / 5);
tree(x2, y2, length * scale, angle - PI / 5);
}
void main() {
"<svg width='100%' height='100%' version='1.1'
xmlns='http://www.w3.org/2000/svg'>".writeln;
tree(width / 2.0, height, length, 3 * PI / 2);
"</svg>".writeln;
}
Turtle Version
This uses the turtle module from the Dragon Curve task, and the module from the Grayscale Image task. {{trans|Logo}}
import grayscale_image, turtle;
void tree(Color)(Image!Color img, ref Turtle t, in uint depth,
in real step, in real scale, in real angle) {
if (depth == 0) return;
t.forward(img, step);
t.right(angle);
img.tree(t, depth - 1, step * scale, scale, angle);
t.left(2 * angle);
img.tree(t, depth - 1, step * scale, scale, angle);
t.right(angle);
t.forward(img, -step);
}
void main() {
auto img = new Image!Gray(330, 300);
auto t = Turtle(165, 270, -90);
img.tree(t, 10, 80, 0.7, 30);
img.savePGM("fractal_tree.pgm");
}
Alternative version
{{trans|Java}} Using DFL.
import dfl.all;
import std.math;
class FractalTree: Form {
private immutable DEG_TO_RAD = PI / 180.0;
this() {
width = 600;
height = 500;
text = "Fractal Tree";
backColor = Color(0xFF, 0xFF, 0xFF);
startPosition = FormStartPosition.CENTER_SCREEN;
formBorderStyle = FormBorderStyle.FIXED_DIALOG;
maximizeBox = false;
}
private void drawTree(Graphics g, Pen p, int x1, int y1, double angle, int depth) {
if (depth == 0) return;
int x2 = x1 + cast(int) (cos(angle * DEG_TO_RAD) * depth * 10.0);
int y2 = y1 + cast(int) (sin(angle * DEG_TO_RAD) * depth * 10.0);
g.drawLine(p, x1, y1, x2, y2);
drawTree(g, p, x2, y2, angle - 20, depth - 1);
drawTree(g, p, x2, y2, angle + 20, depth - 1);
}
protected override void onPaint(PaintEventArgs ea){
super.onPaint(ea);
Pen p = new Pen(Color(0, 0xAA, 0));
drawTree(ea.graphics, p, 300, 450, -90, 9);
}
}
int main() {
int result = 0;
try {
Application.run(new FractalTree);
} catch(Exception e) {
msgBox(e.msg, "Fatal Error", MsgBoxButtons.OK, MsgBoxIcon.ERROR);
result = 1;
}
return result;
}
EasyLang
[https://easylang.online/apps/fractal-tree.html Run it]
=={{header|F_Sharp|F#}}==
{{trans|Perl 6}}
```fsharp
let (cos, sin, pi) = System.Math.Cos, System.Math.Sin, System.Math.PI
let (width, height) = 1000., 1000. // image dimension
let scale = 6./10. // branch scale relative to trunk
let length = 400. // trunk size
let rec tree x y length angle =
if length >= 1. then
let (x2, y2) = x + length * (cos angle), y + length * (sin angle)
printfn "<line x1='%f' y1='%f' x2='%f' y2='%f' style='stroke:rgb(0,0,0);stroke-width:1'/>"
x y x2 y2
tree x2 y2 (length*scale) (angle + pi/5.)
tree x2 y2 (length*scale) (angle - pi/5.)
printfn "<?xml version='1.0' encoding='utf-8' standalone='no'?>
<!DOCTYPE svg PUBLIC '-//W3C//DTD SVG 1.1//EN'
'http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd'>
<svg width='100%%' height='100%%' version='1.1'
xmlns='http://www.w3.org/2000/svg'>"
tree (width/2.) height length (3.*pi/2.)
printfn "</svg>"
Fantom
using fwt
using gfx
class FractalCanvas : Canvas
{
new make () : super() {}
Void drawTree (Graphics g, Int x1, Int y1, Int angle, Int depth)
{
if (depth == 0) return
Int x2 := x1 + (angle.toFloat.toRadians.cos * depth * 10.0).toInt;
Int y2 := y1 + (angle.toFloat.toRadians.sin * depth * 10.0).toInt;
g.drawLine(x1, y1, x2, y2);
drawTree(g, x2, y2, angle - 20, depth - 1);
drawTree(g, x2, y2, angle + 20, depth - 1);
}
override Void onPaint (Graphics g)
{
drawTree (g, 400, 500, -90, 9)
}
}
class FractalTree
{
public static Void main ()
{
Window
{
title = "Fractal Tree"
size = Size(800, 600)
FractalCanvas(),
}.open
}
}
FreeBASIC
{{trans|BBC BASIC}}
' version 17-03-2017
' compile with: fbc -s gui
Const As Double deg2rad = Atn(1) / 45
Dim Shared As Double scale = 0.76
Dim Shared As Double spread = 25 * deg2rad ' convert degree's to rad's
Sub branch(x1 As ULong, y1 As ULong, size As ULong, angle As Double, depth As ULong)
Dim As ULong x2, y2
x2 = x1 + size * Cos(angle)
y2 = y1 + size * Sin(angle)
Line (x1,y1) - (x2,y2), 2 ' palette color green
If depth > 0 Then
branch(x2, y2, size * scale, angle - spread, depth -1)
branch(x2, y2, size * scale, angle + spread, depth -1)
End If
End Sub
' ------=< MAIN >=-----
Dim As Double angle = -90 * deg2rad ' make sure that the tree grows up
Dim As ULong SizeX = 800
Dim As ULong SizeY = SizeX * 3 \ 4
Dim As Double size = SizeY \ 4
Dim As ULong depth = 11
ScreenRes SizeX, SizeY, 8
WindowTitle ("Fractal Tree")
branch(SizeX\2, SizeY, size, angle, depth)
' empty keyboard buffer
While InKey <> "" : Wend
windowtitle ("Fractal Tree, hit any key to end program")
Sleep
End
Frege
{{Works with|Frege|3.23.888-g4e22ab6}}
module FractalTree where
import Java.IO
import Prelude.Math
data AffineTransform = native java.awt.geom.AffineTransform where
native new :: () -> STMutable s AffineTransform
native clone :: Mutable s AffineTransform -> STMutable s AffineTransform
native rotate :: Mutable s AffineTransform -> Double -> ST s ()
native scale :: Mutable s AffineTransform -> Double -> Double -> ST s ()
native translate :: Mutable s AffineTransform -> Double -> Double -> ST s ()
data BufferedImage = native java.awt.image.BufferedImage where
pure native type_3byte_bgr "java.awt.image.BufferedImage.TYPE_3BYTE_BGR" :: Int
native new :: Int -> Int -> Int -> STMutable s BufferedImage
native createGraphics :: Mutable s BufferedImage -> STMutable s Graphics2D
data Color = pure native java.awt.Color where
pure native black "java.awt.Color.black" :: Color
pure native green "java.awt.Color.green" :: Color
pure native white "java.awt.Color.white" :: Color
pure native new :: Int -> Color
data BasicStroke = pure native java.awt.BasicStroke where
pure native new :: Float -> BasicStroke
data RenderingHints = native java.awt.RenderingHints where
pure native key_antialiasing "java.awt.RenderingHints.KEY_ANTIALIASING" :: RenderingHints_Key
pure native value_antialias_on "java.awt.RenderingHints.VALUE_ANTIALIAS_ON" :: Object
data RenderingHints_Key = pure native java.awt.RenderingHints.Key
data Graphics2D = native java.awt.Graphics2D where
native drawLine :: Mutable s Graphics2D -> Int -> Int -> Int -> Int -> ST s ()
native drawOval :: Mutable s Graphics2D -> Int -> Int -> Int -> Int -> ST s ()
native fillRect :: Mutable s Graphics2D -> Int -> Int -> Int -> Int -> ST s ()
native setColor :: Mutable s Graphics2D -> Color -> ST s ()
native setRenderingHint :: Mutable s Graphics2D -> RenderingHints_Key -> Object -> ST s ()
native setStroke :: Mutable s Graphics2D -> BasicStroke -> ST s ()
native setTransform :: Mutable s Graphics2D -> Mutable s AffineTransform -> ST s ()
data ImageIO = mutable native javax.imageio.ImageIO where
native write "javax.imageio.ImageIO.write" :: MutableIO BufferedImage -> String -> MutableIO File -> IO Bool throws IOException
drawTree :: Mutable s Graphics2D -> Mutable s AffineTransform -> Int -> ST s ()
drawTree g t i = do
let len = 10 -- ratio of length to thickness
shrink = 0.75
angle = 0.3 -- radians
i' = i - 1
g.setTransform t
g.drawLine 0 0 0 len
when (i' > 0) $ do
t.translate 0 (fromIntegral len)
t.scale shrink shrink
rt <- t.clone
t.rotate angle
rt.rotate (-angle)
drawTree g t i'
drawTree g rt i'
main = do
let width = 900
height = 800
initScale = 20
halfWidth = fromIntegral width / 2
buffy <- BufferedImage.new width height BufferedImage.type_3byte_bgr
g <- buffy.createGraphics
g.setRenderingHint RenderingHints.key_antialiasing RenderingHints.value_antialias_on
g.setColor Color.black
g.fillRect 0 0 width height
g.setColor Color.green
t <- AffineTransform.new ()
t.translate halfWidth (fromIntegral height)
t.scale initScale initScale
t.rotate pi
drawTree g t 16
f <- File.new "FractalTreeFrege.png"
void $ ImageIO.write buffy "png" f
Output is [http://funwithsoftware.org/images/2016-FractalTreeFrege.png here] due to [[User talk:Short Circuit#Is file uploading blocked forever?|Is file uploading blocked forever?]]
