# Fractal tree

Fractal tree
You are encouraged to solve this task according to the task description, using any language you may know.

Generate and draw a fractal tree.

1. Draw the trunk
2. At the end of the trunk, split by some angle and draw two branches
3. Repeat at the end of each branch until a sufficient level of branching is reached

## 11l

Translation of: Nim
-V
Width = 1000
Height = 1000
TrunkLength = 400
ScaleFactor = 0.6
StartingAngle = 1.5 * math:pi
DeltaAngle = 0.2 * math:pi

F drawTree(outfile, Float x, Float y; len, theta) -> N
I len >= 1
V x2 = x + len * cos(theta)
V y2 = y + len * sin(theta)
outfile.write("<line x1='#.6' y1='#.6' x2='#.6' y2='#.6' style='stroke:white;stroke-width:1'/>\n".format(x, y, x2, y2))
drawTree(outfile, x2, y2, len * ScaleFactor, theta + DeltaAngle)
drawTree(outfile, x2, y2, len * ScaleFactor, theta - DeltaAngle)

V outsvg = File(‘tree.svg’, ‘w’)
outsvg.write(|‘<?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'>
<rect width="100%" height="100%" fill="black"/>
’)
drawTree(outsvg, 0.5 * Width, Height, TrunkLength, StartingAngle)
outsvg.write("</svg>\n")

## Action!

Action! language does not support recursion. Therefore an iterative approach with a stack has been proposed.

DEFINE MAXSIZE="12"

INT ARRAY SinTab=[
0 4 9 13 18 22 27 31 36 40 44 49 53 58 62 66 71 75 79 83
88 92 96 100 104 108 112 116 120 124 128 132 136 139 143
147 150 154 158 161 165 168 171 175 178 181 184 187 190
193 196 199 202 204 207 210 212 215 217 219 222 224 226
228 230 232 234 236 237 239 241 242 243 245 246 247 248
249 250 251 252 253 254 254 255 255 255 256 256 256 256]

INT ARRAY xStack(MAXSIZE),yStack(MAXSIZE),angleStack(MAXSIZE)
BYTE ARRAY lenStack(MAXSIZE),dirStack(MAXSIZE)
BYTE stacksize=[0]

INT FUNC Sin(INT a)
WHILE a<0 DO a==+360 OD
WHILE a>360 DO a==-360 OD
IF a<=90 THEN
RETURN (SinTab(a))
ELSEIF a<=180 THEN
RETURN (SinTab(180-a))
ELSEIF a<=270 THEN
RETURN (-SinTab(a-180))
ELSE
RETURN (-SinTab(360-a))
FI
RETURN (0)

INT FUNC Cos(INT a)
RETURN (Sin(a-90))

BYTE FUNC IsEmpty()
IF stacksize=0 THEN
RETURN (1)
FI
RETURN (0)

BYTE FUNC IsFull()
IF stacksize=MAXSIZE THEN
RETURN (1)
FI
RETURN (0)

PROC Push(INT x,y,angle BYTE len,dir)
IF IsFull() THEN Break() FI
xStack(stacksize)=x yStack(stacksize)=y
angleStack(stacksize)=angle lenStack(stacksize)=len
dirStack(stacksize)=dir
stacksize==+1
RETURN

PROC Pop(INT POINTER x,y,angle BYTE POINTER len,dir)
IF IsEmpty() THEN Break() FI
stacksize==-1
x^=xStack(stacksize) y^=yStack(stacksize)
angle^=angleStack(stacksize) len^=lenStack(stacksize)
dir^=dirStack(stacksize)
RETURN

PROC DrawTree(INT x,y,len,angle,leftAngle,rightAngle)
BYTE depth,dir

Plot(x,y)
x==+Cos(angle)*len/256
y==-Sin(angle)*len/256
DrawTo(x,y)

Push(x,y,angle,len,0)

WHILE IsEmpty()=0
DO
Pop(@x,@y,@angle,@len,@dir)
IF dir<2 THEN
Push(x,y,angle,len,dir+1)
IF dir=0 THEN
angle==-leftAngle
ELSE
angle==+rightAngle
FI

len=13*len/16
Plot(x,y)
x==+Cos(angle)*len/256
y==-Sin(angle)*len/256
DrawTo(x,y)

