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Fractal tree

From Rosetta Code
Task
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


Related tasks



Ada[edit]

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;

Arturo[edit]

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:

Fractal Tree output in Arturo

AutoHotkey[edit]

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[edit]

BASIC256[edit]

Asymmetric fractal tree image created by the BASIC-256 script
graphsize 300,300
 
level = 12 : len =63 # initial values
x = 230: y = 285
rotation = pi/2
 
A1 = pi/27 : A2 = pi/8 # constants which determine shape
C1 = 0.7 : C2 = 0.85
 
dim xs(level+1) : dim ys(level+1) # stacks
 
fastgraphics
color black
rect 0,0,graphwidth,graphheight
refresh
color green
gosub tree
refresh
imgsave "Fractal_tree_BASIC-256.png", "PNG"
end
 
tree:
xs[level] = x : ys[level] = y
gosub putline
if level>0 then
level = level - 1
len = len*C1
rotation = rotation - A1
gosub tree
len = len/C1*C2
rotation = rotation + A1 + A2
gosub tree
rotation = rotation - A2
len = len/C2
level = level + 1
end if
x = xs[level] : y = ys[level]
return
 
putline:
yn = -sin(rotation)*len + y
xn = cos(rotation)*len + x
line x,y,xn,yn
x = xn : y = yn
return

Run BASIC[edit]

 '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[edit]

Output:
Fractal tree bbc.gif








 
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[edit]

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[edit]

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++[edit]

FracTree cpp.png

 
#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[edit]

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[edit]

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[edit]

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[edit]

SVG Version[edit]

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[edit]

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[edit]

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[edit]

Run it

func tree x y deg n . .
if n > 0
set_linewidth n * 0.4
move_pen x y
x += cos deg * n * 1.3 * (randomf + 0.5)
y += sin deg * n * 1.3 * (randomf + 0.5)
draw_line x y
call tree x y deg - 20 n - 1
call tree x y deg + 20 n - 1
.
.
call tree 50 90 -90 10
on mouse_down
clear_screen
call tree 50 90 -90 10
.

F#[edit]

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[edit]

 
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[edit]

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[edit]

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[edit]

 
// 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[]
 

Go[edit]

png converted from output ppm
package main
 
// Files required to build supporting package raster are found in:
// * Bitmap
// * Grayscale image
// * Xiaolin Wu's line algorithm
// * Write a PPM file
 
import (
"math"
"raster"
)
 
const (
width = 400
height = 300
depth = 8
angle = 12
length = 50
frac = .8
)
 
func main() {
g := raster.NewGrmap(width, height)
ftree(g, width/2, height*9/10, length, 0, depth)
g.Bitmap().WritePpmFile("ftree.ppm")
}
 
func ftree(g *raster.Grmap, x, y, distance, direction float64, depth int) {
x2 := x + distance*math.Sin(direction*math.Pi/180)
y2 := y - distance*math.Cos(direction*math.Pi/180)
g.AaLine(x, y, x2, y2)
if depth > 0 {
ftree(g, x2, y2, distance*frac, direction-angle, depth-1)
ftree(g, x2, y2, distance*frac, direction+angle, depth-1)
}
}

Haskell[edit]

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[edit]

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

WOpen provides graphics I/O

Translation of: Java

J[edit]

require'gl2'
 
L0=: 50 NB. initial length
A0=: 1r8p1 NB. initial angle: pi divided by 8
dL=: 0.9 NB. shrink factor for length
dA=: 0.75 NB. shrink factor for angle
N=: 14 NB. number of branches
 
L=: L0*dL^1+i.N NB. lengths of line segments
 
NB. relative angles of successive line segments
A=: A0*(dA^i.N) +/\@:*("1) _1 ^ #:i.2 ^ N
 
NB. end points for each line segment
P=: 0 0+/\@,"2 +.*.inv (L0,0),"2 L,"0"1 A
 
P_C_paint=: gllines_jgl2_ bind (10 + ,/"2 P-"1<./,/P)
wd 0 :0
pc P closeok;
xywh 0 0 250 300;
cc C isigraph rightmove bottommove;
pas 0 0;
pshow;
)

See the talk page for some implementation notes.

