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{{task}} [[File:Pythagoras_tree_java.png|600px||right]]
The [[wp:Pythagoras_tree_%28fractal%29|Pythagoras tree]] is a fractal tree constructed from squares. It is named after Pythagoras because each triple of touching squares encloses a right triangle, in a configuration traditionally used to represent the Pythagorean theorem.
;Task Construct a Pythagoras tree of order 7 using only vectors (no rotation or trigonometric functions).
;Related tasks
- [[Fractal_tree|Fractal tree]]
BASIC256
{{trans|FreeBASIC}}
Subroutine pythagoras_tree(x1, y1, x2, y2, depth)
If depth > 10 Then Return
dx = x2 - x1 : dy = y1 - y2
x3 = x2 - dy : y3 = y2 - dx
x4 = x1 - dy : y4 = y1 - dx
x5 = x4 + (dx - dy) / 2
y5 = y4 - (dx + dy) / 2
#draw the box
Line x1, y1, x2, y2 : Line x2, y2, x3, y3
Line x3, y3, x4, y4 : Line x4, y4, x1, y1
Call pythagoras_tree(x4, y4, x5, y5, depth +1)
Call pythagoras_tree(x5, y5, x3, y3, depth +1)
End Subroutine
w = 800 : h = w * 11 \ 16
w2 = w \ 2 : diff = w \ 12
Clg
FastGraphics
Graphsize w, h
Color green
Call pythagoras_tree(w2 - diff, h - 10, w2 + diff, h - 10, 0)
Refresh
ImgSave "pythagoras_tree.jpg", "jpg"
End
C
A Pythagoras tree constructed from an initial square of side length L, fits exactly in a bounding box of length 6L and width 4L([http://ecademy.agnesscott.edu/~lriddle/ifs/pythagorean/pythSize.htm Proof]). That's why the window dimensions are set to 6L x 4L, where L is entered by the user. The squares increase rapidly, an iteration value of 30 takes 'forever' for a single branch to complete. The colours are picked randomly thus producing the effect of a Pythagorean Christmas Tree. :)
Requires the [http://www.cs.colorado.edu/~main/bgi/cs1300/ WinBGIm] library.
#include<graphics.h>
#include<stdlib.h>
#include<stdio.h>
#include<time.h>
typedef struct{
double x,y;
}point;
void pythagorasTree(point a,point b,int times){
point c,d,e;
c.x = b.x - (a.y - b.y);
c.y = b.y - (b.x - a.x);
d.x = a.x - (a.y - b.y);
d.y = a.y - (b.x - a.x);
e.x = d.x + ( b.x - a.x - (a.y - b.y) ) / 2;
e.y = d.y - ( b.x - a.x + a.y - b.y ) / 2;
if(times>0){
setcolor(rand()%15 + 1);
line(a.x,a.y,b.x,b.y);
line(c.x,c.y,b.x,b.y);
line(c.x,c.y,d.x,d.y);
line(a.x,a.y,d.x,d.y);
pythagorasTree(d,e,times-1);
pythagorasTree(e,c,times-1);
}
}
int main(){
point a,b;
double side;
int iter;
time_t t;
printf("Enter initial side length : ");
scanf("%lf",&side);
printf("Enter number of iterations : ");
scanf("%d",&iter);
a.x = 6*side/2 - side/2;
a.y = 4*side;
b.x = 6*side/2 + side/2;
b.y = 4*side;
initwindow(6*side,4*side,"Pythagoras Tree ?");
srand((unsigned)time(&t));
pythagorasTree(a,b,iter);
getch();
closegraph();
return 0;
}
C++
[[File:pythagoras_treeCpp.png|300px|thumb|]] Windows version {{trans|Java}}
#include <windows.h>
#include <string>
#include <iostream>
const int BMP_SIZE = 720, LINE_LEN = 120, BORDER = 100;
class myBitmap {
public:
myBitmap() : pen( NULL ), brush( NULL ), clr( 0 ), wid( 1 ) {}
~myBitmap() {
DeleteObject( pen ); DeleteObject( brush );
DeleteDC( hdc ); DeleteObject( bmp );
}
bool create( int w, int h ) {
BITMAPINFO bi;
ZeroMemory( &bi, sizeof( bi ) );
bi.bmiHeader.biSize = sizeof( bi.bmiHeader );
bi.bmiHeader.biBitCount = sizeof( DWORD ) * 8;
bi.bmiHeader.biCompression = BI_RGB;
bi.bmiHeader.biPlanes = 1;
bi.bmiHeader.biWidth = w;
bi.bmiHeader.biHeight = -h;
HDC dc = GetDC( GetConsoleWindow() );
bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 );
if( !bmp ) return false;
hdc = CreateCompatibleDC( dc );
SelectObject( hdc, bmp );
ReleaseDC( GetConsoleWindow(), dc );
width = w; height = h;
return true;
}
void clear( BYTE clr = 0 ) {
memset( pBits, clr, width * height * sizeof( DWORD ) );
}
void setBrushColor( DWORD bClr ) {
if( brush ) DeleteObject( brush );
brush = CreateSolidBrush( bClr );
SelectObject( hdc, brush );
}
void setPenColor( DWORD c ) {
clr = c; createPen();
}
void setPenWidth( int w ) {
wid = w; createPen();
}
void saveBitmap( std::string path ) {
BITMAPFILEHEADER fileheader;
BITMAPINFO infoheader;
BITMAP bitmap;
DWORD wb;
GetObject( bmp, sizeof( bitmap ), &bitmap );
DWORD* 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 );
HANDLE 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() const { return hdc; }
int getWidth() const { return width; }
int getHeight() const { return height; }
private:
void createPen() {
if( pen ) DeleteObject( pen );
pen = CreatePen( PS_SOLID, wid, clr );
SelectObject( hdc, pen );
}
HBITMAP bmp; HDC hdc;
HPEN pen; HBRUSH brush;
void *pBits; int width, height, wid;
DWORD clr;
};
class tree {
public:
tree() {
bmp.create( BMP_SIZE, BMP_SIZE ); bmp.clear();
clr[0] = RGB( 90, 30, 0 ); clr[1] = RGB( 255, 255, 0 );
clr[2] = RGB( 0, 255, 255 ); clr[3] = RGB( 255, 255, 255 );
clr[4] = RGB( 255, 0, 0 ); clr[5] = RGB( 0, 100, 190 );
}
void draw( int it, POINT a, POINT b ) {
if( !it ) return;
bmp.setPenColor( clr[it % 6] );
POINT df = { b.x - a.x, a.y - b.y }; POINT c = { b.x - df.y, b.y - df.x };
POINT d = { a.x - df.y, a.y - df.x };
POINT e = { d.x + ( ( df.x - df.y ) / 2 ), d.y - ( ( df.x + df.y ) / 2 )};
drawSqr( a, b, c, d ); draw( it - 1, d, e ); draw( it - 1, e, c );
}
void save( std::string p ) { bmp.saveBitmap( p ); }
private:
void drawSqr( POINT a, POINT b, POINT c, POINT d ) {
HDC dc = bmp.getDC();
MoveToEx( dc, a.x, a.y, NULL );
LineTo( dc, b.x, b.y );
LineTo( dc, c.x, c.y );
LineTo( dc, d.x, d.y );
LineTo( dc, a.x, a.y );
}
myBitmap bmp;