Go
[[file:GoFtree.png|right|thumb|png converted from output ppm]]
package main
// Files required to build supporting package raster are found in:
// * Bitmap
// * Grayscale image
// * Xiaolin Wu's line algorithm
// * Write a PPM file
import (
"math"
"raster"
)
const (
width = 400
height = 300
depth = 8
angle = 12
length = 50
frac = .8
)
func main() {
g := raster.NewGrmap(width, height)
ftree(g, width/2, height*9/10, length, 0, depth)
g.Bitmap().WritePpmFile("ftree.ppm")
}
func ftree(g *raster.Grmap, x, y, distance, direction float64, depth int) {
x2 := x + distance*math.Sin(direction*math.Pi/180)
y2 := y - distance*math.Cos(direction*math.Pi/180)
g.AaLine(x, y, x2, y2)
if depth > 0 {
ftree(g, x2, y2, distance*frac, direction-angle, depth-1)
ftree(g, x2, y2, distance*frac, direction+angle, depth-1)
}
}
Haskell
An elegant yet universal monoidal solution. {{libheader|Gloss}}
import Graphics.Gloss
type Model = [Picture -> Picture]
fractal :: Int -> Model -> Picture -> Picture
fractal n model pict = pictures $ take n $ iterate (mconcat model) pict
tree1 _ = fractal 10 branches $ Line [(0,0),(0,100)]
where branches = [ Translate 0 100 . Scale 0.75 0.75 . Rotate 30
, Translate 0 100 . Scale 0.5 0.5 . Rotate (-30) ]
main = animate (InWindow "Tree" (800, 800) (0, 0)) white $ tree1 . (* 60)
The solution gives rise to a variety of fractal geometric structures. Each one can be used by substituting tree1 in the main function by the desired one.
--animated tree
tree2 t = fractal 8 branches $ Line [(0,0),(0,100)]
where branches = [ Translate 0 100 . Scale 0.75 0.75 . Rotate t
, Translate 0 100 . Scale 0.6 0.6 . Rotate 0
, Translate 0 100 . Scale 0.5 0.5 . Rotate (-2*t) ]
--animated fractal clock
circles t = fractal 10 model $ Circle 100
where model = [ Translate 0 50 . Scale 0.5 0.5 . Rotate t
, Translate 0 (-50) . Scale 0.5 0.5 . Rotate (-2*t) ]
--Pythagoras tree
pithagor _ = fractal 10 model $ rectangleWire 100 100
where model = [ Translate 50 100 . Scale s s . Rotate 45
, Translate (-50) 100 . Scale s s . Rotate (-45)]
s = 1/sqrt 2
--Sierpinski pentagon
pentaflake _ = fractal 5 model $ pentagon
where model = map copy [0,72..288]
copy a = Scale s s . Rotate a . Translate 0 x
pentagon = Line [ (sin a, cos a) | a <- [0,2*pi/5..2*pi] ]
x = 2*cos(pi/5)
s = 1/(1+x)
'''Alternative solution'''
Using the method of the J contribution.
{{libheader|HGL}}
import Graphics.HGL.Window
import Graphics.HGL.Run
import Control.Arrow
import Control.Monad
import Data.List
enumBase :: Int -> Int -> [[Int]]
enumBase n = mapM (enumFromTo 0). replicate n. pred
psPlus (a,b) (p,q) = (a+p, b+q)
toInt :: Double -> Int
toInt = fromIntegral.round
intPoint = toInt *** toInt
pts n =
map (map (intPoint.psPlus (100,0)). ((0,300):). scanl1 psPlus. ((r,300):). zipWith (\h a -> (h*cos a, h*sin a)) rs) hs
where
[r,h,sr,sh] = [50, pi/5, 0.9, 0.75]
rs = take n $ map (r*) $ iterate(*sr) sr
lhs = map (map (((-1)**).fromIntegral)) $ enumBase n 2
rhs = take n $ map (h*) $ iterate(*sh) 1
hs = map (scanl1 (+). zipWith (*)rhs) lhs
fractalTree :: Int -> IO ()
fractalTree n =
runWindow "Fractal Tree" (500,600)
(\w -> setGraphic w (overGraphics ( map polyline $ pts (n-1))) >> getKey w)
main = fractalTree 10
=={{header|Icon}} and {{header|Unicon}}==
procedure main()
WOpen("size=800,600", "bg=black", "fg=white") | stop("*** cannot open window")
drawtree(400,500,-90,9)
WDone()
end
link WOpen
procedure drawtree(x,y,angle,depth)
if depth > 0 then {
x2 := integer(x + cos(dtor(angle)) * depth * 10)
y2 := integer(y + sin(dtor(angle)) * depth * 10)
DrawLine(x,y,x2,y2)
drawtree(x2,y2,angle-20, depth-1)
drawtree(x2,y2,angle+20, depth-1)
}
return
end
{{libheader|Icon Programming Library}} [http://www.cs.arizona.edu/icon/library/src/gprocs/WOpen.icn WOpen provides graphics I/O]
{{trans|Java}}
J
require'gl2'
L0=: 50 NB. initial length
A0=: 1r8p1 NB. initial angle: pi divided by 8
dL=: 0.9 NB. shrink factor for length
dA=: 0.75 NB. shrink factor for angle
N=: 14 NB. number of branches
L=: L0*dL^1+i.N NB. lengths of line segments
NB. relative angles of successive line segments
A=: A0*(dA^i.N) +/\@:*("1) _1 ^ #:i.2 ^ N
NB. end points for each line segment
P=: 0 0+/\@,"2 +.*.inv (L0,0),"2 L,"0"1 A
P_C_paint=: gllines_jgl2_ bind (10 + ,/"2 P-"1<./,/P)
wd 0 :0
pc P closeok;
xywh 0 0 250 300;
cc C isigraph rightmove bottommove;
pas 0 0;
pshow;
)
See the [[Talk:Fractal tree#J Explanation|talk page]] for some implementation notes.
Java
{{libheader|Swing}} {{libheader|AWT}}
import java.awt.Color;
import java.awt.Graphics;
import javax.swing.JFrame;
public class FractalTree extends JFrame {
public FractalTree() {
super("Fractal Tree");
setBounds(100, 100, 800, 600);
setResizable(false);
setDefaultCloseOperation(EXIT_ON_CLOSE);
}
private void drawTree(Graphics g, int x1, int y1, double angle, int depth) {
if (depth == 0) return;
int x2 = x1 + (int) (Math.cos(Math.toRadians(angle)) * depth * 10.0);
int y2 = y1 + (int) (Math.sin(Math.toRadians(angle)) * depth * 10.0);
g.drawLine(x1, y1, x2, y2);
drawTree(g, x2, y2, angle - 20, depth - 1);
drawTree(g, x2, y2, angle + 20, depth - 1);
}
@Override
public void paint(Graphics g) {
g.setColor(Color.BLACK);
drawTree(g, 400, 500, -90, 9);
}
public static void main(String[] args) {
new FractalTree().setVisible(true);
}
}
JavaScript
Implementation using HTML5 canvas element to draw tree structure.
<body>
<canvas id="canvas" width="600" height="500"></canvas>
<script type="text/javascript">
var elem = document.getElementById('canvas');
var context = elem.getContext('2d');
context.fillStyle = '#C0C0C0';
context.lineWidth = 1;
var deg_to_rad = Math.PI / 180.0;
var depth = 9;
function drawLine(x1, y1, x2, y2, brightness){
context.moveTo(x1, y1);
context.lineTo(x2, y2);
}
function drawTree(x1, y1, angle, depth){
if (depth !== 0){
var x2 = x1 + (Math.cos(angle * deg_to_rad) * depth * 10.0);
var y2 = y1 + (Math.sin(angle * deg_to_rad) * depth * 10.0);
drawLine(x1, y1, x2, y2, depth);
drawTree(x2, y2, angle - 20, depth - 1);
drawTree(x2, y2, angle + 20, depth - 1);
}
}
context.beginPath();
drawTree(300, 500, -90, depth);
context.closePath();
context.stroke();
</script>
</body>
</html>
jq
The following generates SVG, which can be viewed by following the link below.