Java[edit]

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[edit]

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[edit]

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

Fractal_tree.svg

Julia[edit]

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[edit]

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[edit]

 
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
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[edit]

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[edit]

----------------------------------------
-- Creates an image of a fractal tree
-- @param {integer} width
-- @param {integer} height
-- @param {integer} fractalDepth
-- @param {integer|float} initSize
-- @param {float} spreadAngle
-- @param {float} [scaleFactor=1.0]
-- @return {image}
----------------------------------------
on fractalTree (width, height, fractalDepth, initSize, spreadAngle, scaleFactor)
if voidP(scaleFactor) then scaleFactor = 1.0
img = image(width, height, 24)
img.fill(img.rect, rgb(0,0,0))
_drawTree(img, width/2, height, -PI/2, fractalDepth, initSize, spreadAngle, scaleFactor)
return img
end
 
on _drawTree (img, x1, y1, angle, depth, size, spreadAngle, scaleFactor)
if (depth) then
x2 = x1 + cos(angle)*depth*size
y2 = y1 + sin(angle)*depth*size
img.draw(x1, y1, x2, y2, [#color:rgb(255,255,255)])
_drawTree(img, x2, y2, angle-spreadAngle, depth-1, size*ScaleFactor, spreadAngle, scaleFactor)
_drawTree(img, x2, y2, angle+spreadAngle, depth-1, size*ScaleFactor, spreadAngle, scaleFactor)
end if
end

Usage:

fractalDepth = 10
initSize = 7.0
spreadAngle = 35*PI/180
scaleFactor = 0.95
img = fractalTree(480, 380, fractalDepth, initSize, spreadAngle, scaleFactor)

[edit]

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[edit]

Bitmap[edit]

Needs LÖVE 2D Engine

 
g, angle = love.graphics, 26 * math.pi / 180
wid, hei = g.getWidth(), g.getHeight()
function rotate( x, y, a )
local s, c = math.sin( a ), math.cos( a )
local a, b = x * c - y * s, x * s + y * c
return a, b
end
function branches( a, b, len, ang, dir )
len = len * .76
if len < 5 then return end
g.setColor( len * 16, 255 - 2 * len , 0 )
if dir > 0 then ang = ang - angle
else ang = ang + angle
end
local vx, vy = rotate( 0, len, ang )
vx = a + vx; vy = b - vy
g.line( a, b, vx, vy )
branches( vx, vy, len, ang, 1 )
branches( vx, vy, len, ang, 0 )
end
function createTree()
local lineLen = 127
local a, b = wid / 2, hei - lineLen
g.setColor( 160, 40 , 0 )
g.line( wid / 2, hei, a, b )
branches( a, b, lineLen, 0, 1 )
branches( a, b, lineLen, 0, 0 )
end
function love.load()
canvas = g.newCanvas( wid, hei )
g.setCanvas( canvas )
createTree()
g.setCanvas()
end
function love.draw()
g.draw( canvas )
end
 

ASCII[edit]

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[edit]

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[
[email protected]{
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]]
 

MathFractalTree.png

NetRexx[edit]

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[edit]

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[edit]

Library: ocaml-cairo
#directory "+cairo"
#load "bigarray.cma"
#load "cairo.cma"
 
let img_name = "/tmp/fractree.png"
let width = 480
let height = 640
 
let level = 9
let line_width = 4.0
 
let color = (1.0, 0.5, 0.0)
 
let pi = 4.0 *. atan 1.0
 
let angle_split = pi *. 0.12
let angle_rand = pi *. 0.12
 
let () =
Random.self_init();
let surf = Cairo.image_surface_create Cairo.FORMAT_RGB24 ~width ~height in
let ctx = Cairo.create surf in
Cairo.set_antialias ctx Cairo.ANTIALIAS_SUBPIXEL;
Cairo.set_line_cap ctx Cairo.LINE_CAP_ROUND;
 