DWORD clr[6];
};
int main( int argc, char* argv[] ) {
POINT ptA = { ( BMP_SIZE >> 1 ) - ( LINE_LEN >> 1 ), BMP_SIZE - BORDER },
ptB = { ptA.x + LINE_LEN, ptA.y };
tree t; t.draw( 12, ptA, ptB );
// change this path
t.save( "?:/pt.bmp" );
return 0;
}
EasyLang
[https://easylang.online/apps/run.html?code=floatvars%0Afunc%20tree%20x1%20y1%20x2%20y2%20depth%20.%20.%0Aif%20depth%20%3C%208%0Adx%20%3D%20x2%20-%20x1%0Ady%20%3D%20y1%20-%20y2%0Ax3%20%3D%20x2%20-%20dy%0Ay3%20%3D%20y2%20-%20dx%0Ax4%20%3D%20x1%20-%20dy%0Ay4%20%3D%20y1%20-%20dx%0Ax5%20%3D%20x4%20%2B%200.5%20%2A%20%28dx%20-%20dy%29%0Ay5%20%3D%20y4%20-%200.5%20%2A%20%28dx%20%2B%20dy%29%0Acolor_green%200.2%20%2B%20depth%20/%2018%0Afill%20%5B%20x1%20y1%20x2%20y2%20x3%20y3%20x4%20y4%20%5D%0Afill%20%5B%20x3%20y3%20x4%20y4%20x5%20y5%20%5D%0Acall%20tree%20x4%20y4%20x5%20y5%20depth%20%2B%201%0Acall%20tree%20x5%20y5%20x3%20y3%20depth%20%2B%201%0A.%0A.%0Acolor_red%200.3%0Acolor_blue%200.1%0Acall%20tree%2041%2090%2059%2090%200 Run it]
=={{header|F_Sharp|F#}}==
<p>Creating an HTML file with an inline SVG. The generation of the tree is done breadth first.</p>
```fsharp
type Point = { x:float; y:float }
type Line = { left : Point; right : Point }
let draw_start_html = """<!DOCTYPE html>
<html><head><title>Phytagoras tree</title>
<style type="text/css">polygon{fill:none;stroke:black;stroke-width:1}</style>
</head><body>
<svg width="640" height="640">"""
let draw_end_html = """Sorry, your browser does not support inline SVG.
</svg></body></html>"""
let svg_square x1 y1 x2 y2 x3 y3 x4 y4 =
sprintf """<polygon points="%i %i %i %i %i %i %i %i" />"""
(int x1) (int y1) (int x2) (int y2) (int x3) (int y3) (int x4) (int y4)
let out (x : string) = System.Console.WriteLine(x)
let sprout line =
let dx = line.right.x - line.left.x
let dy = line.left.y - line.right.y
let line2 = {
left = { x = line.left.x - dy; y = line.left.y - dx };
right = { x = line.right.x - dy ; y = line.right.y - dx }
}
let triangleTop = {
x = line2.left.x + (dx - dy) / 2.;
y = line2.left.y - (dx + dy) / 2.
}
[
{ left = line2.left; right = triangleTop }
{ left = triangleTop; right = line2.right }
]
let draw_square line =
let dx = line.right.x - line.left.x
let dy = line.left.y - line.right.y
svg_square line.left.x line.left.y line.right.x line.right.y
(line.right.x - dy) (line.right.y - dx) (line.left.x - dy) (line.left.y - dx)
let rec generate lines = function
| 0 -> ()
| n ->
let next =
lines
|> List.collect (fun line ->
(draw_square >> out) line
sprout line
)
generate next (n-1)
[<EntryPoint>]
let main argv =
let depth = 1 + if argv.Length > 0 then (System.UInt32.Parse >> int) argv.[0] else 2
out draw_start_html
generate [{ left = { x = 275.; y = 500. }; right = { x = 375.; y = 500. } }] depth
out draw_end_html
0
FreeBASIC
{{trans|zkl}}
' version 03-12-2016
' compile with: fbc -s gui
' or fbc -s console
Sub pythagoras_tree(x1 As Double, y1 As Double, x2 As Double, y2 As Double, depth As ULong)
If depth > 10 Then Return
Dim As Double dx = x2 - x1, dy = y1 - y2
Dim As Double x3 = x2 - dy, y3 = y2 - dx
Dim As Double x4 = x1 - dy, y4 = y1 - dx
Dim As Double x5 = x4 + (dx - dy) / 2
Dim As Double y5 = y4 - (dx + dy) / 2
'draw the box
Line (x1, y1) - (x2, y2) : Line - (x3, y3)
Line - (x4, y4) : Line - (x1, y1)
pythagoras_tree(x4, y4, x5, y5, depth +1)
pythagoras_tree(x5, y5, x3, y3, depth +1)
End Sub
' ------=< MAIN >=------
' max for w is about max screensize - 500
Dim As ULong w = 800, h = w * 11 \ 16
Dim As ULong w2 = w \ 2, diff = w \ 12
ScreenRes w, h, 8
pythagoras_tree(w2 - diff, h -10 , w2 + diff , h -10 , 0)
' BSave "pythagoras_tree.bmp",0
' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End
Go
package main
import (
"image"
"image/color"
"image/draw"
"image/png"
"log"
"os"
)
const (
width, height = 800, 600
maxDepth = 11 // how far to recurse, between 1 and 20 is reasonable
colFactor = uint8(255 / maxDepth) // adjusts the colour so leaves get greener further out
fileName = "pythagorasTree.png"
)
func main() {
img := image.NewNRGBA(image.Rect(0, 0, width, height)) // create new image
bg := image.NewUniform(color.RGBA{255, 255, 255, 255}) // prepare white for background
draw.Draw(img, img.Bounds(), bg, image.ZP, draw.Src) // fill the background
drawSquares(340, 550, 460, 550, img, 0) // start off near the bottom of the image
imgFile, err := os.Create(fileName)
if err != nil {
log.Fatal(err)
}
defer imgFile.Close()
if err := png.Encode(imgFile, img); err != nil {
imgFile.Close()
log.Fatal(err)
}
}
func drawSquares(ax, ay, bx, by int, img *image.NRGBA, depth int) {
if depth > maxDepth {
return
}
dx, dy := bx-ax, ay-by
x3, y3 := bx-dy, by-dx
x4, y4 := ax-dy, ay-dx
x5, y5 := x4+(dx-dy)/2, y4-(dx+dy)/2
col := color.RGBA{0, uint8(depth) * colFactor, 0, 255}
drawLine(ax, ay, bx, by, img, col)
drawLine(bx, by, x3, y3, img, col)
drawLine(x3, y3, x4, y4, img, col)
drawLine(x4, y4, ax, ay, img, col)
drawSquares(x4, y4, x5, y5, img, depth+1)
drawSquares(x5, y5, x3, y3, img, depth+1)
}
func drawLine(x0, y0, x1, y1 int, img *image.NRGBA, col color.RGBA) {
dx := abs(x1 - x0)
dy := abs(y1 - y0)
var sx, sy int = -1, -1
if x0 < x1 {
sx = 1
}
if y0 < y1 {
sy = 1
}
err := dx - dy
for {
img.Set(x0, y0, col)
if x0 == x1 && y0 == y1 {
break
}
e2 := 2 * err
if e2 > -dy {
err -= dy
x0 += sx
}
if e2 < dx {
err += dx
y0 += sy
}
}
}
func abs(x int) int {
if x < 0 {
return -x
}
return x
}
Haskell
Haskell allows us to make highly modular solution.
