Pythagoras tree: Difference between revisions
m (→{{header|Rust}}: Used features of rust version 1.58.0 for println!()) |
|||
| Line 423: | Line 423: | ||
x5 = x4 + 0.5 * (dx - dy) |
x5 = x4 + 0.5 * (dx - dy) |
||
y5 = y4 - 0.5 * (dx + dy) |
y5 = y4 - 0.5 * (dx + dy) |
||
color3 0.3 0.2 + depth / 18 0.1 |
|||
polygon [ x1 y1 x2 y2 x3 y3 x4 y4 ] |
|||
polygon [ x3 y3 x4 y4 x5 y5 ] |
|||
call tree x4 y4 x5 y5 depth + 1 |
call tree x4 y4 x5 y5 depth + 1 |
||
call tree x5 y5 x3 y3 depth + 1 |
call tree x5 y5 x3 y3 depth + 1 |
||
. |
. |
||
. |
. |
||
color3 0.3 0 0.1 |
|||
call tree 41 90 59 90 0</lang> |
call tree 41 90 59 90 0</lang> |
||
Revision as of 14:14, 21 February 2022
You are encouraged to solve this task according to the task description, using any language you may know.
The 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
Ada
<lang Ada>with SDL.Video.Windows.Makers; with SDL.Video.Renderers.Makers; with SDL.Video.Rectangles; with SDL.Events.Events;
procedure Pythagoras_Tree is
Width : constant := 600; Height : constant := 600; Level : constant := 7;
type Point is record X, Y : Float; end record; B1 : constant Point := (X => 250.0, Y => 550.0); B2 : constant Point := (X => 350.0, Y => 550.0);
Window : SDL.Video.Windows.Window; Renderer : SDL.Video.Renderers.Renderer; Event : SDL.Events.Events.Events;
procedure Draw_Pythagoras_Tree (Level : in Natural;
P1, P2 : in Point)
is
use SDL.Video.Rectangles;
Dx : constant Float := P2.X - P1.X;
Dy : constant Float := P1.Y - P2.Y;
R : constant Point := (X => P2.X - Dy, Y => P2.Y - Dx);
L : constant Point := (X => P1.X - Dy, Y => P1.Y - Dx);
M : constant Point := (X => L.X + (Dx - Dy) / 2.0,
Y => L.Y - (Dx + Dy) / 2.0);
CP1 : constant SDL.Video.Rectangles.Point := (C.int (P1.X), C.int (P1.Y));
CP2 : constant SDL.Video.Rectangles.Point := (C.int (P2.X), C.int (P2.Y));
CL : constant SDL.Video.Rectangles.Point := (C.int (L.X), C.int (L.Y));
CR : constant SDL.Video.Rectangles.Point := (C.int (R.X), C.int (R.Y));
CM : constant SDL.Video.Rectangles.Point := (C.int (M.X), C.int (M.Y));
Square : constant SDL.Video.Rectangles.Line_Arrays :=
((CP1, CP2), (CP2, CR), (CR, CL), (CL, CP1));
Triang : constant SDL.Video.Rectangles.Line_Arrays :=
((CR, CL), (CL, CM), (CM, CR));
begin
if Level > 0 then
Renderer.Set_Draw_Colour (Colour => (0, 220, 0, 255));
Renderer.Draw (Lines => Square);
Renderer.Draw (Lines => Triang);
Draw_Pythagoras_Tree (Level - 1, L, M);
Draw_Pythagoras_Tree (Level - 1, M, R);
end if;
end Draw_Pythagoras_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 => "Pythagoras 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));
Renderer.Set_Draw_Colour ((0, 220, 0, 255));
Draw_Pythagoras_Tree (Level, B1, B2); Window.Update_Surface;
Wait; Window.Finalize; SDL.Finalise;
end Pythagoras_Tree;</lang>
AutoHotkey
Requires Gdip Library <lang AutoHotkey>pToken := Gdip_Startup() gdip1() Pythagoras_tree(600, 600, 712, 600, 1) UpdateLayeredWindow(hwnd1, hdc, 0, 0, Width, Height) OnExit, Exit return
Pythagoras_tree(x1, y1, x2, y2, depth){