# width and height define the outer dimensions;
# len defines the trunk size;
# scale defines the branch length relative to the trunk;
def main(width; height; len; scale):
def PI: (1|atan)*4;
def precision(n):
def pow(k): . as $in | reduce range(0;k) as $i (1; .*$in);
if . < 0 then - (-. | precision(n))
else
(10|pow(n)) as $power
| (. * 10 * $power) | floor as $x | ($x % 10) as $r
| ((if $r < 5 then $x else $x + 5 end) / 10 | floor) / $power
end;
def p2: precision(2);
def tree(x; y; len; angle):
if len < 1 then empty
else
(x + len * (angle|cos)) as $x2
| (y + len * (angle|sin)) as $y2
| (if len < 10 then 1 else 2 end) as $swidth
| (if len < 10 then "blue" else "black" end) as $stroke
| "<line x1='\(x|p2)' y1='\(y|p2)' x2='\($x2|p2)' y2='\($y2|p2)' style='stroke:\($stroke); stroke-width:\($swidth)'/>",
tree($x2; $y2; len * scale; angle + PI / 5),
tree($x2; $y2; len * scale; angle - PI / 5)
end
;
"<svg width='100%' height='100%' version='1.1'
xmlns='http://www.w3.org/2000/svg'>",
tree(width / 2; height; len; 3 * PI / 2),
"</svg>"
;
main(1000; 1000; 400; 6/10)
{{out}} $ jq -r -n -r -f Fractal_tree_svg.jq > Fractal_tree.svg
[https://drive.google.com/file/d/0BwMI1gZaY2-MWEI4d1kxNHZ4cGs/view?usp=sharing Fractal_tree.svg]
Julia
{{trans|F#}}
const width = height = 1000.0
const trunklength = 400.0
const scalefactor = 0.6
const startingangle = 1.5 * pi
const deltaangle = 0.2 * pi
function tree(fh, x, y, len, theta)
if len >= 1.0
x2 = x + len * cos(theta)
y2 = y + len * sin(theta)
write(fh, "<line x1='$x' y1='$y' x2='$x2' y2='$y2' style='stroke:rgb(0,0,0);stroke-width:1'/>\n")
tree(fh, x2, y2, len * scalefactor, theta + deltaangle)
tree(fh, x2, y2, len * scalefactor, theta - deltaangle)
end
end
outsvg = open("tree.svg", "w")
write(outsvg,
"""<?xml version='1.0' encoding='utf-8' standalone='no'?>
<!DOCTYPE svg PUBLIC '-//W3C//DTD SVG 1.1//EN'
'http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd'>
<svg width='100%%' height='100%%' version='1.1'
xmlns='http://www.w3.org/2000/svg'>\n""")
tree(outsvg, 0.5 * width, height, trunklength, startingangle)
write(outsvg, "</svg>\n") # view file tree.svg in browser
Kotlin
{{trans|Java}}
// version 1.1.2
import java.awt.Color
import java.awt.Graphics
import javax.swing.JFrame
class FractalTree : JFrame("Fractal Tree") {
init {
background = Color.black
setBounds(100, 100, 800, 600)
isResizable = false
defaultCloseOperation = EXIT_ON_CLOSE
}
private fun drawTree(g: Graphics, x1: Int, y1: Int, angle: Double, depth: Int) {
if (depth == 0) return
val x2 = x1 + (Math.cos(Math.toRadians(angle)) * depth * 10.0).toInt()
val y2 = y1 + (Math.sin(Math.toRadians(angle)) * depth * 10.0).toInt()
g.drawLine(x1, y1, x2, y2)
drawTree(g, x2, y2, angle - 20, depth - 1)
drawTree(g, x2, y2, angle + 20, depth - 1)
}
override fun paint(g: Graphics) {
g.color = Color.white
drawTree(g, 400, 500, -90.0, 9)
}
}
fun main(args: Array<String>) {
FractalTree().isVisible = true
}
Liberty BASIC
LB includes Logo-type turtle commands, so can be drawn that way as well as that shown here.
NoMainWin
sw = 640 : sh = 480
WindowWidth = sw+8 : WindowHeight = sh+31
UpperLeftX = (DisplayWidth -sw)/2
UpperLeftY = (DisplayHeight-sh)/2
Open"Fractal Tree" For Graphics_nf_nsb As #g
#g "Down; Color darkgreen; TrapClose halt"
h$ = "#g"
'initial assignments
initAngle = Acs(-1)*1.5 'radian equivalent of 270 degrees
theta = 29 * (Acs(-1)/180) 'convert 29 degrees to radians
length = 110 'length in pixels
depth = 25 'max recursion depth
'draw the tree
Call tree h$, 320, 470, initAngle, theta, length, depth
#g "Flush; when leftButtonDown halt" 'L-click to exit
Wait
Sub halt handle$
Close #handle$
End
End Sub
Sub tree h$, x, y, initAngle, theta, length, depth
Scan
newX = Cos(initAngle) * length + x
newY = Sin(initAngle) * length + y
#h$ "Line ";x;" ";y;" ";newX;" ";newY
length = length * .78
depth = depth - 1
If depth > 0 Then
Call tree h$, newX, newY, initAngle-theta, theta, length, depth
Call tree h$, newX, newY, initAngle+theta, theta, length, depth
End If
End Sub
Lingo
----------------------------------------
-- Creates an image of a fractal tree
-- @param {integer} width
-- @param {integer} height
-- @param {integer} fractalDepth
-- @param {integer|float} initSize
-- @param {float} spreadAngle
-- @param {float} [scaleFactor=1.0]
-- @return {image}
----------------------------------------
on fractalTree (width, height, fractalDepth, initSize, spreadAngle, scaleFactor)
if voidP(scaleFactor) then scaleFactor = 1.0
img = image(width, height, 24)
img.fill(img.rect, rgb(0,0,0))
_drawTree(img, width/2, height, -PI/2, fractalDepth, initSize, spreadAngle, scaleFactor)
return img
end
on _drawTree (img, x1, y1, angle, depth, size, spreadAngle, scaleFactor)
if (depth) then
x2 = x1 + cos(angle)*depth*size
y2 = y1 + sin(angle)*depth*size
img.draw(x1, y1, x2, y2, [#color:rgb(255,255,255)])
_drawTree(img, x2, y2, angle-spreadAngle, depth-1, size*ScaleFactor, spreadAngle, scaleFactor)
_drawTree(img, x2, y2, angle+spreadAngle, depth-1, size*ScaleFactor, spreadAngle, scaleFactor)
end if
end
Usage:
fractalDepth = 10
initSize = 7.0
spreadAngle = 35*PI/180
scaleFactor = 0.95
img = fractalTree(480, 380, fractalDepth, initSize, spreadAngle, scaleFactor)
Logo
to tree :depth :length :scale :angle
if :depth=0 [stop]
setpensize round :depth/2
forward :length
right :angle
tree :depth-1 :length*:scale :scale :angle
left 2*:angle
tree :depth-1 :length*:scale :scale :angle
right :angle
back :length
end
clearscreen
tree 10 80 0.7 30
Lua
Needs LÖVE 2D Engine
g, angle = love.graphics, 26 * math.pi / 180
wid, hei = g.getWidth(), g.getHeight()
function rotate( x, y, a )
local s, c = math.sin( a ), math.cos( a )
local a, b = x * c - y * s, x * s + y * c
return a, b
end
function branches( a, b, len, ang, dir )
len = len * .76
if len < 5 then return end
g.setColor( len * 16, 255 - 2 * len , 0 )
if dir > 0 then ang = ang - angle
else ang = ang + angle
end
local vx, vy = rotate( 0, len, ang )
vx = a + vx; vy = b - vy
g.line( a, b, vx, vy )
branches( vx, vy, len, ang, 1 )
branches( vx, vy, len, ang, 0 )
end
function createTree()
local lineLen = 127
local a, b = wid / 2, hei - lineLen
g.setColor( 160, 40 , 0 )
g.line( wid / 2, hei, a, b )
branches( a, b, lineLen, 0, 1 )
branches( a, b, lineLen, 0, 0 )
end
function love.load()
canvas = g.newCanvas( wid, hei )
g.setCanvas( canvas )
createTree()
g.setCanvas()
end
function love.draw()
g.draw( canvas )
end
=={{header|Mathematica}} / {{header|Wolfram Language}}==
fractalTree[
pt : {_, _}, \[Theta]orient_: \[Pi]/2, \[Theta]sep_: \[Pi]/9,
depth_Integer: 9] := Module[{pt2},
If[depth == 0, Return[]];
pt2 = pt + {Cos[\[Theta]orient], Sin[\[Theta]orient]}*depth;
DeleteCases[
Flatten@{
Line[{pt, pt2}],
fractalTree[pt2, \[Theta]orient - \[Theta]sep, \[Theta]sep,
depth - 1],
fractalTree[pt2, \[Theta]orient + \[Theta]sep, \[Theta]sep,
depth - 1]
},
Null
]
]
Graphics[fractalTree[{0, 0}, \[Pi]/2, \[Pi]/9]]
[[File:MathFractalTree.png]]
NetRexx
{{trans|Java}} {{libheader|Swing}} {{libheader|AWT}}
/* NetRexx */
options replace format comments java crossref symbols binary
import java.awt.Color