let draw_line (x,y) (dx,dy) =
Cairo.move_to ctx x (float height -. y);
Cairo.line_to ctx dx (float height -. dy);
Cairo.stroke ctx;
in
let set_color (r,g,b) v =
Cairo.set_source_rgb ctx ~red:(r *. v) ~green:(g *. v) ~blue:(b *. v);
in
let trans_pos (x,y) len angle =
let _x = cos angle
and _y = sin angle in
(x +. (_x *. len),
y +. (_y *. len))
in
 
let rec loop ~level ~pos ~line_width ~line_len
~angle ~angle_split ~angle_rand ~intc =
if level > 0 then begin
(* draw the current segment *)
Cairo.set_line_width ctx line_width;
set_color color intc;
let pos_to = trans_pos pos line_len angle in
draw_line pos pos_to;
(* evolution of the parameters *)
let line_width = line_width *. 0.8
and line_len = line_len *. 0.62
and angle_split = angle_split *. 1.02
and angle_rand = angle_rand *. 1.02
and intc = intc *. 0.9
in
let next_loop =
loop ~level:(pred level) ~pos:pos_to ~intc
~line_width ~line_len ~angle_split ~angle_rand
in
(* split *)
let angle_left = angle +. angle_split +. Random.float angle_rand
and angle_right = angle -. angle_split -. Random.float angle_rand
in
next_loop ~angle:angle_left;
next_loop ~angle:angle_right
end
in
 
let pos = (float width *. 0.5, float height *. 0.1)
and line_len = float height *. 0.3
in
loop ~level ~pos ~angle:(pi /. 2.0)
~angle_split ~angle_rand
~line_width ~line_len ~intc:1.0;
 
Cairo_png.surface_write_to_file surf img_name
(*Cairo_png.surface_write_to_channel surf stdout*)

PARI/GP[edit]

Output FracTree1.png
Output FracTree2.png
Output FracTree3.png

This version with recursion, in general, is a translation of JavaScript version. Some tweaks and options were added to make it reusable and outputting different size of a tree.

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[edit]

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[edit]

Translation of: XPL0
Library: Phix/pGUI
-- demo\rosetta\FractalTree.exw
include pGUI.e
 
Ihandle dlg, canvas
cdCanvas cddbuffer, cdcanvas
 
procedure drawTree(integer level, atom angle, atom len, integer x, integer y)
integer xn = x + floor(len*cos(angle))
integer yn = y + floor(len*sin(angle))
integer red = 255-level*8
integer grn = level*12+100
cdCanvasSetForeground(cddbuffer, red*#10000 + grn*#100)
cdCanvasLineWidth(cddbuffer,floor(5-level/3))
cdCanvasLine(cddbuffer, x, 480-y, xn, 480-yn)
if level<12 then
drawTree(level+1, angle-0.4, len*0.8, xn, yn) --left
drawTree(level+1, angle+0.1, len*0.8, xn, yn) --right
end if
end procedure
 
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
cdCanvasActivate(cddbuffer)
cdCanvasClear(cddbuffer)
drawTree(0, -PI/2.0, 80.0, 360, 460)
cdCanvasFlush(cddbuffer)
return IUP_DEFAULT
end function
 
function map_cb(Ihandle ih)
cdcanvas = cdCreateCanvas(CD_IUP, ih)
cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas)
cdCanvasSetBackground(cddbuffer, CD_PARCHMENT)
return IUP_DEFAULT
end function
 
procedure main()
IupOpen()
 
canvas = IupCanvas(NULL)
IupSetAttribute(canvas, "RASTERSIZE", "640x480")
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
 
dlg = IupDialog(canvas,"RESIZE=NO")
IupSetAttribute(dlg, "TITLE", "Fractal Tree")
 
IupShow(dlg)
IupMainLoop()
IupClose()
end procedure
 
main()

PHP[edit]

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

 
<?php
header("Content-type: image/png");
 