Firstly, we define a function mkBranches that produces a pair of minor squares based on a given square. Each square is represented as a list of points.
mkBranches :: [(Float,Float)] -> [[(Float,Float)]]
mkBranches [a, b, c, d] = let d = 0.5 <*> (b <+> (-1 <*> a))
l1 = d <+> orth d
l2 = orth l1
in
[ [a <+> l2, b <+> (2 <*> l2), a <+> l1, a]
, [a <+> (2 <*> l1), b <+> l1, b, b <+> l2] ]
where
(a, b) <+> (c, d) = (a+c, b+d)
n <*> (a, b) = (a*n, b*n)
orth (a, b) = (-b, a)
We then create squares using mkBranches to build a list representing the set of squares. In order to apply this function iteratively to form a 10-generation tree, we also have to define the monadic iteration iterateM within squares.
squares = concat $ take 10 $ iterateM mkBranches start
where start = [(0,100),(100,100),(100,0),(0,0)]
iterateM f x = iterate (>>= f) (pure x)
The raw result returned by squares should be used in the main function in order to be displayed in a new window, saved directly to a SVG file, or printed to a bitmap file.
'''Window output''' {{libheader|Gloss}}
--import should go to the top of the code
import Graphics.Gloss
main = display (InWindow "Pithagoras tree" (400, 400) (0, 0)) white tree
where tree = foldMap lineLoop squares
'''SVG file'''
main = writeFile "pith.svg" svg
where svg = "<svg " ++ attrs ++ foldMap (mkLine . close) squares ++ "</svg>"
attrs = "fill='none' stroke='black' height='400' width='600'>"
mkLine path = "<polyline points ='" ++ foldMap mkPoint path ++ "'/>"
mkPoint (x,y) = show (250+x) ++ "," ++ show (400-y) ++ " "
close lst = lst ++ [head lst]
'''Bitmap image''' {{libheader|easyplot}}
--import should go to the top of the code
import Graphics.EasyPlot
--change PNG by the desired format
main = plot (PNG "pith.png") $ map (mkLine . close) squares
where mkLine = Data2D [Style Lines, Color Black,Title ""] []
close lst = lst ++ [head lst]
=={{header|IS-BASIC}}==
## J
Using the bash shell, gnuplot for graphics, with ijconsole installed on the PATH, and having saved the program in the file /tmp/pt.ijs the following command plots the Pythagoras tree:
```txt
gnuplot --persist -e 'plot"<ijconsole /tmp/pt.ijs"w l'
NB. use on linux: gnuplot --persist -e 'plot"< ijconsole /tmp/pt.ijs"w l'
NB. translated from c
ex=: {.
why=: {:
but_first=: & NB. just for fun
append=: ,
subtract=: -
X=: adverb def ' ex m'
Y=: adverb def 'why m'
pt=: dyad define
'a b'=. y
NB. c.x = b.x - (a.y - b.y);
NB. c.y = b.y - (b.x - a.x);
c=. (b X , a append but_first why b) ,&(-/) (b Y , b ,&ex a)
NB. d.x = a.x - (a.y - b.y);
NB. d.y = a.y - (b.x - a.x);
d=. (a X , a append but_first why b) ,&(-/) (a Y , b ,&ex a)
NB. e.x = d.x + ( b.x - a.x - (a.y - b.y) ) / 2;
NB. e.y = d.y - ( b.x - a.x + a.y - b.y ) / 2;
e=. (d X + -: (b -&ex a) - a subtract but_first why b) , d Y - -: -/ b X , a X , a Y , b Y
if. 0 < x do.
NB. line(a.x,a.y,b.x,b.y); line(c.x,c.y,b.x,b.y); line(c.x,c.y,d.x,d.y); line(a.x,a.y,d.x,d.y);
echo (a ,: b) , (c ,: b) , (c ,: d) ,: (a ,: d)
echo ''
(<: x) pt"2 (d ,: e) ,: (e ,: c) NB. pythagorasTree(d,e,times-1);pythagorasTree(e,c,times-1);
end.
)
NB. a.x = 6*side/2 - side/2;
NB. a.y = 4*side;
NB. b.x = 6*side/2 + side/2;
NB. b.y = 4*side;
petri=: 7&$: :(empty@:(pt (x:inv 5r2 7r2 ,. 4)&*))
petri 1
exit 0
Java
[[File:pythagoras_tree.png|300px|thumb|right]] {{works with|Java|8}}
import java.awt.*;
import java.awt.geom.Path2D;
import javax.swing.*;
public class PythagorasTree extends JPanel {
final int depthLimit = 7;
float hue = 0.15f;
public PythagorasTree() {
setPreferredSize(new Dimension(640, 640));
setBackground(Color.white);
}
private void drawTree(Graphics2D g, float x1, float y1, float x2, float y2,
int depth) {
if (depth == depthLimit)
return;
float dx = x2 - x1;
float dy = y1 - y2;
float x3 = x2 - dy;
float y3 = y2 - dx;
float x4 = x1 - dy;
float y4 = y1 - dx;
float x5 = x4 + 0.5F * (dx - dy);
float y5 = y4 - 0.5F * (dx + dy);
Path2D square = new Path2D.Float();
square.moveTo(x1, y1);
square.lineTo(x2, y2);
square.lineTo(x3, y3);
square.lineTo(x4, y4);
square.closePath();
g.setColor(Color.getHSBColor(hue + depth * 0.02f, 1, 1));
g.fill(square);
g.setColor(Color.lightGray);
g.draw(square);
Path2D triangle = new Path2D.Float();
triangle.moveTo(x3, y3);
triangle.lineTo(x4, y4);
triangle.lineTo(x5, y5);
triangle.closePath();
g.setColor(Color.getHSBColor(hue + depth * 0.035f, 1, 1));
g.fill(triangle);
g.setColor(Color.lightGray);
g.draw(triangle);
drawTree(g, x4, y4, x5, y5, depth + 1);
drawTree(g, x5, y5, x3, y3, depth + 1);
}
@Override
public void paintComponent(Graphics g) {
super.paintComponent(g);
drawTree((Graphics2D) g, 275, 500, 375, 500, 0);
}
public static void main(String[] args) {
SwingUtilities.invokeLater(() -> {
JFrame f = new JFrame();
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.setTitle("Pythagoras Tree");
f.setResizable(false);
f.add(new PythagorasTree(), BorderLayout.CENTER);
f.pack();
f.setLocationRelativeTo(null);
f.setVisible(true);
});
}
}
JavaScript
{{trans|Java}}
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<style>
canvas {
position: absolute;
top: 45%;
left: 50%;
width: 640px;
height: 640px;
margin: -320px 0 0 -320px;
}
</style>
</head>
<body>
<canvas></canvas>
<script>
'use strict';
var canvas = document.querySelector('canvas');
canvas.width = 640;
canvas.height = 640;
var g = canvas.getContext('2d');
var depthLimit = 7;
var hue = 0.15;
function drawTree(x1, y1, x2, y2, depth) {
if (depth == depthLimit)
return;
var dx = x2 - x1;
var dy = y1 - y2;
var x3 = x2 - dy;
var y3 = y2 - dx;
var x4 = x1 - dy;
var y4 = y1 - dx;
var x5 = x4 + 0.5 * (dx - dy);
var y5 = y4 - 0.5 * (dx + dy);