import java.awt.Graphics
import javax.swing.JFrame
class RFractalTree public extends JFrame
properties constant
isTrue = (1 == 1)
isFalse = \isTrue
-- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
method RFractalTree() public
super('Fractal Tree')
setBounds(100, 100, 800, 600)
setResizable(isFalse)
setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE)
return
-- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
method drawTree(g = Graphics, x1 = int, y1 = int, angle = double, depth = int) private
if depth \= 0 then do
x2 = x1 + (int Math.cos(Math.toRadians(angle)) * depth * 10.0)
y2 = y1 + (int Math.sin(Math.toRadians(angle)) * depth * 10.0)
g.drawLine(x1, y1, x2, y2)
drawTree(g, x2, y2, angle - 20, depth - 1)
drawTree(g, x2, y2, angle + 20, depth - 1)
end
return
-- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
method paint(g = Graphics) public
g.setColor(Color.BLACK)
drawTree(g, 400, 500, -90, 9)
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method main(args = String[])public static
RFractalTree().setVisible(isTrue)
return
OCaml
{{libheader|ocaml-cairo}}
#directory "+cairo"
#load "bigarray.cma"
#load "cairo.cma"
let img_name = "/tmp/fractree.png"
let width = 480
let height = 640
let level = 9
let line_width = 4.0
let color = (1.0, 0.5, 0.0)
let pi = 4.0 *. atan 1.0
let angle_split = pi *. 0.12
let angle_rand = pi *. 0.12
let () =
Random.self_init();
let surf = Cairo.image_surface_create Cairo.FORMAT_RGB24 ~width ~height in
let ctx = Cairo.create surf in
Cairo.set_antialias ctx Cairo.ANTIALIAS_SUBPIXEL;
Cairo.set_line_cap ctx Cairo.LINE_CAP_ROUND;
let draw_line (x,y) (dx,dy) =
Cairo.move_to ctx x (float height -. y);
Cairo.line_to ctx dx (float height -. dy);
Cairo.stroke ctx;
in
let set_color (r,g,b) v =
Cairo.set_source_rgb ctx ~red:(r *. v) ~green:(g *. v) ~blue:(b *. v);
in
let trans_pos (x,y) len angle =
let _x = cos angle
and _y = sin angle in
(x +. (_x *. len),
y +. (_y *. len))
in
let rec loop ~level ~pos ~line_width ~line_len
~angle ~angle_split ~angle_rand ~intc =
if level > 0 then begin
(* draw the current segment *)
Cairo.set_line_width ctx line_width;
set_color color intc;
let pos_to = trans_pos pos line_len angle in
draw_line pos pos_to;
(* evolution of the parameters *)
let line_width = line_width *. 0.8
and line_len = line_len *. 0.62
and angle_split = angle_split *. 1.02
and angle_rand = angle_rand *. 1.02
and intc = intc *. 0.9
in
let next_loop =
loop ~level:(pred level) ~pos:pos_to ~intc
~line_width ~line_len ~angle_split ~angle_rand
in
(* split *)
let angle_left = angle +. angle_split +. Random.float angle_rand
and angle_right = angle -. angle_split -. Random.float angle_rand
in
next_loop ~angle:angle_left;
next_loop ~angle:angle_right
end
in
let pos = (float width *. 0.5, float height *. 0.1)
and line_len = float height *. 0.3
in
loop ~level ~pos ~angle:(pi /. 2.0)
~angle_split ~angle_rand
~line_width ~line_len ~intc:1.0;
Cairo_png.surface_write_to_file surf img_name
(*Cairo_png.surface_write_to_channel surf stdout*)
PARI/GP
[[File:FracTree1.png|right|thumb|Output FracTree1.png]] [[File:FracTree2.png|right|thumb|Output FracTree2.png]] [[File:FracTree3.png|right|thumb|Output FracTree3.png]]
This version with recursion, in general, is a translation of JavaScript version. Some tweaks and options were added to make it reusable and outputting different size of a tree.
{{trans|JavaScript}}
{{Works with|PARI/GP|2.7.4 and above}}
\\ Fractal tree (w/recursion)
\\ 4/10/16 aev
plotline(x1,y1,x2,y2)={plotmove(0, x1,y1);plotrline(0,x2-x1,y2-y1);}
plottree(x,y,a,d)={
my(x2,y2,d2r=Pi/180.0,a1=a*d2r,d1);
if(d<=0, return(););
if(d>0, d1=d*10.0;
x2=x+cos(a1)*d1;
y2=y+sin(a1)*d1;
plotline(x,y,x2,y2);
plottree(x2,y2,a-20,d-1);
plottree(x2,y2,a+20,d-1),
return();
);
}
FractalTree(depth,size)={
my(dx=1,dy=0,ttlb="Fractal Tree, depth ",ttl=Str(ttlb,depth));
print1(" *** ",ttl); print(", size ",size);
plotinit(0);
plotcolor(0,6); \\green
plotscale(0, -size,size, 0,size);
plotmove(0, 0,0);
plottree(0,0,90,depth);
plotdraw([0,size,size]);
}
{\\ Executing:
FractalTree(9,500); \\FracTree1.png
FractalTree(12,1100); \\FracTree2.png
FractalTree(15,1500); \\FracTree3.png
}
{{Output}}
*** Fractal Tree, depth 9, size 500
*** last result computed in 140 ms.
*** Fractal Tree, depth 12, size 1100
*** last result computed in 236 ms.
*** Fractal Tree, depth 15, size 1500
*** last result computed in 1,095 ms
Perl
using the [http://search.cpan.org/~lds/GD-2.45/GD/Simple.pm GD::Simple] module.
use GD::Simple;
my ($width, $height) = (1000,1000); # image dimension
my $scale = 6/10; # branch scale relative to trunk
my $length = 400; # trunk size
my $img = GD::Simple->new($width,$height);
$img->fgcolor('black');
$img->penSize(1,1);
tree($width/2, $height, $length, 270);
print $img->png;
sub tree
{
my ($x, $y, $len, $angle) = @_;
return if $len < 1;
$img->moveTo($x,$y);
$img->angle($angle);
$img->line($len);
($x, $y) = $img->curPos();
tree($x, $y, $len*$scale, $angle+35);
tree($x, $y, $len*$scale, $angle-35);
}
Perl 6
Image is created in [[wp:SVG|SVG]] format.
my ($width, $height) = (1000,1000); # image dimension
my $scale = 6/10; # branch scale relative to trunk
my $length = 400; # trunk size
say "<?xml version='1.0' encoding='utf-8' standalone='no'?>
<!DOCTYPE svg PUBLIC '-//W3C//DTD SVG 1.1//EN'
'http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd'>
<svg width='100%' height='100%' version='1.1'
xmlns='http://www.w3.org/2000/svg'>";
tree($width/2, $height, $length, 3*pi/2);
say "</svg>";
multi tree($, $, $length where { $length < 1}, $) {}
multi tree($x, $y, $length, $angle)
{
my ($x2, $y2) = ( $x + $length * $angle.cos, $y + $length * $angle.sin);
say "<line x1='$x' y1='$y' x2='$x2' y2='$y2' style='stroke:rgb(0,0,0);stroke-width:1'/>";
tree($x2, $y2, $length*$scale, $angle + pi/5);
tree($x2, $y2, $length*$scale, $angle - pi/5);
}
Phix
{{Trans|XPL0}} {{libheader|pGUI}}
--
-- demo\rosetta\FractalTree.exw
--
include pGUI.e
Ihandle dlg, canvas
cdCanvas cddbuffer, cdcanvas
procedure drawTree(integer level, atom angle, atom len, integer x, integer y)
integer xn = x + floor(len*cos(angle))
integer yn = y + floor(len*sin(angle))
integer red = 255-level*8
integer grn = level*12+100
cdCanvasSetForeground(cddbuffer, red*#10000 + grn*#100)
cdCanvasLineWidth(cddbuffer,floor(5-level/3))
cdCanvasLine(cddbuffer, x, 480-y, xn, 480-yn)
if level<12 then
drawTree(level+1, angle-0.4, len*0.8, xn, yn) --left
drawTree(level+1, angle+0.1, len*0.8, xn, yn) --right
end if
end procedure
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
cdCanvasActivate(cddbuffer)
cdCanvasClear(cddbuffer)
drawTree(0, -PI/2.0, 80.0, 360, 460)
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_PARCHMENT)
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", "640x480")
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
dlg = IupDialog(canvas,"RESIZE=NO")
IupSetAttribute(dlg, "TITLE", "Fractal Tree")
IupSetCallback(dlg, "K_ANY", Icallback("esc_close"))
IupShow(dlg)
IupMainLoop()
IupClose()
end procedure
main()
PHP
Image is created with GD module. Code adapted from the JavaScript version.