$width = 512;
$height = 512;
$img = imagecreatetruecolor($width,$height);
$bg = imagecolorallocate($img,255,255,255);
imagefilledrectangle($img, 0, 0, $width, $width, $bg);
 
$depth = 8;
function drawTree($x1, $y1, $angle, $depth){
 
global $img;
 
if ($depth != 0){
$x2 = $x1 + (int)(cos(deg2rad($angle)) * $depth * 10.0);
$y2 = $y1 + (int)(sin(deg2rad($angle)) * $depth * 10.0);
 
imageline($img, $x1, $y1, $x2, $y2, imagecolorallocate($img,0,0,0));
 
drawTree($x2, $y2, $angle - 20, $depth - 1);
drawTree($x2, $y2, $angle + 20, $depth - 1);
}
}
 
drawTree($width/2, $height, -90, $depth);
 
imagepng($img);
imagedestroy($img);
?>
 

PicoLisp[edit]

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[edit]

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:

[1]

PostScript[edit]

%!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[edit]

#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[edit]

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[edit]

#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

PB FractalTree.png

Processing[edit]

Using rotation[edit]

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[edit]

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[edit]

Using rotation[edit]

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[edit]

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[edit]

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[edit]

_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[edit]

[ $ "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
-1 4 turn
-450 1 fly
500 1 tree

R[edit]

Translation of: PARI/GP
Works with: R version 3.3.3 and above
File:FRTR9.png
Output FRTR9.png
File:FRTR12.png
Output FRTR12.png
File:FRTR15.png
Output FRTR15.png
 
## Recursive FT plotting
plotftree <- function(x, y, a, d, c) {
x2=y2=0; d2r=pi/180.0; a1 <- a*d2r; d1=0;
if(d<=0) {return()}
if(d>0)
{ d1=d*10.0;
x2=x+cos(a1)*d1;
y2=y+sin(a1)*d1;
segments(x*c, y*c, x2*c, y2*c, col='darkgreen');
plotftree(x2,y2,a-20,d-1,c);
plotftree(x2,y2,a+20,d-1,c);
#return(2);
}
}
## Plotting Fractal Tree. aev 3/27/17
## ord - order/depth, c - scale, xsh - x-shift, fn - file name,
## ttl - plot title.
pFractalTree <- function(ord, c=1, xsh=0, fn="", ttl="") {
cat(" *** START FRT:", date(), "\n");
m=640;
if(fn=="") {pf=paste0("FRTR", ord, ".png")} else {pf=paste0(fn, ".png")};
if(ttl=="") {ttl=paste0("Fractal tree, order - ", ord)};
cat(" *** Plot file -", pf, "title:", ttl, "\n");
##plot(NA, xlim=c(0,m), ylim=c(-m,0), xlab="", ylab="", main=ttl);
plot(NA, xlim=c(0,m), ylim=c(0,m), xlab="", ylab="", main=ttl);
plotftree(m/2+xsh,100,90,ord,c);
dev.copy(png, filename=pf, width=m, height=m);
dev.off(); graphics.off();
cat(" *** END FRT:",date(),"\n");
}
## Executing:
pFractalTree(9);
pFractalTree(12,0.6,210);
pFractalTree(15,0.35,600);
 
Output:
> pFractalTree(9);
 *** START FRT: Tue Mar 28 16:49:49 2017 
 *** Plot file - FRTR9.png title: Fractal tree, order - 9 
 *** END FRT: Tue Mar 28 16:49:50 2017 
> pFractalTree(12,0.6,210);
 *** START FRT: Tue Mar 28 17:32:15 2017 
 *** Plot file - FRTR12.png title: Fractal tree, order - 12 
 *** END FRT: Tue Mar 28 17:32:16 2017 
> pFractalTree(15,0.35,600);
 *** START FRT: Tue Mar 28 17:38:34 2017 
 *** Plot file - FRTR15.png title: Fractal tree, order - 15 
 *** END FRT: Tue Mar 28 17:38:41 2017 
 

Racket[edit]

Tree-racket.png
 
#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[edit]

(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[edit]