g.beginPath();
g.moveTo(x1, y1);
g.lineTo(x2, y2);
g.lineTo(x3, y3);
g.lineTo(x4, y4);
g.closePath();
g.fillStyle = HSVtoRGB(hue + depth * 0.02, 1, 1);
g.fill();
g.strokeStyle = "lightGray";
g.stroke();
g.beginPath();
g.moveTo(x3, y3);
g.lineTo(x4, y4);
g.lineTo(x5, y5);
g.closePath();
g.fillStyle = HSVtoRGB(hue + depth * 0.035, 1, 1);
g.fill();
g.strokeStyle = "lightGray";
g.stroke();
drawTree(x4, y4, x5, y5, depth + 1);
drawTree(x5, y5, x3, y3, depth + 1);
}
/* copied from stackoverflow */
function HSVtoRGB(h, s, v) {
var r, g, b, i, f, p, q, t;
i = Math.floor(h * 6);
f = h * 6 - i;
p = v * (1 - s);
q = v * (1 - f * s);
t = v * (1 - (1 - f) * s);
switch (i % 6) {
case 0: r = v, g = t, b = p; break;
case 1: r = q, g = v, b = p; break;
case 2: r = p, g = v, b = t; break;
case 3: r = p, g = q, b = v; break;
case 4: r = t, g = p, b = v; break;
case 5: r = v, g = p, b = q; break;
}
return "rgb("
+ Math.round(r * 255) + ","
+ Math.round(g * 255) + ","
+ Math.round(b * 255) + ")";
}
function draw() {
g.clearRect(0, 0, canvas.width, canvas.height);
drawTree(275, 500, 375, 500, 0);
}
draw();
</script>
</body>
</html>
Julia
{{trans|PARI/GP}}
using Gadfly
using DataFrames
const xarray = zeros(Float64, 80000)
const yarray = zeros(Float64, 80000)
const arraypos = ones(Int32,1)
const maxdepth = zeros(Int32, 1)
function addpoints(x1, y1, x2, y2)
xarray[arraypos[1]] = x1
xarray[arraypos[1]+1] = x2
yarray[arraypos[1]] = y1
yarray[arraypos[1]+1] = y2
arraypos[1] += 2
end
function pythtree(ax, ay, bx, by, depth)
if(depth > maxdepth[1])
return
end
dx=bx-ax; dy=ay-by;
x3=bx-dy; y3=by-dx;
x4=ax-dy; y4=ay-dx;
x5=x4+(dx-dy)/2; y5=y4-(dx+dy)/2;
addpoints(ax, ay, bx, by)
addpoints(bx, by, x3, y3)
addpoints(x3, y3, x4, y4)
addpoints(x4, y4, ax, ay)
pythtree(x4, y4, x5, y5, depth + 1)
pythtree(x5, y5, x3, y3, depth + 1)
end
function pythagorastree(x1, y1, x2, y2, size, maxdep)
maxdepth[1] = maxdep
println("Pythagoras Tree, depth $(maxdepth[1]), size $size, starts at ($x1, $y1, $x2, $y2)");
pythtree(x1, y1, x2, y2, 0);
df = DataFrame(x=xarray[1:arraypos[1]-1], y=-yarray[1:arraypos[1]-1])
plot(df, x=:x, y=:y, Geom.path(), Theme(default_color="green", point_size=0.4mm))
end
pythagorastree(275.,500.,375.,500.,640., 9)
Kotlin
{{trans|Java}}
// version 1.1.2
import java.awt.*
import java.awt.geom.Path2D
import javax.swing.*
class PythagorasTree : JPanel() {
val depthLimit = 7
val hue = 0.15f
init {
preferredSize = Dimension(640, 640)
background = Color.white
}
private fun drawTree(g: Graphics2D, x1: Float, y1: Float,
x2: Float, y2: Float, depth: Int) {
if (depth == depthLimit) return
val dx = x2 - x1
val dy = y1 - y2
val x3 = x2 - dy
val y3 = y2 - dx
val x4 = x1 - dy
val y4 = y1 - dx
val x5 = x4 + 0.5f * (dx - dy)
val y5 = y4 - 0.5f * (dx + dy)
val square = Path2D.Float()
with (square) {
moveTo(x1, y1)
lineTo(x2, y2)
lineTo(x3, y3)
lineTo(x4, y4)
closePath()
}
g.color = Color.getHSBColor(hue + depth * 0.02f, 1.0f, 1.0f)
g.fill(square)
g.color = Color.lightGray
g.draw(square)
val triangle = Path2D.Float()
with (triangle) {
moveTo(x3, y3)
lineTo(x4, y4)
lineTo(x5, y5)
closePath()
}
g.color = Color.getHSBColor(hue + depth * 0.035f, 1.0f, 1.0f)
g.fill(triangle)
g.color = Color.lightGray
g.draw(triangle)
drawTree(g, x4, y4, x5, y5, depth + 1)
drawTree(g, x5, y5, x3, y3, depth + 1)
}
override fun paintComponent(g: Graphics) {
super.paintComponent(g)
drawTree(g as Graphics2D, 275.0f, 500.0f, 375.0f, 500.0f, 0)
}
}
fun main(args: Array<String>) {
SwingUtilities.invokeLater {
val f = JFrame()
with (f) {
defaultCloseOperation = JFrame.EXIT_ON_CLOSE
title = "Pythagoras Tree"
isResizable = false
add(PythagorasTree(), BorderLayout.CENTER)
pack()
setLocationRelativeTo(null);
setVisible(true)
}
}
}
M2000 Interpreter
Cartesian Coordinates
{{trans|zkl}}
MODULE Pythagoras_tree {
CLS 5, 0 ' MAGENTA, NO SPLIT SCREEN
PEN 14 ' YELLOW
\\ code from zkl/Free Basic
LET w = scale.x, h = w * 11 div 16
LET w2 = w div 2, diff = w div 12
LET TreeOrder = 6
pythagoras_tree(w2 - diff, h -10, w2 + diff, h -10, 0)
SUB pythagoras_tree(x1, y1, x2, y2, depth)
IF depth > TreeOrder THEN EXIT SUB
LOCAL dx = x2 - x1, dy = y1 - y2
LOCAL x3 = x2 - dy, y3 = y2 - dx
LOCAL x4 = x1 - dy, y4 = y1 - dx
LOCAL x5 = x4 + (dx - dy) / 2
LOCAL y5 = y4 - (dx + dy) / 2
MOVE x1, y1
DRAW TO x2, y2
DRAW TO x3, y3
DRAW TO x4, y4
DRAW TO x1, y1
pythagoras_tree(x4, y4, x5, y5, depth +1)
pythagoras_tree(x5, y5, x3, y3, depth +1)
END SUB
}
Pythagoras_tree
Polar Coordinates
MODULE Pythagoras_Example{
CLS 5, 0 ' MAGENTA, split line = 0
PEN 14 ' YELLOW
\\ Linux smoothing not work (we can use the statement but without effect)
IF ISWINE ELSE SMOOTH ON
\\ PYTHAGORAS TREE
\\ by definition all variables ar type of a double
GLOBAL p=7, p4=PI/4, p2=PI/2, s2=SQRT(2)/2
MODULE center_p (r, t){
MODULE pythagoras_tree (r, dx, depth) {
r2=r-p2
DRAW ANGLE r, dx
DRAW ANGLE r2, dx
DRAW ANGLE r, -dx
DRAW ANGLE r2, -dx
IF depth>10 THEN EXIT
s3=dx*s2
depth++
STEP ANGLE r+p4, s3*2
CALL pythagoras_tree r-p4, s3, depth
STEP ANGLE r, -dx-s3
STEP ANGLE r, s3
STEP ANGLE r+p4, -s3
CALL pythagoras_tree r+p4, s3, depth
STEP ANGLE r-p4, s3
}
MOVE SCALE.X/2, SCALE.Y/2
STEP ANGLE PI-p4+r, t*s2
CALL pythagoras_tree r, t, 1
}
r=PI/3
pixels=100
center_p r, 100*TWIPSX
center_p r+PI, 100*TWIPSX
CopyImageToClipboard()
Sub CopyImageToClipboard()
LOCAL Scr$=""
MOVE 0,0
COPY SCALE.X, SCALE.Y TO Scr$
CLIPBOARD Scr$
END SUB
}
Pythagoras_Example
PARI/GP
[[File:PythTree1.png|right|thumb|Output PythTree1.png]]
This version with recursion, in general, is a translation of zkl version. Almost "as is", so, outputting upside-down tree.