<?php
header("Content-type: image/png");
$width = 512;
$height = 512;
$img = imagecreatetruecolor($width,$height);
$bg = imagecolorallocate($img,255,255,255);
imagefilledrectangle($img, 0, 0, $width, $width, $bg);
$depth = 8;
function drawTree($x1, $y1, $angle, $depth){
global $img;
if ($depth != 0){
$x2 = $x1 + (int)(cos(deg2rad($angle)) * $depth * 10.0);
$y2 = $y1 + (int)(sin(deg2rad($angle)) * $depth * 10.0);
imageline($img, $x1, $y1, $x2, $y2, imagecolorallocate($img,0,0,0));
drawTree($x2, $y2, $angle - 20, $depth - 1);
drawTree($x2, $y2, $angle + 20, $depth - 1);
}
}
drawTree($width/2, $height, -90, $depth);
imagepng($img);
imagedestroy($img);
?>
PicoLisp
This uses the 'brez' line drawing function from [[Bitmap/Bresenham's line algorithm#PicoLisp]].
(load "@lib/math.l")
(de fractalTree (Img X Y A D)
(unless (=0 D)
(let (R (*/ A pi 180.0) DX (*/ (cos R) D 0.2) DY (*/ (sin R) D 0.2))
(brez Img X Y DX DY)
(fractalTree Img (+ X DX) (+ Y DY) (+ A 30.0) (dec D))
(fractalTree Img (+ X DX) (+ Y DY) (- A 30.0) (dec D)) ) ) )
(let Img (make (do 300 (link (need 400 0)))) # Create image 400 x 300
(fractalTree Img 200 300 -90.0 10) # Draw tree
(out "img.pbm" # Write to bitmap file
(prinl "P1")
(prinl 400 " " 300)
(mapc prinl Img) ) )
PostScript
%!PS
%%BoundingBox: 0 0 300 300
%%EndComments
/origstate save def
/ld {load def} bind def
/m /moveto ld /g /setgray ld /t /translate ld
/r /rotate ld /l /lineto ld
/rl /rlineto ld /s /scale ld
%%EndProlog
/PerturbateAngle {} def
/PerturbateLength {} def
% ** To add perturbations, define properly PerturbateAngle and PerturbateLength, e.g.
% /PerturbateAngle {realtime 20 mod realtime 2 mod 1 eq {add} {sub} ifelse} def
% /PerturbateLength {realtime 10 mod 100 div realtime 2 mod 1 eq {add} {sub} ifelse} def
/fractree { % [INITLENGTH, SPLIT, SFACTOR, BRANCHES]
dup 3 get 0 gt
{
0 0 m dup 0 get 0 exch l
gsave
dup 0 get 0 exch t
dup 1 get PerturbateAngle r
dup 2 get dup PerturbateLength s
dup aload pop 1 sub 4 array astore fractree stroke
grestore
gsave
dup 0 get 0 exch t
dup 1 get neg PerturbateAngle r
dup 2 get dup PerturbateLength s
dup aload pop 1 sub 4 array astore fractree stroke
grestore
} if pop
} def
%
/BRANCHES 14 def
/INITLENGTH 50 def
/SPLIT 35 def
/SFACTOR .75 def
%
% BB check
%0 0 m 300 0 rl 0 300 rl -300 0 rl closepath stroke
%
0 g 150 0 t
[INITLENGTH SPLIT SFACTOR BRANCHES] fractree stroke
%
showpage origstate restore
%%EOF
Shorter version:
%!PS-Adobe-3.0
%%BoundingBox: 0 0 300 300
/!0 { dup 1 sub dup 0 gt } def
/trunk { 0 0 moveto 0 60 translate 0 0 lineto stroke } def
/branch { gsave scale rotate dup d exch sub d div setgray tree grestore } def
/L { 30 .8 .8 branch } def
/M {-10 .7 .7 branch } def
/R {-35 .7 .7 branch } def
/tree { trunk !0 { L M R } if pop } def
/d 10 def 5 setlinewidth 1 setlinecap 170 20 translate d tree pop
%%EOF
=={{header|POV-Ray}}==
#include "colors.inc"
#include "transforms.inc"
#declare CamLoc = <0, 5, 0>;
#declare CamLook = <0,0,0>;
camera
{
location CamLoc
look_at CamLook
rotate y*90
}
light_source
{
CamLoc
color White
}
#declare Init_Height = 10;
#declare Spread_Ang = 35;
#declare Branches = 14;
#declare Scaling_Factor = 0.75;
#macro Stick(P0, P1)
cylinder {
P0, P1, 0.02
texture { pigment { Green } }
}
#end
#macro FractalTree(O, D, S, R, B)
#if (B > 0)
Stick(O, O+D*S)
FractalTree(O+D*S, vtransform(D, transform{rotate y*R}),
S*Scaling_Factor, R, B-1)
FractalTree(O+D*S, vtransform(D, transform{rotate -y*R}),
S*Scaling_Factor, R, B-1)
#end
#end
union {
FractalTree(<-2,0,0>, <1,0,0>, 1, Spread_Ang, Branches)
}
Prolog
SWI-Prolog has a graphic interface : XPCE.
fractal :-
new(D, window('Fractal')),
send(D, size, size(800, 600)),
drawTree(D, 400, 500, -90, 9),
send(D, open).
drawTree(_D, _X, _Y, _Angle, 0).
drawTree(D, X1, Y1, Angle, Depth) :-
X2 is X1 + cos(Angle * pi / 180.0) * Depth * 10.0,
Y2 is Y1 + sin(Angle * pi / 180.0) * Depth * 10.0,
new(Line, line(X1, Y1, X2, Y2, none)),
send(D, display, Line),
A1 is Angle - 30,
A2 is Angle + 30,
De is Depth - 1,
drawTree(D, X2, Y2, A1, De),
drawTree(D, X2, Y2, A2, De).
PureBasic
#Spread_Ang = 35
#Scaling_Factor = 0.75
#Deg_to_Rad = #PI / 180
#SizeH = 500
#SizeV = 375
#Init_Size = 100
Procedure drawTree(x1, y1, Size, theta, depth)
Protected x2 = x1 + Cos(theta * #Deg_to_Rad) * Size, y2 = y1 + Sin(theta * #Deg_to_Rad) * Size
LineXY(x1, y1, x2, y2, RGB(255, 255, 255))
If depth <= 0
ProcedureReturn
EndIf
;draw left branch
drawTree(x2, y2, Size * #Scaling_Factor, theta - #Spread_Ang, depth - 1)
;draw right branch
drawTree(x2, y2, Size * #Scaling_Factor, theta + #Spread_Ang, depth - 1)
EndProcedure
OpenWindow(0, 0, 0, #SizeH, #SizeV, "Fractal Tree", #PB_Window_SystemMenu)
Define fractal = CreateImage(#PB_Any, #SizeH, #SizeV, 32)
ImageGadget(0, 0, 0, 0, 0, ImageID(fractal))
If StartDrawing(ImageOutput(fractal))
drawTree(#SizeH / 2, #SizeV, #Init_Size, -90, 9)
StopDrawing()
SetGadgetState(0, ImageID(fractal))
EndIf
Repeat: Until WaitWindowEvent(10) = #PB_Event_CloseWindow
[[Image:PB_FractalTree.png]]
Python
[[File:fractal-tree-python.png|right|thumb]] {{libheader|pygame}}
import pygame, math
pygame.init()
window = pygame.display.set_mode((600, 600))
pygame.display.set_caption("Fractal Tree")
screen = pygame.display.get_surface()
def drawTree(x1, y1, angle, depth):
if depth:
x2 = x1 + int(math.cos(math.radians(angle)) * depth * 10.0)
y2 = y1 + int(math.sin(math.radians(angle)) * depth * 10.0)
pygame.draw.line(screen, (255,255,255), (x1, y1), (x2, y2), 2)
drawTree(x2, y2, angle - 20, depth - 1)
drawTree(x2, y2, angle + 20, depth - 1)
def input(event):
if event.type == pygame.QUIT:
exit(0)
drawTree(300, 550, -90, 9)
pygame.display.flip()
while True:
input(pygame.event.wait())
R
{{trans|PARI/GP}} {{Works with|R|3.3.3 and above}} [[File:FRTR9.png|200px|right|thumb|Output FRTR9.png]] [[File:FRTR12.png|200px|right|thumb|Output FRTR12.png]] [[File:FRTR15.png|200px|right|thumb|Output FRTR15.png]]
## Recursive FT plotting
plotftree <- function(x, y, a, d, c) {
x2=y2=0; d2r=pi/180.0; a1 <- a*d2r; d1=0;
if(d<=0) {return()}
if(d>0)
{ d1=d*10.0;
x2=x+cos(a1)*d1;
y2=y+sin(a1)*d1;
segments(x*c, y*c, x2*c, y2*c, col='darkgreen');
plotftree(x2,y2,a-20,d-1,c);
plotftree(x2,y2,a+20,d-1,c);
#return(2);