global G, hwnd1, hdc, Width, Height
if (depth > 7)
Return
Pen := Gdip_CreatePen(0xFF808080, 1) Brush1 := Gdip_BrushCreateSolid(0xFFFFE600) Brush2 := Gdip_BrushCreateSolid(0xFFFAFF00) Brush3 := Gdip_BrushCreateSolid(0xFFDBFF00) Brush4 := Gdip_BrushCreateSolid(0xFFDBFF00) Brush5 := Gdip_BrushCreateSolid(0xFF9EFF00) Brush6 := Gdip_BrushCreateSolid(0xFF80FF00) Brush7 := Gdip_BrushCreateSolid(0xFF60FF00) 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 box/triangle Gdip_FillPolygon(G, Brush%depth%, x1 "," y1 "|" x2 "," y2 "|" x3 "," y3 "|" x4 "," y4 "|" x1 "," y1) Gdip_FillPolygon(G, Brush%depth%, x4 "," y4 "|" x5 "," y5 "|" x3 "," y3 "|" x4 "," y4)
; draw outline Gdip_DrawLines(G, Pen, x1 "," y1 "|" x2 "," y2 "|" x3 "," y3 "|" x4 "," y4 "|" x1 "," y1) Gdip_DrawLines(G, Pen, x4 "," y4 "|" x5 "," y5 "|" x3 "," y3 "|" x4 "," y4) Pythagoras_tree(x4, y4, x5, y5, depth+1) Pythagoras_tree(x5, y5, x3, y3, depth+1)
}
gdip1(){
global Width := A_ScreenWidth, Height := A_ScreenHeight Gui, 1: -Caption +E0x80000 +LastFound +OwnDialogs +Owner +AlwaysOnTop Gui, 1: Show, NA hwnd1 := WinExist() OnMessage(0x201, "WM_LBUTTONDOWN") hbm := CreateDIBSection(Width, Height) hdc := CreateCompatibleDC() obm := SelectObject(hdc, hbm) G := Gdip_GraphicsFromHDC(hdc) Gdip_SetSmoothingMode(G, 4)
}
- ---------------------------------------------------------------
WM_LBUTTONDOWN(){
PostMessage, 0xA1, 2
}
- ---------------------------------------------------------------
gdip2(){
global Gdip_DeleteBrush(pBrush) Gdip_DeletePen(pPen) SelectObject(hdc, obm) DeleteObject(hbm) DeleteDC(hdc) Gdip_DeleteGraphics(G)
}
- ---------------------------------------------------------------
exit: gdip2() ExitApp return</lang>
BASIC256
<lang BASIC256> 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 </lang>
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(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 WinBGIm library. <lang C>
- 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;
}</lang>
C++
Windows version
<lang cpp>#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;
}</lang>
EasyLang
<lang>func tree x1 y1 x2 y2 depth . .
if depth < 8 dx = x2 - x1 dy = y1 - y2 x3 = x2 - dy y3 = y2 - dx x4 = x1 - dy y4 = y1 - dx x5 = x4 + 0.5 * (dx - dy) y5 = y4 - 0.5 * (dx + dy) color3 0.3 0.2 + depth / 18 0.1 polygon [ x1 y1 x2 y2 x3 y3 x4 y4 ] polygon [ x3 y3 x4 y4 x5 y5 ] call tree x4 y4 x5 y5 depth + 1 call tree x5 y5 x3 y3 depth + 1 .
. color3 0.3 0 0.1 call tree 41 90 59 90 0</lang>
F#
Creating an HTML file with an inline SVG. The generation of the tree is done breadth first.
<lang 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</lang>
FreeBASIC
<lang freebasic>' 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</lang>
Go
<lang 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 }</lang>
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.
<lang haskell>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)</lang>
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.