{{trans|zkl}}
{{Works with|PARI/GP|2.7.4 and above}}
\\ Pythagoras Tree (w/recursion)
\\ 4/11/16 aev
plotline(x1,y1,x2,y2)={plotmove(0, x1,y1);plotrline(0,x2-x1,y2-y1);}
pythtree(ax,ay,bx,by,d=0)={
my(dx,dy,x3,y3,x4,y4,x5,y5);
if(d>10, return());
dx=bx-ax; dy=ay-by;
x3=bx-dy; y3=by-dx;
x4=ax-dy; y4=ay-dx;
x5=x4+(dx-dy)\2; y5=y4-(dx+dy)\2;
plotline(ax,ay,bx,by);
plotline(bx,by,x3,y3);
plotline(x3,y3,x4,y4);
plotline(x4,y4,ax,ay);
pythtree(x4,y4,x5,y5,d+1);
pythtree(x5,y5,x3,y3,d+1);
}
PythagorTree(x1,y1,x2,y2,depth=9,size)={
my(dx=1,dy=0,ttlb="Pythagoras Tree, depth ",ttl=Str(ttlb,depth));
print1(" *** ",ttl); print(", size ",size);
print(" *** Start: ",x1,",",y1,",",x2,",",y2);
plotinit(0);
plotcolor(0,6); \\green
plotscale(0, -size,size, size,0 );
plotmove(0, 0,0);
pythtree(x1,y1, x2,y2);
plotdraw([0,size,size]);
}
{\\ Executing:
PythagorTree(275,500,375,500,9,640); \\PythTree1.png
}
{{Output}}
*** Pythagoras Tree, depth 9, size 640
*** Start: 275,500,375,500
Perl
{{trans|Sidef}}
use Imager;
sub tree {
my ($img, $x1, $y1, $x2, $y2, $depth) = @_;
return () if $depth <= 0;
my $dx = ($x2 - $x1);
my $dy = ($y1 - $y2);
my $x3 = ($x2 - $dy);
my $y3 = ($y2 - $dx);
my $x4 = ($x1 - $dy);
my $y4 = ($y1 - $dx);
my $x5 = ($x4 + 0.5 * ($dx - $dy));
my $y5 = ($y4 - 0.5 * ($dx + $dy));
# Square
$img->polygon(
points => [
[$x1, $y1],
[$x2, $y2],
[$x3, $y3],
[$x4, $y4],
],
color => [0, 255 / $depth, 0],
);
# Triangle
$img->polygon(
points => [
[$x3, $y3],
[$x4, $y4],
[$x5, $y5],
],
color => [0, 255 / $depth, 0],
);
tree($img, $x4, $y4, $x5, $y5, $depth - 1);
tree($img, $x5, $y5, $x3, $y3, $depth - 1);
}
my ($width, $height) = (1920, 1080);
my $img = Imager->new(xsize => $width, ysize => $height);
$img->box(filled => 1, color => 'white');
tree($img, $width/2.3, $height, $width/1.8, $height, 10);
$img->write(file => 'pythagoras_tree.png');
Perl 6
We'll generate a SVG image.
class Square {
has Complex ($.position, $.edge);
method size { $!edge.abs }
method svg-polygon {
qq[<polygon points="{join ' ', map
{ ($!position + $_ * $!edge).reals.join(',') },
0, 1, 1+1i, 1i}" style="fill:lime;stroke=black" />]
}
method left-child {
self.new:
position => $!position + i*$!edge,
edge => sqrt(2)/2*cis(pi/4)*$!edge;
}
method right-child {
self.new:
position => $!position + i*$!edge + self.left-child.edge,
edge => sqrt(2)/2*cis(-pi/4)*$!edge;
}
}
BEGIN say '<svg width="500" height="500">';
END say '</svg>';
sub tree(Square $s, $level = 0) {
return if $level > 8;
say $s.svg-polygon;
tree($s.left-child, $level+1);
tree($s.right-child, $level+1);
}
tree Square.new: :position(250+0i), :edge(60+0i);
Phix
{{Trans|Java}} {{libheader|pGUI}}
---- demo\rosetta\PythagorasTree.exw
--
include pGUI.e
Ihandle dlg, canvas
cdCanvas cddbuffer, cdcanvas
function rgb(integer r, integer g, integer b)
return r*#10000 + g*#100 + b
end function
procedure drawTree(atom x1, atom y1, atom x2, atom y2, integer depth)
atom dx = x2 - x1
atom dy = y1 - y2
atom x3 = x2 - dy
atom y3 = y2 - dx
atom x4 = x1 - dy
atom y4 = y1 - dx
atom x5 = x4 + 0.5 * (dx - dy)
atom y5 = y4 - 0.5 * (dx + dy)
integer r = 250-depth*20
cdCanvasSetForeground(cddbuffer, rgb(r,#FF,0))
cdCanvasBegin(cddbuffer,CD_FILL)
cdCanvasVertex(cddbuffer, x1, 640-y1)
cdCanvasVertex(cddbuffer, x2, 640-y2)
cdCanvasVertex(cddbuffer, x3, 640-y3)
cdCanvasVertex(cddbuffer, x4, 640-y4)
cdCanvasEnd(cddbuffer)
cdCanvasSetForeground(cddbuffer, CD_GRAY)
cdCanvasBegin(cddbuffer,CD_CLOSED_LINES)
cdCanvasVertex(cddbuffer, x1, 640-y1)
cdCanvasVertex(cddbuffer, x2, 640-y2)
cdCanvasVertex(cddbuffer, x3, 640-y3)
cdCanvasVertex(cddbuffer, x4, 640-y4)
cdCanvasEnd(cddbuffer)
cdCanvasSetForeground(cddbuffer, rgb(r-depth*10,#FF,0))
cdCanvasBegin(cddbuffer,CD_FILL)
cdCanvasVertex(cddbuffer, x3, 640-y3)
cdCanvasVertex(cddbuffer, x4, 640-y4)
cdCanvasVertex(cddbuffer, x5, 640-y5)
cdCanvasEnd(cddbuffer)
cdCanvasSetForeground(cddbuffer, CD_GRAY)
cdCanvasBegin(cddbuffer,CD_CLOSED_LINES)
cdCanvasVertex(cddbuffer, x3, 640-y3)
cdCanvasVertex(cddbuffer, x4, 640-y4)
cdCanvasVertex(cddbuffer, x5, 640-y5)
cdCanvasEnd(cddbuffer)
if depth<8 then
drawTree(x4, y4, x5, y5, depth + 1)
drawTree(x5, y5, x3, y3, depth + 1)