}
}
## Plotting Fractal Tree. aev 3/27/17
## ord - order/depth, c - scale, xsh - x-shift, fn - file name,
## ttl - plot title.
pFractalTree <- function(ord, c=1, xsh=0, fn="", ttl="") {
cat(" *** START FRT:", date(), "\n");
m=640;
if(fn=="") {pf=paste0("FRTR", ord, ".png")} else {pf=paste0(fn, ".png")};
if(ttl=="") {ttl=paste0("Fractal tree, order - ", ord)};
cat(" *** Plot file -", pf, "title:", ttl, "\n");
##plot(NA, xlim=c(0,m), ylim=c(-m,0), xlab="", ylab="", main=ttl);
plot(NA, xlim=c(0,m), ylim=c(0,m), xlab="", ylab="", main=ttl);
plotftree(m/2+xsh,100,90,ord,c);
dev.copy(png, filename=pf, width=m, height=m);
dev.off(); graphics.off();
cat(" *** END FRT:",date(),"\n");
}
## Executing:
pFractalTree(9);
pFractalTree(12,0.6,210);
pFractalTree(15,0.35,600);
{{Output}}
> pFractalTree(9);
*** START FRT: Tue Mar 28 16:49:49 2017
*** Plot file - FRTR9.png title: Fractal tree, order - 9
*** END FRT: Tue Mar 28 16:49:50 2017
> pFractalTree(12,0.6,210);
*** START FRT: Tue Mar 28 17:32:15 2017
*** Plot file - FRTR12.png title: Fractal tree, order - 12
*** END FRT: Tue Mar 28 17:32:16 2017
> pFractalTree(15,0.35,600);
*** START FRT: Tue Mar 28 17:38:34 2017
*** Plot file - FRTR15.png title: Fractal tree, order - 15
*** END FRT: Tue Mar 28 17:38:41 2017
Racket
[[File:tree-racket.png|right|thumb]]
#lang racket
(require graphics/turtles)
(define (tree n)
(when (> n 1)
(draw (/ n 2))
(tprompt (split* (turn 60) (turn -60))
(tree (/ n 2)))
(draw (/ n 2))
(turn 5)
(tree (- n 1))))
(turtles #t) (move 100) (turn 90) (move -200)
(tree 35)
(save-turtle-bitmap "tree.png" 'png)
Ring
load "guilib.ring"
new qapp
{
win1 = new qwidget() {
setwindowtitle("drawing using qpainter")
setgeometry(100,100,500,500)
label1 = new qlabel(win1) {
setgeometry(10,10,400,400)
settext("")
}
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)
sizex = 400
sizey = 200
depth = 10
tree(self, sizex, 0, sizey/2, 90, depth)
endpaint()
}
label1 { setpicture(p1) show() }
func tree myObj, x1, y1, size, angle, depth
myObj{
scale = 0.76
spread = 25
x2 = x1 + size * cos(angle)
y2 = y1 + size * sin(angle)
drawline(x1, y1, x2, y2)
if depth > 0
tree(self, x2, y2, size * scale, angle - spread, depth - 1)
tree(self, x2, y2, size * scale, angle + spread, depth - 1) ok}
Output:
[[File:CalmoSoftFractalTree.jpg]]
Ruby
{{libheader|Shoes}}
Shoes.app(:title => "Fractal Tree", :width => 600, :height => 600) do
background "#fff"
stroke "#000"
@deg_to_rad = Math::PI / 180.0
def drawTree(x1, y1, angle, depth)
if depth != 0
x2 = x1 + (Math.cos(angle * @deg_to_rad) * depth * 10.0).to_i
y2 = y1 + (Math.sin(angle * @deg_to_rad) * depth * 10.0).to_i
line x1, y1, x2, y2
drawTree(x2, y2, angle - 20, depth - 1)
drawTree(x2, y2, angle + 20, depth - 1)
end
end
drawTree(300,550,-90,9)
end
Rust
{{libheader|Piston}}
//Cargo deps :
// piston = "0.35.0"
// piston2d-graphics = "0.23.0"
// piston2d-opengl_graphics = "0.49.0"
// pistoncore-glutin_window = "0.42.0"
extern crate piston;
extern crate graphics;
extern crate opengl_graphics;
extern crate glutin_window;
use piston::window::WindowSettings;
use piston::event_loop::{Events, EventSettings};
use piston::input::RenderEvent;
use glutin_window::GlutinWindow as Window;
use opengl_graphics::{GlGraphics, OpenGL};
use graphics::{clear, line, Context};
const ANG: f64 = 20.0;
const COLOR: [f32; 4] = [1.0, 0.0, 0.5, 1.0];
const LINE_THICKNESS: f64 = 5.0;
const DEPTH: u32 = 11;
fn main() {
let mut window: Window = WindowSettings::new("Fractal Tree", [1024, 768])
.opengl(OpenGL::V3_2)
.exit_on_esc(true)
.build()
.unwrap();
let mut gl = GlGraphics::new(OpenGL::V3_2);
let mut events = Events::new(EventSettings::new());
while let Some(e) = events.next(&mut window) {
if let Some(args) = e.render_args() {
gl.draw(args.viewport(), |c, g| {
clear([1.0, 1.0, 1.0, 1.0], g);
draw_fractal_tree(512.0, 700.0, 0.0, DEPTH, c, g);
});
}
}
}
fn draw_fractal_tree(x1: f64, y1: f64, angle: f64, depth: u32, c: Context, g: &mut GlGraphics) {
let x2 = x1 + angle.to_radians().sin() * depth as f64 * 10.0;
let y2 = y1 - angle.to_radians().cos() * depth as f64 * 10.0;
line(
COLOR,
LINE_THICKNESS * depth as f64 * 0.2,
[x1, y1, x2, y2],
c.transform,
g,
);
if depth > 0 {
draw_fractal_tree(x2, y2, angle - ANG, depth - 1, c, g);
draw_fractal_tree(x2, y2, angle + ANG, depth - 1, c, g);
}
}
Scala
Adapted from the Java version. Screenshot below.
import swing._
import java.awt.{RenderingHints, BasicStroke, Color}
object FractalTree extends SimpleSwingApplication {
val DEPTH = 9
def top = new MainFrame {
contents = new Panel {
preferredSize = new Dimension(600, 500)
override def paintComponent(g: Graphics2D) {
draw(300, 460, -90, DEPTH)
def draw(x1: Int, y1: Int, angle: Double, depth: Int) {
if (depth > 0) {
val x2 = x1 + (math.cos(angle.toRadians) * depth * 10).toInt
val y2 = y1 + (math.sin(angle.toRadians) * depth * 10).toInt
g.setColor(Color.getHSBColor(0.25f - depth * 0.125f / DEPTH, 0.9f, 0.6f))
g.setStroke(new BasicStroke(depth))
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
g.drawLine(x1, y1, x2, y2)
draw(x2, y2, angle - 20, depth - 1)
draw(x2, y2, angle + 20, depth - 1)
}
}
}
}
}
}
[[File:scalaTree.png]]
Scheme
The tree is created as a list of line segments, which can then be drawn on a required device. For this program, the tree is output to an eps file.
(import (scheme base)
(scheme file)
(scheme inexact)
(scheme write))
(define *scale* 10) ; controls overall size of tree
(define *split* 20) ; controls angle of split (in degrees)
;; construct lines for tree as list of 5-tuples (x1 y1 x2 y2 depth)
;; - x1 y1 is start point
;; - angle of this line, in radians
;; - depth, depth within tree (controls length of line)
(define (create-tree x1 y1 angle depth)
(define (degrees->radians d)
(let ((pi 3.14159265358979323846264338327950288419716939937510582097))
(* d pi 1/180)))
;
(if (zero? depth)
'()
(let ((x2 (+ x1 (* (cos (degrees->radians angle)) depth *scale*)))
(y2 (+ y1 (* (sin (degrees->radians angle)) depth *scale*))))
(append (list (map truncate (list x1 y1 x2 y2 depth)))
(create-tree x2 y2 (- angle *split*) (- depth 1))
(create-tree x2 y2 (+ angle *split*) (- depth 1))))))
;; output the tree to an eps file
(define (output-tree-as-eps filename tree)
(when (file-exists? filename) (delete-file filename))
(with-output-to-file
filename
(lambda ()
(display "%!PS-Adobe-3.0 EPSF-3.0\n%%BoundingBox: 0 0 800 800\n")
;; add each line - sets linewidth based on depth in tree
(for-each (lambda (line)
(display
(string-append "newpath\n"
(number->string (list-ref line 0)) " "
(number->string (list-ref line 1)) " "
"moveto\n"
(number->string (list-ref line 2)) " "
(number->string (list-ref line 3)) " "
"lineto\n"
(number->string (truncate (/ (list-ref line 4) 2)))
" setlinewidth\n"
"stroke\n"
)))
tree)
(display "\n%%EOF"))))
(output-tree-as-eps "fractal.eps" (create-tree 400 200 90 9))
Scilab
===L-System approach=== This script uses complex numbers to represent (x,y) coordinates: real part as x position, and imaginary part as y position. The tree is generated using an L-system approach, and the lines are then drawn by interpreting the resulting sentence. The output is plotted onto graphic window.
right_angle = angle/2; //angles to the right or to the left left_angle = 0.8*angle; //can be set independently or //as function of 'angle'
//L-system definition: //Alphabet: FBD[]+- //F: go forward B: go backwards //[: start new branch ]: end current branch //+: branch to the right -: branch to the left //D: double line (forward then backward) //Axiom: D //Rule: D -> F[+D-D]B
//L-system sentence generation sentence = 'D' rule = 'F[+D-D]B'; for i=1:depth sentence = strsubst(sentence,'D',rule); end sentence = strsplit(sentence)';
//Empty tree tree_size = 1.0... + length(find(sentence=='F'|sentence=='B'))... + 2 * length(find(sentence=='D')); tree=zeros(tree_size,1);
//Drawing the tree branch_level = 0; curr_angle = trunk_angle; curr_pos = 1;
for ind = 1:size(sentence,'c') charac = sentence(ind);
select charac
case 'F' then //Draw line forward
tree(curr_pos+1) = tree(curr_pos)...