IF IsFull()=0 THEN
Push(x,y,angle,len,0)
FI
FI
OD

RETURN

PROC Main()
BYTE CH=$02FC,COLOR1=$02C5,COLOR2=$02C6 Graphics(8+16) Color=1 COLOR1=$BA
COLOR2=$B2 DrawTree(140,191,40,110,35,15) DO UNTIL CH#$FF OD
CH=$FF RETURN Output: ## Ada Library: SDLAda with Ada.Numerics.Elementary_Functions; with SDL.Video.Windows.Makers; with SDL.Video.Renderers.Makers; with SDL.Video.Rectangles; with SDL.Events.Events; procedure Fractal_Tree is Width : constant := 600; Height : constant := 600; Level : constant := 13; Length : constant := 130.0; X_Start : constant := 475.0; Y_Start : constant := 580.0; A_Start : constant := -1.54; Angle_1 : constant := 0.10; Angle_2 : constant := 0.35; C_1 : constant := 0.71; C_2 : constant := 0.87; Window : SDL.Video.Windows.Window; Renderer : SDL.Video.Renderers.Renderer; Event : SDL.Events.Events.Events; procedure Draw_Tree (Level : in Natural; Length : in Float; Angle : in Float; X, Y : in Float) is use SDL; use Ada.Numerics.Elementary_Functions; Pi : constant := Ada.Numerics.Pi; X_2 : constant Float := X + Length * Cos (Angle, 2.0 * Pi); Y_2 : constant Float := Y + Length * Sin (Angle, 2.0 * Pi); Line : constant SDL.Video.Rectangles.Line_Segment := ((C.int (X), C.int (Y)), (C.int (X_2), C.int (Y_2))); begin if Level > 0 then Renderer.Set_Draw_Colour (Colour => (0, 220, 0, 255)); Renderer.Draw (Line => Line); Draw_Tree (Level - 1, C_1 * Length, Angle + Angle_1, X_2, Y_2); Draw_Tree (Level - 1, C_2 * Length, Angle - Angle_2, X_2, Y_2); end if; end Draw_Tree; procedure Wait is use type SDL.Events.Event_Types; begin loop while SDL.Events.Events.Poll (Event) loop if Event.Common.Event_Type = SDL.Events.Quit then return; end if; end loop; delay 0.100; end loop; end Wait; begin if not SDL.Initialise (Flags => SDL.Enable_Screen) then return; end if; SDL.Video.Windows.Makers.Create (Win => Window, Title => "Fractal tree", Position => SDL.Natural_Coordinates'(X => 10, Y => 10), Size => SDL.Positive_Sizes'(Width, Height), Flags => 0); SDL.Video.Renderers.Makers.Create (Renderer, Window.Get_Surface); Renderer.Set_Draw_Colour ((0, 0, 0, 255)); Renderer.Fill (Rectangle => (0, 0, Width, Height)); Draw_Tree (Level, Length, A_Start, X_Start, Y_Start); Window.Update_Surface; Wait; Window.Finalize; SDL.Finalise; end Fractal_Tree;  ## Amazing Hopper Translation of: BBCBasic "Una suma que no quería salir, pero ya salió" :D /* Execute with:$ hopper jm/tree.jambo -x -o bin/tree
$rxvt -g 280x250 -fn "xft:FantasqueSansMono-Regular:pixelsize=1" -e ./bin/tree */ #include <jambo.h> Main Set '25, 0.76, 160, 100, 10' Init 'Spread, Scale, SizeX, SizeY, Depth' Color back '22', Cls Color back '15' Set '{SizeX} Mul by (2), -30, Div(SizeY,2), 90, Depth' Gosub 'Branch' Pause End Subrutines Define 'Branch, x1, y1, size, angle, depth' x2=0, y2=0 Let ( x2 := #(x1 + size * cos(d2r(angle))) ) Let ( y2 := #(y1 + size * sin(d2r(angle))) ) Draw a line ( #(180-y1), #(180-x1), #(180-y2), #(180-x2)) If ( #( depth > 0) ) Set (x2, y2, {size} Mul by 'Scale', {angle} Minus 'Spread',\ Minus one(depth)) Gosub 'Branch' Set (x2, y2, {size} Mul by 'Scale', {angle} Plus 'Spread',\ Minus one(depth)) Gosub 'Branch' End If Return ## Arturo width: 1000 height: 1000 trunkLength: 400 scaleFactor: 0.6 startingAngle: 1.5 * pi deltaAngle: 0.2 * pi drawTree: function [out x y len theta][ if len < 1 -> return null x2: x + len * cos theta y2: y + len * sin theta 'out ++ ~"<line x1='|x|' y1='|y|' x2='|x2|' y2='|y2|' style='stroke: white; stroke-width:1'/>\n" drawTree out x2 y2 len*scaleFactor theta+deltaAngle drawTree out x2 y2 len*scaleFactor theta-deltaAngle ] svg: { <?