end if
end procedure
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
cdCanvasActivate(cddbuffer)
drawTree(275, 500, 375, 500, 0)
cdCanvasFlush(cddbuffer)
return IUP_DEFAULT
end function
function map_cb(Ihandle ih)
cdcanvas = cdCreateCanvas(CD_IUP, ih)
cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas)
cdCanvasSetBackground(cddbuffer, CD_WHITE)
cdCanvasSetForeground(cddbuffer, CD_RED)
return IUP_DEFAULT
end function
function esc_close(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if
return IUP_CONTINUE
end function
procedure main()
IupOpen()
canvas = IupCanvas(NULL)
IupSetAttribute(canvas, "RASTERSIZE", "640x640")
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
dlg = IupDialog(canvas,"RESIZE=NO")
IupSetAttribute(dlg, "TITLE", "Pythagoras Tree")
IupSetCallback(dlg, "K_ANY", Icallback("esc_close"))
IupShow(dlg)
IupMainLoop()
IupClose()
end procedure
main()
Processing
{{trans|Sidef}}
void tree(float x1, float y1, float x2, float y2, int depth) {
if (depth <= 0) {
return;
}
float dx = (x2 - x1);
float dy = (y1 - y2);
float x3 = (x2 - dy);
float y3 = (y2 - dx);
float x4 = (x1 - dy);
float y4 = (y1 - dx);
float x5 = (x4 + 0.5*(dx - dy));
float y5 = (y4 - 0.5*(dx + dy));
// square
beginShape();
fill(0.0, 255.0/depth, 0.0);
vertex(x1, y1);
vertex(x2, y2);
vertex(x3, y3);
vertex(x4, y4);
vertex(x1, y1);
endShape();
// triangle
beginShape();
fill(0.0, 255.0/depth, 0.0);
vertex(x3, y3);
vertex(x4, y4);
vertex(x5, y5);
vertex(x3, y3);
endShape();
tree(x4, y4, x5, y5, depth-1);
tree(x5, y5, x3, y3, depth-1);
}
void setup() {
size(1920, 1080);
background(255);
stroke(0, 255, 0);
tree(width/2.3, height, width/1.8, height, 10);
}
PureBasic
{{trans|FreeBasic}}
EnableExplicit
DisableDebugger
Procedure.d maxXY(a.d,b.d,c.d,d.d)
If a<b : Swap a,b : EndIf
If a<c : Swap a,c : EndIf
If a<d : Swap a,d : EndIf
ProcedureReturn a
EndProcedure
Procedure.d minXY(a.d,b.d,c.d,d.d)
If a>b : Swap a,b : EndIf
If a>c : Swap a,c : EndIf
If a>d : Swap a,d : EndIf
ProcedureReturn a
EndProcedure
Procedure Ptree(x1.d, y1.d, x2.d, y2.d, d.i=0)
If d>10 : ProcedureReturn : EndIf
Define dx.d=x2-x1,
dy.d=y1-y2,
x3.d=x2-dy,
y3.d=y2-dx,
x4.d=x1-dy,
y4.d=y1-dx,
x5.d=x4+(dx-dy)/2.0,
y5.d=y4-(dx+dy)/2.0,
p1.d=(maxXY(x1,x2,x3,x4)+minXY(x1,x2,x3,x4))/2.0,
p2.d=(maxXY(y1,y2,y3,y4)+minXY(y1,y2,y3,y4))/2.0,
p3.d=(maxXY(x1,x2,x3,x4)-minXY(x1,x2,x3,x4))
FrontColor(RGB(Random(125,1),Random(255,125),Random(125,1)))
LineXY(x1,y1,x2,y2)
LineXY(x2,y2,x3,y3)
LineXY(x3,y3,x4,y4)
LineXY(x4,y4,x1,y1)
BoxedGradient(minXY(x1,x2,x3,x4),minXY(y1,y2,y3,y4),p3,p3)
FillArea(p1,p2,-1)
Ptree(x4,y4,x5,y5,d+1)
Ptree(x5,y5,x3,y3,d+1)
EndProcedure
Define w1.i=800,
h1.i=w1*11/16,
w2.i=w1/2,
di.i=w1/12
If OpenWindow(0,#PB_Ignore,#PB_Ignore,w1,h1,"Pythagoras tree")
If CreateImage(0,w1,h1,24,0) And StartDrawing(ImageOutput(0))
DrawingMode(#PB_2DDrawing_Gradient)
BackColor($000000)
Ptree(w2-di,h1-10,w2+di,h1-10)
StopDrawing()
EndIf
ImageGadget(0,0,0,0,0,ImageID(0))
Repeat : Until WaitWindowEvent(50)=#PB_Event_CloseWindow
EndIf
End
Python
Using [https://docs.python.org/3/library/turtle.html turtle graphics] and the Zkl example for the calculations.
from turtle import goto, pu, pd, color, done
def level(ax, ay, bx, by, depth=0):
if depth > 0:
dx,dy = bx-ax, ay-by
x3,y3 = bx-dy, by-dx
x4,y4 = ax-dy, ay-dx
x5,y5 = x4 + (dx - dy)/2, y4 - (dx + dy)/2
goto(ax, ay), pd()
for x, y in ((bx, by), (x3, y3), (x4, y4), (ax, ay)):
goto(x, y)
pu()
level(x4,y4, x5,y5, depth - 1)
level(x5,y5, x3,y3, depth - 1)
if __name__ == '__main__':
color('red', 'yellow')
pu()
level(-100, 500, 100, 500, depth=8)
done()
R
{{trans|PARI/GP}} {{Works with|R|3.3.3 and above}} [[File:PYTHTR9.png|200px|right|thumb|Output PYTHTR9.png]] [[File:PYTHTR7.png|200px|right|thumb|Output PYTHTR7.png]]
## Recursive PT plotting
pythtree <- function(ax,ay,bx,by,d) {
if(d<0) {return()}; clr="darkgreen";
dx=bx-ax; dy=ay-by;
x3=bx-dy; y3=by-dx;
x4=ax-dy; y4=ay-dx;
x5=x4+(dx-dy)/2; y5=y4-(dx+dy)/2;
segments(ax,-ay,bx,-by, col=clr);
segments(bx,-by,x3,-y3, col=clr);
segments(x3,-y3,x4,-y4, col=clr);
segments(x4,-y4,ax,-ay, col=clr);
pythtree(x4,y4,x5,y5,d-1);
pythtree(x5,y5,x3,y3,d-1);