+ trunk * ratio^branch_level * exp(curr_angle*%i);
curr_pos = curr_pos + 1;
case 'B' then //Draw line backwards
tree(curr_pos+1) = tree(curr_pos)...
+ trunk * ratio^branch_level * exp((%pi+curr_angle)*%i);
curr_pos = curr_pos + 1;
case '[' then //New branch
branch_level = branch_level + 1;
case '+' then //Turn right
curr_angle = curr_angle - right_angle;
case '-' then //Turn left
curr_angle = curr_angle + right_angle + left_angle;
case ']' then //End of branch
branch_level = branch_level - 1;
curr_angle = curr_angle - left_angle;
case 'D' then //Double line
tree(curr_pos+1) = tree(curr_pos)...
+ trunk * ratio^branch_level * exp(curr_angle*%i);
tree(curr_pos+2) = tree(curr_pos+1)...
+ trunk * ratio^branch_level * exp((%pi+curr_angle)*%i);
curr_pos = curr_pos + 2;
end
end
scf(); clf(); xname('Fractal tree: '+string(depth)+' levels') plot2d(real(tree),imag(tree),14); set(gca(),'isoview','on'); set(gca(),'axes_visible',['off','off','off']);
### Recursive approach
{{trans|PHP}}
<lang>width = 512;
height = 512;
img=scf();
set(img,'figure_size',[width,height]);
function drawTree(x1, y1, angle, depth)
if depth ~= 0 then
x2 = x1 + cos(angle * %pi/180) * depth * 10;
y2 = y1 + sin(angle * %pi/180) * depth * 10;
plot2d([x1 x2],[y1 y2],14);
drawTree(x2, y2, angle - 20, depth - 1);
drawTree(x2, y2, angle + 20, depth - 1);
end
endfunction
drawTree(width/2,height,90,10);
set(gca(),'isoview','on');
Seed7
$ include "seed7_05.s7i";
include "float.s7i";
include "math.s7i";
include "draw.s7i";
include "keybd.s7i";
const float: DEG_TO_RAD is PI / 180.0;
const proc: drawTree (in integer: x1, in integer: y1, in float: angle, in integer: depth) is func
local
var integer: x2 is 0;
var integer: y2 is 0;
begin
if depth <> 0 then
x2 := x1 + trunc(cos(angle * DEG_TO_RAD) * flt(depth * 10));
y2 := y1 + trunc(sin(angle * DEG_TO_RAD) * flt(depth * 10));
lineTo(x1, y1, x2, y2, white);
drawTree(x2, y2, angle - 20.0, depth - 1);
drawTree(x2, y2, angle + 20.0, depth - 1);
end if;
end func;
const proc: main is func
begin
screen(600, 500);
clear(curr_win, black);
KEYBOARD := GRAPH_KEYBOARD;
drawTree(300, 470, -90.0, 9);
ignore(getc(KEYBOARD));
end func;
Original source: [http://seed7.sourceforge.net/algorith/graphic.htm#fractree]
Sidef
{{trans|Perl}}
func tree(img, x, y, scale=6/10, len=400, angle=270) {
len < 1 && return()
img.moveTo(x, y)
img.angle(angle)
img.line(len)
var (x1, y1) = img.curPos
tree(img, x1, y1, scale, len*scale, angle+35)
tree(img, x1, y1, scale, len*scale, angle-35)
}
require('GD::Simple')
var (width=1000, height=1000)
var img = %s|GD::Simple|.new(width, height)
img.fgcolor('black')
img.penSize(1, 1)
tree(img, width/2, height)
File('tree.png').write(img.png, :raw)
Smalltalk
This example is coded for Squeak Smalltalk.
Object subclass: #FractalTree
instanceVariableNames: ''
classVariableNames: ''
poolDictionaries: ''
category: 'RosettaCode'
Methods for FractalTree class:
tree: aPoint length: aLength angle: anAngle
| p a |
(aLength > 10) ifTrue: [
p := Pen new.
p up.
p goto: aPoint.
p turn: anAngle.
p down.
5 timesRepeat: [
p go: aLength / 5.
p turn: 5.
].
a := anAngle - 30.
3 timesRepeat: [
self tree: p location length: aLength * 0.7 angle: a.
a := a + 30.
]
].
draw
Display restoreAfter: [
Display fillWhite.
self tree: 700@700 length: 200 angle: 0.
]
Now open a new Workspace and enter:
FractalTree new draw.
SVG
[[File:Fractal tree.svg|thumb|right]] In the same style as [[Dragon curve#SVG]]. SVG has no parameterized definitions, so the recursion must be unrolled.
<?xml version="1.0" standalone="yes"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 20010904//EN"
"http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd">
<svg xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink"
width="400" height="320">
<style type="text/css"><![CDATA[
line { stroke: black; stroke-width: .05; }
circle { fill: black; }
]]></style>
<defs>
<g id="stem"> <line x1="0" y1="0" x2="0" y2="-1"/> </g>
<g id="l0"><use xlink:href="#stem"/></g>
<!-- These are identical except for the id and href. -->
<g id="l1"> <use xlink:href="#l0" transform="translate(0, -1) rotate(-35) scale(.7)"/>
<use xlink:href="#l0" transform="translate(0, -1) rotate(+35) scale(.7)"/>
<use xlink:href="#stem"/></g>
<g id="l2"> <use xlink:href="#l1" transform="translate(0, -1) rotate(-35) scale(.7)"/>
<use xlink:href="#l1" transform="translate(0, -1) rotate(+35) scale(.7)"/>
<use xlink:href="#stem"/></g>
<g id="l3"> <use xlink:href="#l2" transform="translate(0, -1) rotate(-35) scale(.7)"/>
<use xlink:href="#l2" transform="translate(0, -1) rotate(+35) scale(.7)"/>
<use xlink:href="#stem"/></g>
<g id="l4"> <use xlink:href="#l3" transform="translate(0, -1) rotate(-35) scale(.7)"/>
<use xlink:href="#l3" transform="translate(0, -1) rotate(+35) scale(.7)"/>
<use xlink:href="#stem"/></g>
<g id="l5"> <use xlink:href="#l4" transform="translate(0, -1) rotate(-35) scale(.7)"/>
<use xlink:href="#l4" transform="translate(0, -1) rotate(+35) scale(.7)"/>
<use xlink:href="#stem"/></g>
<g id="l6"> <use xlink:href="#l5" transform="translate(0, -1) rotate(-35) scale(.7)"/>
<use xlink:href="#l5" transform="translate(0, -1) rotate(+35) scale(.7)"/>
<use xlink:href="#stem"/></g>
<g id="l7"> <use xlink:href="#l6" transform="translate(0, -1) rotate(-35) scale(.7)"/>
<use xlink:href="#l6" transform="translate(0, -1) rotate(+35) scale(.7)"/>
<use xlink:href="#stem"/></g>
<g id="l8"> <use xlink:href="#l7" transform="translate(0, -1) rotate(-35) scale(.7)"/>
<use xlink:href="#l7" transform="translate(0, -1) rotate(+35) scale(.7)"/>
<use xlink:href="#stem"/></g>
<g id="l9"> <use xlink:href="#l8" transform="translate(0, -1) rotate(-35) scale(.7)"/>
<use xlink:href="#l8" transform="translate(0, -1) rotate(+35) scale(.7)"/>
<use xlink:href="#stem"/></g>
</defs>
<g transform="translate(200, 320) scale(100)">
<use xlink:href="#l9"/>
</g>
</svg>
Swift
[http://i.imgur.com/F8Fyn1i.png Image] - Link, since uploads seem to be disabled currently. In a playground:
extension CGFloat {
func degrees_to_radians() -> CGFloat {
return CGFloat(M_PI) * self / 180.0
}
}
extension Double {
func degrees_to_radians() -> Double {
return Double(M_PI) * self / 180.0
}
}
class Tree: UIView {
func drawTree(x1: CGFloat, y1: CGFloat, angle: CGFloat, depth:Int){
if depth == 0 {
return
}