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'> <rect width="100%" height="100%" fill="black"/> } drawTree svg 0.5*width height trunkLength startingAngle 'svg ++ "</svg>" write "fractal.svg" svg  Output: ## AutoHotkey Image - Link, since uploads seem to be disabled currently. Library: 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 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 Output:  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  ### IS-BASIC 100 PROGRAM "Tree.bas" 110 OPTION ANGLE DEGREES 120 GRAPHICS HIRES 2 130 SET PALETTE 0,170 140 PLOT 640,10;ANGLE 90; 150 CALL TREE(200) 160 DEF TREE(N) 170 IF N<24 THEN EXIT DEF 180 PLOT FORWARD N;RIGHT 25; 190 CALL TREE(N*.75) 200 PLOT LEFT 50; 210 CALL TREE(N*.75) 220 PLOT RIGHT 25,BACK N, 230 END DEF ## C Library: SDL Library: SGE or Library: cairo #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++ #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 Translation of: Java Library: Swing Library: 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 Translation of: Java Library: Swing Library: 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 Translation of: 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 Translation of: Raku 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. Translation of: 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 Translation of: 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 # Fractal tree # color 555 proc tree x y deg n . . if n > 0 linewidth n * 0.4 move x y x += cos deg * n * 1.3 * (randomf + 0.5) y += sin deg * n * 1.3 * (randomf + 0.5) line x y tree x y deg - 20 n - 1 tree x y deg + 20 n - 1 . . timer 0 on timer clear tree 50 10 90 10 timer 2 .  ## Evaldraw Evaldraw version creates a 3D tree with a camera rotating around the tree. static ratio = .75; static branchlength = 60; static max_branches = 4; struct vec3{x,y,z;}; () { t=klock(); srand(t * 1); zero1 = .5+.5*cos(t); maxbranches = int( 1+1 + zero1*5); cls(0); clz(1e32); distcam = -70; camrot = .5 * t; ca=distcam * cos(camrot); sa=distcam * sin(camrot); setcam(sa,-50,ca,camrot,0); angle = 2*pi / 8; branchlen = 10+50 * zero1; tree(maxbranches, 0, branchlen, 0,0,0, pi / 2, 0, angle); moveto(0,0); printf("N=%g, frame=%5.0f, cam:%3.0f", maxbranches, numframes, camrot / pi * 180); printf("\n%gx%g",xres,yres); sleep(16); } tree(mb, n, blen, x,y,z, ang_yx, ang_yz, angle) { n++; if( n> mb ) return; len = blen / n * ratio; c = 64 + 128 * n/7; setcol(100,c,38); dx=0; dy=0; dz=0; double mat[9]; vec3 axis = {0,0,1}; ang2mat(ang_yz, ang_yx, mat); transformPoint(axis,mat); dx=axis.x; dy=-axis.y; dz=axis.z; ox = x; oy = y; oz = z; x += len * dx; y += -len * dy; z += len * dz; rd = 8 / n; rd2 = 7 / (n+1); drawcone(ox,oy,oz,rd,x,y,z,rd2,DRAWCONE_FLAT + DRAWCONE_NOPHONG); nextangle = /*(-.5+1*rnd*pi) * */angle; tree(mb, n, blen, x, y, z, ang_yx - angle, ang_yz, nextangle); tree(mb, n, blen, x, y, z, ang_yx + angle, ang_yz, nextangle); tree(mb, n, blen, x, y, z, ang_yx, ang_yz - angle, nextangle); tree(mb, n, blen, x, y, z, ang_yx, ang_yz + angle, nextangle); } ang2mat(hang,vang,mat[9]) { mat[6] = cos(vang)*sin(hang); mat[0] = cos(hang); mat[7] = sin(vang); mat[1] = 0; mat[8] = cos(vang)*cos(hang); mat[2] =-sin(hang); mat[3] = mat[7]*mat[2] - mat[8]*mat[1]; mat[4] = mat[8]*mat[0] - mat[6]*mat[2]; mat[5] = mat[6]*mat[1] - mat[7]*mat[0]; } transformPoint(vec3 v, thisRot[9]) { NewX = v.x * thisRot[0] + v.y * thisRot[1] + v.z * thisRot[2]; NewY = v.x * thisRot[3] + v.y * thisRot[4] + v.z * thisRot[5]; NewZ = v.x * thisRot[6] + v.y * thisRot[7] + v.z * thisRot[8]; v.x=newx; v.y=newy; v.z=newz; }  ## Delphi Works with: Delphi version 6.0 procedure DrawTree(Image: TImage; X1, Y1: integer; Angle: double; Depth: integer); var X2,Y2: integer; begin if Depth = 0 then exit; X2:=trunc(X1 + cos(DegToRad(Angle)) * Depth * 5); Y2:=trunc(Y1 + sin(DegToRad(Angle)) * Depth * 5); Image.Canvas.Pen.Color:=ColorMap47[MulDiv(High(ColorMap47),Depth,11)]; Image.Canvas.Pen.Width:=MulDiv(Depth,5,10); Image.Canvas.MoveTo(X1,Y1); Image.Canvas.LineTo(X2,Y2); DrawTree(Image, X2, Y2, Angle - 10, Depth - 1); DrawTree(Image, X2, Y2, Angle + 35, Depth - 1); end; procedure ShowFactalTree(Image: TImage); begin ClearImage(Image,clBlack); DrawTree(Image, 250, 350, -90, 11); Image.Invalidate; end;  Output:  Elapsed Time: 31.913 ms.  ## F# Translation of: Raku 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 Translation of: 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 version 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 here due to Is file uploading blocked forever? ## Frink // Draw Fractal Tree in Frink // Define the tree function FractalTree[x1, y1, angleval, lengthval, graphicsobject] := { if lengthval > 1 { // Define current line end points (x2 and y2) x2 = x1 + ((cos[angleval degrees]) * lengthval) y2 = y1 + ((sin[angleval degrees]) * lengthval) // Draw line - notice that graphicsobject is the graphics object passed into the function. graphicsobject.line[x1,y1,x2,y2] // Calculate branches. You can change the lengthval multiplier factor and angleval summand to create different trees FractalTree[x2, y2, angleval - 20, lengthval * 0.7, graphicsobject] FractalTree[x2, y2, angleval + 20, lengthval * 0.7, graphicsobject] } } // Create graphics object g = new graphics // Start the recursive function. In Frink, a -90° angle moves from the bottom of the screen to the top. FractalTree[0, 0, -90, 30, g] // Show the final tree g.show[] ## FutureBasic _window = 1 _wndWidth = 680 void local fn BuildWindow window _window, @"Fractal Tree", ( 0, 0, _wndWidth, 600 ) WindowSetBackgroundColor( _window, fn ColorBlack ) WindowSubclassContentView( _window ) end fn local fn PlotFractalTree( x1 as double, y1 as double, size as long, angle as double, spread as long, depth as long, scale as double ) double x2, y2 pen 1.0, fn ColorGreen, NSLineCapStyleSquare // Convert angle to radians x2 = x1 + size * cos(angle * pi / 180) y2 = y1 + size * sin(angle * pi / 180) line x1, y1, x2, y2 if ( depth > 0 ) fn PlotFractalTree( x2, y2, size * scale, angle - spread, spread, depth - 1, scale ) fn PlotFractalTree( x2, y2, size * scale, angle + spread, spread, depth - 1, scale ) end if end fn void local fn DoDialog( ev as long, tag as long ) select ( tag ) case _windowContentViewTag double spread = ( 80.0 / (_wndWidth / 2 ) ) * 90 fn PlotFractalTree( _wndWidth / 2, 550, 140, -90, spread, 10, 0.75 ) end select select ( ev ) case _windowWillClose : end end select end fn on dialog fn DoDialog fn BuildWindow HandleEvents ## Go 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. Library: 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 $pentagon where model = map copy [0,72..288] copy a = Scale s s . Rotate a . Translate 0 x pentagon = Line [ (sin a, cos a) | a <- [0,2*pi/5..2*pi] ] x = 2*cos(pi/5) s = 1/(1+x)  Alternative solution Using the method of the J contribution. Library: HGL import Graphics.HGL.Window import Graphics.HGL.Run import Control.Arrow import Control.Monad import Data.List enumBase :: Int -> Int -> [[Int]] enumBase n = mapM (enumFromTo 0). replicate n. pred psPlus (a,b) (p,q) = (a+p, b+q) toInt :: Double -> Int toInt = fromIntegral.round intPoint = toInt *** toInt pts n = map (map (intPoint.psPlus (100,0)). ((0,300):). scanl1 psPlus. ((r,300):). zipWith (\h a -> (h*cos a, h*sin a)) rs) hs where [r,h,sr,sh] = [50, pi/5, 0.9, 0.75] rs = take n$ 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  ## Icon and 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  Translation of: Java ## J require'gl2' coinsert'jgl2' 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 wd {{)n pc P closeok; setp wh 480 640; cc C isidraw flush; pshow; }} gllines <.(10 + ,/"2 P-"1<./,/P)  See the talk page for some implementation notes. ## Java Library: Swing Library: 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. <html> <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; $y2; len * scale; angle - PI / 5) end ; "<svg width='100%' height='100%' version='1.1' xmlns='http://www.w3.org/2000/svg'>", tree(width / 2; height; len; 3 * PI / 2), "</svg>" ; main(1000; 1000; 400; 6/10) Output:$ jq -r -n -r -f Fractal_tree_svg.jq > Fractal_tree.svg