}
## Plotting Pythagoras Tree. aev 3/27/17
## x1,y1,x2,y2 - starting position
## ord - order/depth, fn - file name, ttl - plot title.
pPythagorasT <- function(x1, y1,x2, y2, ord, fn="", ttl="") {
cat(" *** START PYTHT:", date(), "\n");
m=640; i=j=k=m1=m-2; x=y=d=dm=0;
if(fn=="") {pf=paste0("PYTHTR", ord, ".png")} else {pf=paste0(fn, ".png")};
if(ttl=="") {ttl=paste0("Pythagoras tree, order - ", ord)};
cat(" *** Plot file -", pf, "title:", ttl, "\n");
plot(NA, xlim=c(0,m), ylim=c(-m,0), xlab="", ylab="", main=ttl);
pythtree(x1,y1, x2,y2, ord);
dev.copy(png, filename=pf, width=m, height=m);
dev.off(); graphics.off();
cat(" *** END PYTHT:",date(),"\n");
}
## Executing:
pPythagorasT(275,500,375,500,9)
pPythagorasT(275,500,375,500,7)
{{Output}}
> pPythagorasT(275,500,375,500,9)
*** START PYTHT: Tue Mar 28 15:57:19 2017
*** Plot file - PYTHTR9.png title: Pythagoras tree, order - 9
*** END PYTHT: Tue Mar 28 15:57:20 2017
> pPythagorasT(275,500,375,500,7)
*** START PYTHT: Tue Mar 28 15:59:25 2017
*** Plot file - PYTHTR7.png title: Pythagoras tree, order - 7
*** END PYTHT: Tue Mar 28 15:59:25 2017
Racket
#lang racket
(require racket/draw pict)
(define (draw-pythagoras-tree order x0 y0 x1 y1)
(λ (the-dc dx dy)
(define (inr order x0 y0 x1 y1)
(when (positive? order)
(let* ((y0-1 (- y0 y1))
(x1-0 (- x1 x0))
(x2 (+ x1 y0-1))
(y2 (+ y1 x1-0))
(x3 (+ x0 y0-1))
(y3 (+ y0 x1-0))
(x4 (+ x2 x3 (/ (+ x0 x2) -2)))
(y4 (+ y2 y3 (/ (+ y0 y2) -2)))
(path (new dc-path%)))
(send* path [move-to x0 y0]
[line-to x1 y1] [line-to x2 y2] [line-to x3 y3]
[close])
(send the-dc draw-path path dx dy)
(inr (sub1 order) x3 y3 x4 y4)
(inr (sub1 order) x4 y4 x2 y2))))
(define old-brush (send the-dc get-brush))
(define old-pen (send the-dc get-pen))
(send the-dc set-pen (new pen% [width 1] [color "black"]))
(inr (add1 order) x0 y0 x1 y1)
(send the-dc set-brush old-brush)
(send the-dc set-pen old-pen)))
(dc (draw-pythagoras-tree 7 (+ 200 32) 255 (- 200 32) 255) 400 256)
Ring
# Project : Pythagoras tree
load "guilib.ring"
paint = null
new qapp
{
win1 = new qwidget() {
setwindowtitle("Pythagoras tree")
setgeometry(100,100,800,600)
label1 = new qlabel(win1) {
setgeometry(10,10,800,600)
settext("")
}
new qpushbutton(win1) {
setgeometry(150,500,100,30)
settext("draw")
setclickevent("draw()")
}
show()
}
exec()
}
func draw
p1 = new qpicture()
color = new qcolor() {
setrgb(0,0,255,255)
}
pen = new qpen() {
setcolor(color)
setwidth(1)
}
paint = new qpainter() {
begin(p1)
setpen(pen)
w = 800
h = floor(w*11/16)
w2 = floor(w/2)
diff = floor(w/12)
pythagorastree(w2 - diff,h -10,w2 + diff ,h -10 ,0)
endpaint()
}
label1 { setpicture(p1) show() }
return
func pythagorastree(x1,y1,x2,y2,depth)
if depth > 10
return
ok
dx = x2 - x1
dy = y1 - y2
x3 = x2 - dy
y3 = y2 - dx
x4 = x1 - dy
y4 = y1 - dx
x5 = x4 + floor((dx - dy) / 2)
y5 = y4 - floor((dx + dy) / 2)
paint.drawline(x1,y1,x2,y2)
paint.drawline(x2,y2,x3,y3)
paint.drawline(x4,y4,x1,y1)
pythagorastree(x4, y4, x5, y5, depth +1)
pythagorastree(x5, y5, x3, y3, depth +1)
Output: https://www.dropbox.com/s/a1gtue7tvmaj2je/PythagorasTree.jpg?dl=0
Scala
Java Swing Interoperability
import java.awt._
import java.awt.geom.Path2D
import javax.swing.{JFrame, JPanel, SwingUtilities, WindowConstants}
object PythagorasTree extends App {
SwingUtilities.invokeLater(() => {
new JFrame {
class PythagorasTree extends JPanel {
setPreferredSize(new Dimension(640, 640))
setBackground(Color.white)
override def paintComponent(g: Graphics): Unit = {
val (depthLimit, hue) = (7, 0.15f)
def drawTree(g: Graphics2D, x1: Float, y1: Float, x2: Float, y2: Float, depth: Int): Unit = {
if (depth == depthLimit) return
val (dx, dy) = (x2 - x1, y1 - y2)
val (x3, y3) = (x2 - dy, y2 - dx)
val (x4, y4) = (x1 - dy, y1 - dx)
val (x5, y5) = (x4 + 0.5F * (dx - dy), y4 - 0.5F * (dx + dy))
val square = new Path2D.Float {
moveTo(x1, y1); lineTo(x2, y2); lineTo(x3, y3); lineTo(x4, y4); closePath()
}
val triangle = new Path2D.Float {
moveTo(x3, y3); lineTo(x4, y4); lineTo(x5, y5); closePath()
}
g.setColor(Color.getHSBColor(hue + depth * 0.02f, 1, 1))
g.fill(square)
g.setColor(Color.lightGray)
g.draw(square)
g.setColor(Color.getHSBColor(hue + depth * 0.035f, 1, 1))
g.fill(triangle)
g.setColor(Color.lightGray)
g.draw(triangle)
drawTree(g, x4, y4, x5, y5, depth + 1)
drawTree(g, x5, y5, x3, y3, depth + 1)
}
super.paintComponent(g)
drawTree(g.asInstanceOf[Graphics2D], 275, 500, 375, 500, 0)
}
}
setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE)
setTitle("Pythagoras Tree")
setResizable(false)
add(new PythagorasTree, BorderLayout.CENTER)
pack()
setLocationRelativeTo(null)
setVisible(true)
}
})
}
Scilab
===L-System approach===
This solution uses complex numbers to represent vectors, and it draws the contour of the tree. By "uncommenting" the six commented lines inside the select structure, it will also draw the triangles between the squares. The output is a new graphic window.