let ang = angle.degrees_to_radians()
let x2:CGFloat = x1 + ( cos(ang) as CGFloat) * CGFloat(depth) * (self.frame.width / 60)
let y2:CGFloat = y1 + ( sin(ang) as CGFloat) * CGFloat(depth) * (self.frame.width / 60)
let line = drawLine(x1, y1: y1, x2: x2, y2: y2)
line.stroke()
drawTree(x2, y1: y2, angle: angle - 20, depth: depth - 1)
drawTree(x2, y1: y2, angle: angle + 20, depth: depth - 1)
}
func drawLine(x1:CGFloat, y1:CGFloat, x2:CGFloat, y2:CGFloat) -> UIBezierPath
{
let path = UIBezierPath()
path.moveToPoint(CGPoint(x: x1,y: y1))
path.addLineToPoint(CGPoint(x: x2,y: y2))
path.lineWidth = 1
return path
}
override func drawRect(rect: CGRect) {
let color = UIColor(red: 1.0, green: 0.0, blue: 0.0, alpha: 1.0)
color.set()
drawTree(self.frame.width / 2 , y1: self.frame.height * 0.8, angle: -90 , depth: 9 )
}
}
let tree = Tree(frame: CGRectMake(0, 0, 300, 300))
tree
Tcl
{{libheader|Tk}}
package require Tk
set SIZE 800
set SCALE 4.0
set BRANCHES 14
set ROTATION_SCALE 0.85
set INITIAL_LENGTH 50.0
proc draw_tree {w x y dx dy size theta depth} {
global SCALE ROTATION_SCALE
$w create line $x $y [expr {$x + $dx*$size}] [expr {$y + $dy*$size}]
if {[incr depth -1] >= 0} {
set x [expr {$x + $dx*$size}]
set y [expr {$y + $dy*$size}]
set ntheta [expr {$theta * $ROTATION_SCALE}]
# Draw left branch
draw_tree $w $x $y \
[expr {$dx*cos($theta) + $dy*sin($theta)}] \
[expr {$dy*cos($theta) - $dx*sin($theta)}] \
[expr {$size * (rand() + $SCALE - 1) / $SCALE}] $ntheta $depth
# Draw right branch
draw_tree $w $x $y \
[expr {$dx*cos(-$theta) + $dy*sin(-$theta)}] \
[expr {$dy*cos(-$theta) - $dx*sin(-$theta)}] \
[expr {$size * (rand() + $SCALE - 1) / $SCALE}] $ntheta $depth
}
}
pack [canvas .c -width $SIZE -height $SIZE]
draw_tree .c [expr {$SIZE/2}] [expr {$SIZE-10}] 0.0 -1.0 $INITIAL_LENGTH \
[expr {3.1415927 / 8}] $BRANCHES
TUSCRIPT
Image is created in SVG-format
$$ MODE TUSCRIPT
dest="fracaltree.svg"
ERROR/STOP CREATE (dest,fdf-o,-std-)
ACCESS d: WRITE/ERASE/RECORDS/UTF8 $dest s,text
MODE DATA
$$ header=*
<?xml version="1.0" standalone="yes"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 20010904//EN"
"http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd">
<svg xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink"
width="400" height="320">
<style type="text/css"><![CDATA[
line { stroke: brown; stroke-width: .05; }
]]></style>
$$ WRITE/NEXT d header
$$ defsbeg=*
<defs>
<g id="stem"> <line x1="0" y1="0" x2="0" y2="-1"/> </g>
<g id="l"><use xlink:href="#stem"/></g>
$$ WRITE/NEXT d defsbeg
$$ LOOP n=10,21
$$ id=n+1,lastnr=VALUE(n)
$$ g=*
<g id="{id}"> <use xlink:href="#{n}" transform="translate(0, -1) rotate(-35) scale(.7)"/>
<use xlink:href="#{n}" transform="translate(0, -1) rotate(+35) scale(.7)"/> <use xlink:href="#stem"/></g>
$$ WRITE/NEXT d g
$$ ENDLOOP
$$ defsend = *
</defs>
<g transform="translate(200, 320) scale(100)">
<use xlink:href="#{lastnr}"/>
</g>
$$ MODE TUSCRIPT
WRITE/NEXT d defsend
WRITE/NEXT d "</svg>"
ENDACCESS d
TypeScript
{{trans|JavaScript}}
// Set up canvas for drawing
var canvas: HTMLCanvasElement = document.createElement('canvas')
canvas.width = 600
canvas.height = 500
document.body.appendChild(canvas)
var ctx: CanvasRenderingContext2D = canvas.getContext('2d')
ctx.fillStyle = '#000'
ctx.lineWidth = 1
// constants
const degToRad: number = Math.PI / 180.0
const totalDepth: number = 9
/** Helper function that draws a line on the canvas */
function drawLine(x1: number, y1: number, x2: number, y2: number): void {
ctx.moveTo(x1, y1)
ctx.lineTo(x2, y2)
}
/** Draws a branch at the given point and angle and then calls itself twice */
function drawTree(x1: number, y1: number, angle: number, depth: number): void {
if (depth !== 0) {
let x2: number = x1 + (Math.cos(angle * degToRad) * depth * 10.0)
let y2: number = y1 + (Math.sin(angle * degToRad) * depth * 10.0)
drawLine(x1, y1, x2, y2)
drawTree(x2, y2, angle - 20, depth - 1)
drawTree(x2, y2, angle + 20, depth - 1)
}
}
// actual drawing of tree
ctx.beginPath()
drawTree(300, 500, -90, totalDepth)
ctx.closePath()
ctx.stroke()
XPL0
[[File:FtreeXPL0.png|200px|thumb|right|Output]]
include c:\cxpl\codes;
proc DrawBranch(Lev, Dir, Len, X, Y);
int Lev; real Dir, Len; int X, Y;
int Red, Grn;
[Move(X, Y);
X:= X + fix(Len*Cos(Dir));
Y:= Y + fix(Len*Sin(Dir));
Red:= 255-Lev*8; Grn:= Lev*12+100;
Line(X, Y, Red<<16+Grn<<8);
if Lev < 12 then \limit level of recursion
[DrawBranch(Lev+1, Dir-0.4, Len*0.8, X, Y); \left
DrawBranch(Lev+1, Dir+0.1, Len*0.8, X, Y); \right
];
];
[SetVid($112); \set 640x480x24 video graphics mode
DrawBranch(0, -3.14159/2.0, 80.0, 360, 460);
if ChIn(1) then []; \wait for keystroke
SetVid(3); \restore normal text mode
]
zkl
Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl {{trans|BBC BASIC}}{{trans|XPL0}} [[File:FractalTree.zkl.jpg|250px|thumb|right]]
fcn fractalTree(){
scale:=0.76;
sizeX:=400; sizeY:=300;
bitmap:=PPM(sizeX*2,sizeY*2,0xFF|FF|FF);
branch:='wrap(x1,y1,size,angle,depth){
ar:=angle.toRad();
x2:=x1 - size*ar.cos();
y2:=y1 + size*ar.sin();
color:=(0xff-depth*8).shiftLeft(16) + (depth*12+100).shiftLeft(8);
bitmap.line(x1,y1, x2,y2, color);
if(depth){
self.fcn(x2,y2,scale*size,angle - 30,depth - 1,vm.pasteArgs(5));
self.fcn(x2,y2,scale*size,angle + 8, depth - 1,vm.pasteArgs(5));
}
};
branch(sizeX,0,sizeY/2,90.0,10);
bitmap.write(File("foo.ppm","wb"));
}();
The funkyness (pasteArgs) in the recursion (self.fcn) is due to the closure ('wrap): the closed over args are stashed in the arglist, they need to be added to the parameters when recursing.
ZX Spectrum Basic
{{trans|BASIC256}}
10 LET level=12: LET long=45
20 LET x=127: LET y=0
30 LET rotation=PI/2
40 LET a1=PI/9: LET a2=PI/9
50 LET c1=0.75: LET c2=0.75
60 DIM x(level): DIM y(level)
70 BORDER 0: PAPER 0: INK 4: CLS
80 GO SUB 100
90 STOP
100 REM Tree
110 LET x(level)=x: LET y(level)=y
120 GO SUB 1000
130 IF level=1 THEN GO TO 240
140 LET level=level-1
150 LET long=long*c1
160 LET rotation=rotation-a1
170 GO SUB 100
180 LET long=long/c1*c2
190 LET rotation=rotation+a1+a2
200 GO SUB 100
210 LET rotation=rotation-a2
220 LET long=long/c2
230 LET level=level+1
240 LET x=x(level): LET y=y(level)
250 RETURN
1000 REM Draw
1010 LET yn=-SIN rotation*long+y
1020 LET xn=COS rotation*long+x
1030 PLOT x,y: DRAW xn-x,y-yn
1040 LET x=xn: LET y=yn
1050 RETURN
[[Category:Geometry]]