## Julia

Translation of: 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

Translation of: 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
}


## Lambdatalk

1) defining the function tree:

{def tree
{lambda {:e     // last branch length
:s     // trunks length
:k     // ratio between two following branches
:a     // rotate left
:b}    // rotate right
{if {< :s :e}
then
else M:s T:a
{tree :e {* :k :s} :k :a :b}
T-{+ :a :b}
{tree :e {* :k :s} :k :a :b}
T:b M-:s }}}

2) Calling this function generates a sequence of commands mooving a pen:
• Tθ rotates the drawing direction "θ" degrees from the previous one
• and Md draws a segment "d" pixels in this direction.

{def T {tree 1 190 {/ 2 3} 15 45}}

and produces 40995 words beginning with:

M190 T15 M126.66666666666666 T15 M84.44444444444443 T15 M56.29629629629628 T15 M37.53086419753085 T15 M25.020576131687235 T15
M16.680384087791488 T15 M11.120256058527659 T15 M7.413504039018439 T15 M4.942336026012292 T15 M3.2948906840081946 ...

3) These words are sent to a the turtle lambdatalk primitive
which is a graphic device translating the sequence of Md and Tθ
into a sequence of SVG points x0 y0 x1 y1 ... xn yn
which will feed the points attribute of a polyline SVG element:

{svg {@ width="580px" height="580px" style="box-shadow:0 0 8px #000;"}
{polyline
{@ points="{turtle 230 570 180 {T}}"
fill="transparent" stroke="#fff" stroke-width="1"
}}}

This is an abstract of the output:

<svg width="580px" height="580px" style="box-shadow:0 0 8px #000;">
<polyline points="230 580 230 380 195 251 151 174 109 132 75 113 49 106 32 106 21 109 ...
... 413 286 324 286 230 380 230 580 "
fill="transparent" stroke="#888" stroke-width="1">
</polyline>
</svg>

The complete ouput can be seen displayed in http://lambdaway.free.fr/lambdawalks/?view=fractal_tree


## 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} [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)])
end if
end

Usage:

fractalDepth = 10
initSize = 7.0
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

### Bitmap

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
canvas = g.newCanvas( wid, hei )
g.setCanvas( canvas )
createTree()
g.setCanvas()
end
function love.draw()
g.draw( canvas )
end


### ASCII

Using the Bitmap class and text renderer from here, then extending...

function Bitmap:tree(x, y, angle, depth, forkfn, lengfn)
if depth <= 0 then return end
local fork, leng = forkfn(), lengfn()
local x2 = x + depth * leng * math.cos(angle)
local y2 = y - depth * leng * math.sin(angle)
self:line(math.floor(x), math.floor(y), math.floor(x2), math.floor(y2))
self:tree(x2, y2, angle+fork, depth-1, forkfn, lengfn)
self:tree(x2, y2, angle-fork, depth-1, forkfn, lengfn)
end

bitmap = Bitmap(128*3,128)
bitmap:tree( 64, 120, math.pi/2, 8, function() return 0.3 end, function() return 3 end)
bitmap:tree(192, 120, math.pi/2, 8, function() return 0.6 end, function() return 2.5 end)
bitmap:tree(320, 120, math.pi/2, 8, function() return 0.2+math.random()*0.3 end, function() return 2.0+math.random()*2.0 end)
bitmap:render({[0x000000]='.', [0xFFFFFFFF]='█'})

Output:

Shown at 25% scale:

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## Mathematica / 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]]


## MiniScript

This GUI implementation is for use with Mini Micro.

drawTree = function(x1, y1, angle, depth)
fork_angle = 20
base_len = 9
if depth > 0 then
radians = angle * pi / 180
x2 = x1 + cos(radians) * depth * base_len
y2 = y1 + sin(radians) * depth * base_len
gfx.line x1, y1, x2, y2, "#008000"
drawTree x2, y2, angle - fork_angle, depth - 1
drawTree x2, y2, angle + fork_angle, depth - 1
end if
end function
clear
gfx.clear "#87CEEB"
drawTree 480, 10, 90, 11
img = gfx.getImage(0, 0, 960, 640)
file.saveImage "/usr/fractalTree.png", img


## NetRexx

Translation of: Java
Library: Swing
Library: 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

## Nim

Translation of: Julia
import math
import strformat

const
Width = 1000
Height = 1000
TrunkLength = 400
ScaleFactor = 0.6
StartingAngle = 1.5 * PI
DeltaAngle = 0.2 * PI

proc drawTree(outfile: File; x, y, len, theta: float) =
if len >= 1:
let x2 = x + len * cos(theta)
let y2 = y + len * sin(theta)
outfile.write(
fmt"<line x1='{x}' y1='{y}' x2='{x2}' y2='{y2}' style='stroke:white;stroke-width:1'/>\n")
outfile.drawTree(x2, y2, len * ScaleFactor, theta + DeltaAngle)
outFile.drawTree(x2, y2, len * ScaleFactor, theta - DeltaAngle)

let outsvg = open("tree.svg", fmWrite)
outsvg.write("""<?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
<rect width="100%" height="100%" fill="black"/>\n""")

outsvg.drawTree(0.5 * Width, Height, TrunkLength, StartingAngle)
outsvg.write("</svg>\n")   # View file tree.svg in browser.


## OCaml

Library: ocaml-cairo
#directory "+cairo"

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

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.