<lang haskell>squares = concat $ take 10 $ iterateM mkBranches start
where start = [(0,100),(100,100),(100,0),(0,0)]
iterateM f x = iterate (>>= f) (pure x)</lang>
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
<lang haskell>--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</lang>
SVG file <lang haskell>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]</lang>
Bitmap image
<lang haskell>--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]</lang>
IS-BASIC
<lang IS-BASIC>100 PROGRAM "Pythagor.bas" 110 OPTION ANGLE DEGREES 120 LET SQ2=SQR(2) 130 SET VIDEO MODE 1:SET VIDEO COLOUR 0:SET VIDEO X 42:SET VIDEO Y 25 140 OPEN #101:"video:" 150 SET PALETTE 0,141 160 DISPLAY #101:AT 1 FROM 1 TO 25 170 PLOT 580,20;ANGLE 90; 180 CALL BROCCOLI(225,10) 190 DO 200 LOOP WHILE INKEY$="" 210 TEXT 220 DEF BROCCOLI(X,Y) 230 IF X<Y THEN EXIT DEF 240 CALL SQUARE(X) 250 PLOT FORWARD X,LEFT 45, 260 CALL BROCCOLI(X/SQ2,Y) 270 PLOT RIGHT 90,FORWARD X/SQ2, 280 CALL BROCCOLI(X/SQ2,Y) 290 PLOT BACK X/SQ2,LEFT 45,BACK X, 300 END DEF 310 DEF SQUARE(X) 320 FOR I=1 TO 4 330 PLOT FORWARD X;RIGHT 90; 340 NEXT 350 END DEF</lang>
J
Using the bash shell, gnuplot for graphics, with ijconsole installed on the PATH, and having saved the program in the file /tmp/pt.ijs the following command plots the Pythagoras tree:
gnuplot --persist -e 'plot"<ijconsole /tmp/pt.ijs"w l'
<lang J> NB. use on linux: gnuplot --persist -e 'plot"< ijconsole /tmp/pt.ijs"w l'
NB. translated from c
ex=: {. why=: {: but_first=: & NB. just for fun append=: , subtract=: -
X=: adverb def ' ex m' Y=: adverb def 'why m'
pt=: dyad define
'a b'=. y
NB. c.x = b.x - (a.y - b.y); NB. c.y = b.y - (b.x - a.x); c=. (b X , a append but_first why b) ,&(-/) (b Y , b ,&ex a) NB. d.x = a.x - (a.y - b.y); NB. d.y = a.y - (b.x - a.x); d=. (a X , a append but_first why b) ,&(-/) (a Y , b ,&ex a)
NB. e.x = d.x + ( b.x - a.x - (a.y - b.y) ) / 2; NB. e.y = d.y - ( b.x - a.x + a.y - b.y ) / 2; e=. (d X + -: (b -&ex a) - a subtract but_first why b) , d Y - -: -/ b X , a X , a Y , b Y
if. 0 < x do. NB. line(a.x,a.y,b.x,b.y); line(c.x,c.y,b.x,b.y); line(c.x,c.y,d.x,d.y); line(a.x,a.y,d.x,d.y); echo (a ,: b) , (c ,: b) , (c ,: d) ,: (a ,: d) echo (<: x) pt"2 (d ,: e) ,: (e ,: c) NB. pythagorasTree(d,e,times-1);pythagorasTree(e,c,times-1); end.
)
NB. a.x = 6*side/2 - side/2;
NB. a.y = 4*side;
NB. b.x = 6*side/2 + side/2;
NB. b.y = 4*side;
petri=: 7&$: :(empty@:(pt (x:inv 5r2 7r2 ,. 4)&*))
petri 1 exit 0 </lang>
Java
<lang java>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);
});
}
}</lang>
JavaScript
<lang javascript><!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></lang>
jq
Adapted from Wren
Works with gojq, the Go implementation of jq
The jq program presented here generates SVG, which can readily be viewed in a browser, at least if the file suffix is .svg.