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:

fractal tree image

Ring[edit]

 
load "guilib.ring"
 
new qapp
{
win1 = new qwidget() {
setwindowtitle("drawing using qpainter")
setgeometry(100,100,500,500)
label1 = new qlabel(win1) {
setgeometry(10,10,400,400)
settext("")
}
draw()
show()
}
exec()
}
 
func draw
p1 = new qpicture()
color = new qcolor() {
setrgb(0,0,255,255)
}
pen = new qpen() {
setcolor(color)
setwidth(1)
}
new qpainter() {
begin(p1)
setpen(pen)
 
sizex = 400
sizey = 200
depth = 10
 
tree(self, sizex, 0, sizey/2, 90, depth)
 
endpaint()
}
label1 { setpicture(p1) show() }
 
func tree myObj, x1, y1, size, angle, depth
myObj{
scale = 0.76
spread = 25
x2 = x1 + size * cos(angle)
y2 = y1 + size * sin(angle)
drawline(x1, y1, x2, y2)
if depth > 0
tree(self, x2, y2, size * scale, angle - spread, depth - 1)
tree(self, x2, y2, size * scale, angle + spread, depth - 1) ok}
 

Output:

CalmoSoftFractalTree.jpg

Ruby[edit]

Library: Shoes
Shoes.app(:title => "Fractal Tree", :width => 600, :height => 600) do
background "#fff"
stroke "#000"
@deg_to_rad = Math::PI / 180.0
 
def drawTree(x1, y1, angle, depth)
if depth != 0
x2 = x1 + (Math.cos(angle * @deg_to_rad) * depth * 10.0).to_i
y2 = y1 + (Math.sin(angle * @deg_to_rad) * depth * 10.0).to_i
 
line x1, y1, x2, y2
 
drawTree(x2, y2, angle - 20, depth - 1)
drawTree(x2, y2, angle + 20, depth - 1)
end
end
 
drawTree(300,550,-90,9)
end

Rust[edit]

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[edit]

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)
}
}
}
}
}
}

ScalaTree.png

Scheme[edit]

The tree is created as a list of line segments, which can then be drawn on a required device. For this program, the tree is output to an eps file.

 
(import (scheme base)
(scheme file)
(scheme inexact)
(scheme write))
 
(define *scale* 10) ; controls overall size of tree
(define *split* 20) ; controls angle of split (in degrees)
 
;; construct lines for tree as list of 5-tuples (x1 y1 x2 y2 depth)
;; - x1 y1 is start point
;; - angle of this line, in radians
;; - depth, depth within tree (controls length of line)
(define (create-tree x1 y1 angle depth)
(define (degrees->radians d)
(let ((pi 3.14159265358979323846264338327950288419716939937510582097))
(* d pi 1/180)))
;
(if (zero? depth)
'()
(let ((x2 (+ x1 (* (cos (degrees->radians angle)) depth *scale*)))
(y2 (+ y1 (* (sin (degrees->radians angle)) depth *scale*))))
(append (list (map truncate (list x1 y1 x2 y2 depth)))
(create-tree x2 y2 (- angle *split*) (- depth 1))
(create-tree x2 y2 (+ angle *split*) (- depth 1))))))
 
;; output the tree to an eps file
(define (output-tree-as-eps filename tree)
(when (file-exists? filename) (delete-file filename))
(with-output-to-file
filename
(lambda ()
(display "%!PS-Adobe-3.0 EPSF-3.0\n%%BoundingBox: 0 0 800 800\n")
 
;; add each line - sets linewidth based on depth in tree
(for-each (lambda (line)
(display
(string-append "newpath\n"
(number->string (list-ref line 0)) " "
(number->string (list-ref line 1)) " "
"moveto\n"
(number->string (list-ref line 2)) " "
(number->string (list-ref line 3)) " "
"lineto\n"
(number->string (truncate (/ (list-ref line 4) 2)))
" setlinewidth\n"
"stroke\n"
)))
tree)
(display "\n%%EOF"))))
 
(output-tree-as-eps "fractal.eps" (create-tree 400 200 90 9))
 