Translation of: JavaScript
Works with: PARI/GP version 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 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);
}


## Phix

Translation of: XPL0
Library: Phix/pGUI
Library: Phix/online

You can run this online here.

--
-- demo\rosetta\FractalTree.exw
-- ============================
--
with javascript_semantics
include pGUI.e

Ihandle dlg, canvas
cdCanvas cddbuffer, cdcanvas

procedure drawTree(integer level, atom angle, len, integer x, y)
integer xn = x + floor(len*cos(angle)),
yn = y + floor(len*sin(angle)),
red = 255-level*8,
green = level*12+100
cdCanvasSetForeground(cddbuffer, red*#10000 + green*#100)
cdCanvasSetLineWidth(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*/, /*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

procedure main()
IupOpen()

canvas = IupCanvas("RASTERSIZE=640x480")
IupSetCallbacks(canvas, {"MAP_CB", Icallback("map_cb"),
"ACTION", Icallback("redraw_cb")})

dlg = IupDialog(canvas,"RESIZE=NO")
IupSetAttribute(dlg, "TITLE", "Fractal Tree")

IupShow(dlg)
if platform()!=JS then
IupMainLoop()
IupClose()
end if
end procedure

main()


## PHP

Image is created with GD module. Code adapted from the JavaScript version.

<?php

$width = 512;$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) ) ) ## Plain English To run: Start up. Clear the screen to the lightest blue color. Pick a brownish color. Put the screen's bottom minus 1/2 inch into the context's spot's y coord. Draw a tree given 3 inches. Refresh the screen. Wait for the escape key. Shut down. To draw a tree given a size: If the size is less than 1/32 inch, exit. Put the size divided by 1/4 inch into the pen size. If the size is less than 1/4 inch, pick a greenish color. Remember where we are. Stroke the size. Turn left 1/16 of the way. Draw another tree given the size times 2/3. Turn right 1/16 of the way. Turn right 1/16 of the way. Draw a third tree given the size times 2/3. Turn left 1/16 of the way. Go back to where we were. Output: ## PL/pgSQL Works with: Postgres This piece of code generates the coordinates of each branch, builds a version in the standardized geometry representation format: WKT. A temporary table contains the results: coordinates and WKT representation of each branch. In a query (Postgres + postgis function), we can draw a unique geometry that can be displayed in a tool like QGis or DBeaver database manager for example. The query exploits the notion of CTE and its recursive form. drop table if exists my_temp_tree_table; do $$declare _length numeric := 1; -- a little random _random_length_reduction_max numeric := 0.6; _fork_angle numeric := pi()/12; -- a little random _random_angle numeric := pi()/12; _depth numeric := 9 ; begin create temporary table my_temp_tree_table as WITH RECURSIVE branch(azimuth, x1, y1, x2, y2, len, n) AS ( VALUES (pi()/2, 0.0, 0.0, 0.0, _length, _length, _depth) UNION all select azimuth+a, x2, y2, round((x2+cos(azimuth+a)*len)::numeric, 2), round((y2+sin(azimuth+a)*len)::numeric, 2), (len*(_random_length_reduction_max+(random()*(1-_random_length_reduction_max))))::numeric, n-1 FROM branch cross join ( select ((-_fork_angle)+(_random_angle)*(random()-0.5)) a union select ((_fork_angle)+(_random_angle)*(random()-0.5)) a2 ) a WHERE n > 0 ) select x1, y1, x2, y2, 'LINESTRING('||x1||' '||y1||','||x2||' '||y2||')' as wkt from branch ; end$$ ; -- coordinates and WKT select * from my_temp_tree_table; -- binary version (postgis) of each branch select ST_GeomFromEWKT('SRID=4326;'||wkt) geom from my_temp_tree_table; -- a unique geometry select st_union(ST_GeomFromEWKT('SRID=4326;'||wkt)) geom from my_temp_tree_table;  Output: coordinates and WKT x1 |y1 |x2 |y2 |wkt | -----+----+-----+----+---------------------------------+ 0.0| 0.0| 0.0| 1|LINESTRING(0.0 0.0,0.0 1) | 0.0| 1| 0.15|1.99|LINESTRING(0.0 1,0.15 1.99) | 0.0| 1|-0.29|1.96|LINESTRING(0.0 1,-0.29 1.96) | 0.15|1.99| 0.36|2.68|LINESTRING(0.15 1.99,0.36 2.68) | 0.15|1.99| 0.05|2.70|LINESTRING(0.15 1.99,0.05 2.70) | ...  ### a simple unparameterized version, without randomness WITH RECURSIVE noeuds(azimuth, x0, y0, x, y, len, n) AS ( VALUES (pi()/2, 0::real, 0::real, 0::real, 10::real, 10::real, 9::int) UNION all select azimuth+a, x, y, (x+cos(azimuth+a)*len)::real, (y+sin(azimuth+a)*len)::real, (len/2)::real, n-1 FROM noeuds cross join (select (-pi()/7)::real a union select (pi()/7)::real a2) a WHERE n > 0 ) , branche as ( select '('||x0||' '||y0||','||x||' '||y||')' b from noeuds ) select ST_GeomFromEWKT('SRID=4326;MULTILINESTRING('||string_agg(b, ',')||')') tree from branche  ## 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  ## 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 ## Processing #### Using rotation void setup() { size(600, 600); background(0); stroke(255); drawTree(300, 550, 9); } void drawTree(float x, float y, int depth) { float forkAngle = radians(20); float baseLen = 10.0; if (depth > 0) { pushMatrix(); translate(x, y - baseLen * depth); line(0, baseLen * depth, 0, 0); rotate(forkAngle); drawTree(0, 0, depth - 1); rotate(2 * -forkAngle); drawTree(0, 0, depth - 1); popMatrix(); } }  #### Calculating coordinates Translation of: Python void setup() { size(600, 600); background(0); stroke(255); drawTree(300, 550, -90, 9); } void drawTree(float x1, float y1, float angle, int depth) { float forkAngle = 20; float baseLen = 10.0; if (depth > 0) { float x2 = x1 + cos(radians(angle)) * depth * baseLen; float y2 = y1 + sin(radians(angle)) * depth * baseLen; line(x1, y1, x2, y2); drawTree(x2, y2, angle - forkAngle, depth - 1); drawTree(x2, y2, angle + forkAngle, depth - 1); } }  ### Processing Python mode #### Using rotation Translation of: Processing def setup(): size(600, 600) background(0) stroke(255) drawTree(300, 550, 9) def drawTree(x, y, depth): fork_ang = radians(20) base_len = 10 if depth > 0: pushMatrix() translate(x, y - baseLen * depth) line(0, baseLen * depth, 0, 0) rotate(fork_ang) drawTree(0, 0, depth - 1) rotate(2 * -fork_ang) drawTree(0, 0, depth - 1) popMatrix()  #### Calculating coordinates Translation of: Python def setup(): size(600, 600) background(0) stroke(255) drawTree(300, 550, -90, 9) def drawTree(x1, y1, angle, depth): fork_angle = 20 base_len = 10.0 if depth > 0: x2 = x1 + cos(radians(angle)) * depth * base_len y2 = y1 + sin(radians(angle)) * depth * base_len line(x1, y1, x2, y2) drawTree(x2, y2, angle - fork_angle, depth - 1) drawTree(x2, y2, angle + fork_angle, depth - 1)  ## Python Library: 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): fork_angle = 20 base_len = 10.0 if depth > 0: x2 = x1 + int(math.cos(math.radians(angle)) * depth * base_len) y2 = y1 + int(math.sin(math.radians(angle)) * depth * base_len) pygame.draw.line(screen, (255,255,255), (x1, y1), (x2, y2), 2) drawTree(x2, y2, angle - fork_angle, depth - 1) drawTree(x2, y2, angle + fork_angle, 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())  ## QB64 _Title "Fractal Tree" Const sw% = 640 Const sh% = 480 Screen _NewImage(sw, sh, 8) Cls , 15: Color 2 Call tree(sw \ 2, sh - 10, _Pi * 1.5, _Pi / 180 * 29, 112, 15) Sleep System Sub tree (x As Integer, y As Integer, initAngle As Double, theta As Double, length As Double, depth As Integer) Dim As Integer iL, newX, newY, iX, iY, iD iL = length: iX = x: iY = y: iD = depth newX = Cos(initAngle) * length + iX newY = Sin(initAngle) * length + iY Line (iX, iY)-(newX, newY) iL = length * .78 iD = iD - 1 If iD > 0 Then Call tree(newX, newY, initAngle - theta, theta, iL, iD) Call tree(newX, newY, initAngle + theta, theta, iL, iD) End If End Sub ## Quackery [$ "turtleduck.qky" loadfile ] now!

[ [ 1 1
30 times
[ tuck + ]
swap join ] constant
do ]                  is phi  (       --> n/d )

[ 2dup 5 1 v< iff
2drop done
2dup 5 1 v/
proper 2drop wide
2dup walk
1 5 turn
2dup phi v/
2dup recurse
-2 5 turn
recurse
1 5 turn
-v fly ]               is tree ( n/d -->     )

turtle
20 frames
-1 4 turn
-450 1 fly
500 1 tree
1 frames
Output:

## R

Translation of: PARI/GP
Works with: R version 3.3.3 and above
## 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

#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)


## Raku

(formerly Perl 6) Image is created in 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);
}