//L-system definition: //Alphabet: UTDB+-[] //U: go upwards T: top of the square //D: go downwards B: bottom of the square //[: start new branch ]: end current branch //+: branch to the right -: branch to the left //Axiom: UTDB //Rule: T -> [+UTD-UTD]
//L-system sentence generation sentence = 'UTDB' rule = '[+UTD-UTD]'; for i=1:depth sentence = strsubst(sentence,'T',rule); end sentence = strsplit(sentence)';
//Empty tree tree_size = 1.0... + length(find(sentence == "U" | sentence == "T" |... sentence == "D" | sentence == "B"))... + 2 * length(find(sentence == "]" | sentence == "-" |... sentence == "+")); tree=zeros(tree_size,1);
//Vectorial operation to calculate a new point in the tree deff('z = new_point(origin,rho,theta)',... 'z = origin + rho * exp(%i*theta)');
//Drawing the tree curr_angle = %pi/2; curr_pos = 1; ratio = 1/sqrt(2); for ind = 1:size(sentence,'c') charac = sentence(ind);
select charac
case 'U' then //Draw line upwards
tree(curr_pos+1) = new_point(tree(curr_pos),side,curr_angle);
curr_pos = curr_pos + 1;
case 'T' then //Draw top of the square
curr_angle = curr_angle - %pi/2;
tree(curr_pos+1) = new_point(tree(curr_pos),side,curr_angle);
curr_pos = curr_pos + 1;
case 'D' then //Draw line downwards
curr_angle = curr_angle - %pi/2;
tree(curr_pos+1) = new_point(tree(curr_pos),side,curr_angle);
curr_pos = curr_pos + 1;
case 'B' then //Draw the bottom
curr_angle = curr_angle - %pi/2;
tree(curr_pos+1) = new_point(tree(curr_pos),side,curr_angle);
curr_pos = curr_pos + 1;
case '[' then //Start branch
side = side * ratio;
case '+' then //Start going to the left
curr_angle = curr_angle - %pi/4;
// tree(curr_pos+1) = new_point(tree(curr_pos),side,curr_angle); // tree(curr_pos+2) = new_point(tree(curr_pos+1),side,%pi+curr_angle); // curr_pos = curr_pos + 2; curr_angle = curr_angle + %pi/2;
case '-' then //Start going to the left
// tree(curr_pos+1) = new_point(tree(curr_pos),side,curr_angle); // tree(curr_pos+2) = new_point(tree(curr_pos+1),side,%pi+curr_angle); // curr_pos = curr_pos + 2; curr_angle = curr_angle + %pi/2; case ']' then side = side / ratio; curr_angle = curr_angle - %pi/4; // tree(curr_pos+1) = new_point(tree(curr_pos),side,curr_angle); // tree(curr_pos+2) = new_point(tree(curr_pos+1),side,%pi+curr_angle); // curr_pos = curr_pos + 2; curr_angle = curr_angle + %pi;
else
error('L-system sentence error');
end
end
scf(); clf(); xname('Pythagoras tree: '+string(depth)+' levels') plot2d(real(tree),imag(tree),14); set(gca(),'isoview','on'); set(gca(),'axes_visible',['off','off','off']);
### Recursive approach
A minor change was made so that the final depth of the tree is an argument of <code>fcn</code>, and not a condition set within itself.
{{trans|zkl}}
<lang>function []=fcn(bitmap,ax,ay,bx,by,depth)
if depth < 0 then
return
end
dx = bx - ax; dy = ay - by;
x3 = bx + dy; y3 = by + dx;
x4 = ax + dy; y4 = ay + dx;
x5 = x4 + (dx + dy)/2; y5 = y4 + (dx - dy)/2;
scf(bitmap);
plot2d([x3 x4 x5],[y3 y4 y5],-2)
plot2d([ax bx],[ay by]); plot2d([bx x3],[by y3]);
plot2d([x3 x4],[y3 y4]); plot2d([x4 ax],[y4 ay]);
fcn(bitmap,x4,y4,x5,y5,depth-1);
fcn(bitmap,x5,y5,x3,y3,depth-1);
endfunction
plot_win = scf();
final_depth = 8;
clf();
fcn(plot_win,275,500,375,500,final_depth)
scf(plot_win);
xname('Pythagoras tree: '+string(final_depth)+' levels');
set(gca(),'isoview','on');
set(gca(),'axes_visible',['off','off','off']);
Sidef
{{trans|Java}}
require('Imager')
func tree(img, x1, y1, x2, y2, depth) {
depth <= 0 && return()
var dx = (x2 - x1)
var dy = (y1 - y2)
var x3 = (x2 - dy)
var y3 = (y2 - dx)
var x4 = (x1 - dy)
var y4 = (y1 - dx)
var x5 = (x4 + 0.5*(dx - dy))
var y5 = (y4 - 0.5*(dx + dy))
# square
img.polygon(
points => [
[x1, y1],
[x2, y2],
[x3, y3],
[x4, y4],
],
color => [0, 255/depth, 0],
)
# triangle
img.polygon(
points => [
[x3, y3],
[x4, y4],
[x5, y5],
],
color => [0, 255/depth, 0],
)
tree(img, x4, y4, x5, y5, depth - 1)
tree(img, x5, y5, x3, y3, depth - 1)
}
var (width=1920, height=1080)
var img = %O<Imager>.new(xsize => width, ysize => height)
img.box(filled => 1, color => 'white')
tree(img, width/2.3, height, width/1.8, height, 10)
img.write(file => 'pythagoras_tree.png')
Output image: [https://github.com/trizen/rc/blob/master/img/pythagoras-tree-sidef.png Pythagoras tree]
Yabasic
{{trans|FreeBASIC}}
Sub pythagoras_tree(x1, y1, x2, y2, depth)
local dx, dy, x3, y3, x4, y4, x5, y5
If depth > limit Return
dx = x2 - x1 : dy = y1 - y2
x3 = x2 - dy : y3 = y2 - dx
x4 = x1 - dy : y4 = y1 - dx
x5 = x4 + (dx - dy) / 2
y5 = y4 - (dx + dy) / 2
//draw the box
color 255 - depth * 20, 255, 0
fill triangle x1, y1, x2, y2, x3, y3
fill triangle x3, y3, x4, y4, x1, y1
fill triangle x4, y4, x5, y5, x3, y3
pythagoras_tree(x4, y4, x5, y5, depth +1)
pythagoras_tree(x5, y5, x3, y3, depth +1)
End Sub
// ------=< MAIN >=------
w = 800 : h = int(w * 11 / 16)
w2 = int(w / 2) : diff = int(w / 12)
limit = 12
open window w, h
//backcolor 0, 0, 0
clear window
pythagoras_tree(w2 - diff, h -10 , w2 + diff , h -10 , 1)
zkl
I added green crosses at three of the vertexes of the new square to simulate leaves on the tree. {{trans|Java}} Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl [[File:PythagorasTreeWithLeafs.zkl.jpg|300px|thumb|right]]
fcn pythagorasTree{
bitmap:=PPM(640,640,0xFF|FF|FF); // White background
fcn(bitmap, ax,ay, bx,by, depth=0){
if(depth>10) return();
dx,dy:=bx-ax, ay-by;
x3,y3:=bx-dy, by-dx;
x4,y4:=ax-dy, ay-dx;
x5,y5:=x4 + (dx - dy)/2, y4 - (dx + dy)/2;
bitmap.cross(x3,y3);bitmap.cross(x4,y4);bitmap.cross(x5,y5);
bitmap.line(ax,ay, bx,by, 0); bitmap.line(bx,by, x3,y3, 0);
bitmap.line(x3,y3, x4,y4, 0); bitmap.line(x4,y4, ax,ay, 0);
self.fcn(bitmap,x4,y4, x5,y5, depth+1);
self.fcn(bitmap,x5,y5, x3,y3, depth+1);
}(bitmap,275,500, 375,500);
bitmap.writeJPGFile("pythagorasTree.jpg",True);
}();