Scilab[edit]

L-System approach[edit]

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[edit]

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');

Seed7[edit]

$ 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[edit]

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[edit]

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[edit]

Fractal tree.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[edit]

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[edit]

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[edit]

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[edit]

Image is created in SVG-format

 
$$ MODE TUSCRIPT
dest="fracaltree.svg"
ERROR/STOP CREATE (dest,fdf-o,-std-)
ACCESS d: WRITE/ERASE/RECORDS/UTF8 $dest s,text
MODE DATA
$$ header=*
<?xml version="1.0" standalone="yes"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 20010904//EN"
"http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd">
<svg xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink"
width="400" height="320">
<style type="text/css"><![CDATA[
line { stroke: brown; stroke-width: .05; }
]]></style>
$$ WRITE/NEXT d header
$$ defsbeg=*
<defs>
<g id="stem"> <line x1="0" y1="0" x2="0" y2="-1"/> </g>
<g id="l"><use xlink:href="#stem"/></g>
$$ WRITE/NEXT d defsbeg
$$ LOOP n=10,21
$$ id=n+1,lastnr=VALUE(n)
$$ g=*
<g id="{id}"> <use xlink:href="#{n}" transform="translate(0, -1) rotate(-35) scale(.7)"/>
<use xlink:href="#{n}" transform="translate(0, -1) rotate(+35) scale(.7)"/> <use xlink:href="#stem"/></g>
$$ WRITE/NEXT d g
$$ ENDLOOP
$$ defsend = *
</defs>
<g transform="translate(200, 320) scale(100)">
<use xlink:href="#{lastnr}"/>
</g>
$$ MODE TUSCRIPT
WRITE/NEXT d defsend
WRITE/NEXT d "</svg>"
ENDACCESS d
 

TypeScript[edit]

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[edit]

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 r = Radians.call(angle)
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[edit]

Output
include c:\cxpl\codes;
 
proc DrawBranch(Lev, Dir, Len, X, Y);
int Lev; real Dir, Len; int X, Y;
int Red, Grn;
[Move(X, Y);
X:= X + fix(Len*Cos(Dir));
Y:= Y + fix(Len*Sin(Dir));
Red:= 255-Lev*8; Grn:= Lev*12+100;
Line(X, Y, Red<<16+Grn<<8);
if Lev < 12 then \limit level of recursion
[DrawBranch(Lev+1, Dir-0.4, Len*0.8, X, Y); \left
DrawBranch(Lev+1, Dir+0.1, Len*0.8, X, Y); \right
];
];
 
[SetVid($112); \set 640x480x24 video graphics mode
DrawBranch(0, -3.14159/2.0, 80.0, 360, 460);
if ChIn(1) then []; \wait for keystroke
SetVid(3); \restore normal text mode
]

zkl[edit]

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

Translation of: BBC BASIC
Translation of: XPL0
FractalTree.zkl.jpg
fcn fractalTree(){
scale:=0.76;
sizeX:=400; sizeY:=300;
bitmap:=PPM(sizeX*2,sizeY*2,0xFF|FF|FF);
branch:='wrap(x1,y1,size,angle,depth){
ar:=angle.toRad();
x2:=x1 - size*ar.cos();
y2:=y1 + size*ar.sin();
color:=(0xff-depth*8).shiftLeft(16) + (depth*12+100).shiftLeft(8);
bitmap.line(x1,y1, x2,y2, color);
if(depth){
self.fcn(x2,y2,scale*size,angle - 30,depth - 1,vm.pasteArgs(5));
self.fcn(x2,y2,scale*size,angle + 8, depth - 1,vm.pasteArgs(5));
}
};
branch(sizeX,0,sizeY/2,90.0,10);
bitmap.write(File("foo.ppm","wb"));
}();

The funkyness (pasteArgs) in the recursion (self.fcn) is due to the closure ('wrap): the closed over args are stashed in the arglist, they need to be added to the parameters when recursing.

ZX Spectrum Basic[edit]

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