## Red

Red [Needs: 'View]

color: brown
width: 9
view/tight/options/flags/no-wait [	; click image to grow tree
img: image 1097x617 draw [
pen brown line-width 9 line 500x600 500x500] [grow]
] [offset: 0x0] [no-border]

ends: reduce [500x500 pi * 3 / 2]	; list of terminal nodes
da: pi * 30 / 180	; angle of branches in radians
ea: pi * 5 / 180	; offset added to angle to break symmetry

l: 200			; branches initial lenght
scale: 0.7		; branches scale factor
grow: does [		; grows branches
l: l * scale
color: 2 * color + leaf / 3
width: width - 1
newends: copy []
foreach [p a] ends [
a1: a + da - ea
p1: p + as-pair l * cos a1 l * sin a1
a2: a - da - ea
p2: p + as-pair l * cos a2 l * sin a2
append img/draw compose/deep [
pen (color)	line-width (width) line (p1) (p) (p2)]
append newends reduce [p1 a1 p2 a2]
]
ends: newends
]

Output:

## 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
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:

## Ruby

Library: Shoes
Shoes.app(:title => "Fractal Tree", :width => 600, :height => 600) do
background "#fff"
stroke "#000"

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

Library: 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)
}
}
}
}
}
}


## 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)
(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.

trunk = 1;                  //trunk length
ratio = 0.8;                //size ratio between two consecutive branches
depth = 9;                  //final number of branch levels
orign = 0;                  //origin of the tree (should be complex)
angle = 45*%pi/180;         //angle between two branches [rad]
trunk_angle = 90*%pi/180;   //angle between trunk and X-axis [rad]

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

Translation of: PHP
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');


$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: [2] ## Sidef Translation of: 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 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 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  ## Standard ML Works with PolyML open XWindows; open Motif; fun toI {x=x,y=y} = {x=Real.toInt IEEEReal.TO_NEAREST x,y=Real.toInt IEEEReal.TO_NEAREST y} ; fun drawOnTop win usegc ht hs {x=l1,y=l2} {x=r1,y=r2} = let val xy = {x=l1 - ht * (l2-r2) , y = l2 - ht * (r1-l1) } val zt = {x=r1 - ht * (l2-r2) , y= r2 - ht * (r1-l1) } val ab = {x= ( (#x xy + #x zt) + hs * (#y zt - #y xy ) )/2.0 , y = ( (#y zt + #y xy) - hs * (#x zt - #x xy )) /2.0 } in if abs (l1 - #x xy ) < 0.9 andalso abs (l2 - #y xy ) < 0.9 then XFlush (XtDisplay win) else (XFillPolygon (XtWindow win) usegc [ (XPoint o toI) {x=l1,y=l2}, (XPoint o toI ) xy , (XPoint o toI ) ab , (XPoint o toI ) zt , (XPoint o toI ) {x=r1,y=r2} ] Convex CoordModeOrigin ; drawOnTop win usegc (0.87*ht) hs xy ab ; drawOnTop win usegc (0.93*ht) hs ab zt ) end ; val demoWindow = fn () => let val shell = XtAppInitialise "" "tree" "top" [] [ XmNwidth 800, XmNheight 650] ; val main = XmCreateMainWindow shell "main" [ XmNmappedWhenManaged true ] ; val canvas = XmCreateDrawingArea main "drawarea" [ XmNwidth 800, XmNheight 650] ; val usegc = DefaultGC (XtDisplay canvas) ; in XtSetCallbacks canvas [ (XmNexposeCallback , (fn (w,c,t) => ( drawOnTop canvas usegc 8.0 0.85 {x=385.0,y=645.0} {x=415.0,y=645.0} ; t) ) ) ] XmNarmCallback ; XtManageChild canvas ; XtManageChild main ; XtRealizeWidget shell end ; demoWindow (); ## Tcl Library: 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"
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>
$$WRITE/NEXT d defsbeg$$ 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)"/>
$$WRITE/NEXT d g$$ 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

Translation of: 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()


## Wren

Translation of: Kotlin
Library: DOME
import "graphics" for Canvas, Color
import "dome" for Window
import "math" for Math

var Radians = Fn.new { |d| d * Num.pi / 180 }

class FractalTree {
construct new(width, height) {
Window.title = "Fractal Tree"
Window.resize(width, height)
Canvas.resize(width, height)
_fore = Color.white
}

init() {
drawTree(400, 500, -90, 9)
}

drawTree(x1, y1, angle, depth) {
if (depth == 0) return
var x2 = x1 + (Math.cos(r) * depth * 10).truncate
var y2 = y1 + (Math.sin(r) * depth * 10).truncate
Canvas.line(x1, y1, x2, y2, _fore)
drawTree(x2, y2, angle - 20, depth - 1)
drawTree(x2, y2, angle + 20, depth - 1)
}

update() {}

draw(alpha) {}
}

var Game = FractalTree.new(800, 600)

## XPL0

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
];
];

## zkl

Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl

Translation of: BBC BASIC
Translation of: XPL0
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){
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

Translation of: 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