Notice that the SVG viewBox dimensions are computed dynamically. <lang jq>
- viewBox = <min-x> <min-y> <width> <height>
- Input: {svg, minx, miny, maxx, maxy}
def svg:
"<svg viewBox='\(.minx - 4|floor) \(.miny - 4 |floor) \(6 + .maxx - .minx|ceil) \(6 + .maxy - .miny|ceil)'", " preserveAspectRatio='xMinYmin meet'", " xmlns='http://www.w3.org/2000/svg' >", .svg, "</svg>";
def minmax($xy):
.minx = ([.minx, $xy[0]]|min) | .miny = ([.miny, $xy[1]]|min) | .maxx = ([.maxx, $xy[0]]|max) | .maxy = ([.maxy, $xy[1]]|max) ;
- default values for $fill and $stroke are provided
def Polygon( $ary; $fill; $stroke):
def rnd: 1000*.|round/1000;
($fill // "none") as $fill
| ($stroke // "black") as $stroke
| ($ary | map(rnd) | join(" ")) as $a
| .svg += "\n<polygon points='\($a)' fill='\($fill)' stroke='\($stroke)' />"
| minmax($ary | [ ([ .[ range(0;length;2)]] |min), ([ .[range(1;length;2)]]|min) ] )
| minmax($ary | [ ([ .[ range(0;length;2)]] |max), ([ .[range(1;length;2)]]|max) ] ) ;
def Square($A; $B; $C; $D; $fill; $stroke):
Polygon( $A + $B + $C + $D; $fill; $stroke);
def Triangle($A; $B; $C; $fill; $stroke):
Polygon( $A + $B + $C; $fill; $stroke);
def PythagorasTree:
def drawTree($x1; $y1; $x2; $y2; $depth):
if $depth <= 0 then .
else ($x2 - $x1) as $dx
| ($y1 - $y2) as $dy
| ($x2 - $dy) as $x3
| ($y2 - $dx) as $y3
| ($x1 - $dy) as $x4
| ($y1 - $dx) as $y4
| ($x4 + 0.5 * ($dx - $dy)) as $x5
| ($y4 - 0.5 * ($dx + $dy)) as $y5
# draw a square
| "rgb(\(256 - $depth * 20), 0, 0)" as $col
| Square([$x1, $y1]; [$x2, $y2]; [$x3, $y3] ; [$x4, $y4] ; $col; "lightgray")
# draw a triangle
| "rgb( 128, \(256 - $depth * 20), 128)" as $col
| Triangle([$x3, $y3]; [$x4, $y4]; [$x5, $y5]; $col; "lightgray")
| drawTree($x4; $y4; $x5; $y5; $depth - 1)
| drawTree($x5; $y5; $x3; $y3; $depth - 1)
end ;
{svg: "", minx: infinite, miny: infinite, maxx: -infinite, maxy: -infinite}
| drawTree(275; 500; 375; 500; 7);
PythagorasTree | svg </lang>
- Output:
Julia
<lang Julia>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)</lang>
Kotlin
<lang scala>// 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)
}
}
}</lang>
M2000 Interpreter
Cartesian Coordinates
<lang M2000 Interpreter> 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 </lang>
Polar Coordinates
<lang M2000 Interpreter> 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 </lang>
Mathematica / Wolfram Language
<lang Mathematica>n = 7; colors = Blend[{Orange, Yellow, Green}, #] & /@ Subdivide[n - 1]; ClearAll[NextConfigs, NewConfig] NewConfig[b1_List, b2_List] := Module[{diff, perp},
diff = b2 - b1;
perp = Cross[b2 - b1];
<|"quad" -> Polygon[{b1, b2, b2 + perp, b1 + perp}], "triang" -> Polygon[{b1 + 1.5 perp + diff/2, b1 + perp, b2 + perp}]|>
]
NextConfigs[config_Association] := Module[{tr},
tr = config["triangs"]All, 1; tr = Join[NewConfig @@@ tr[[All, {2, 1}]], NewConfig @@@ tr[[All, {1, 3}]]]; <|"quads" -> trAll, "quad", "triangs" -> trAll, "triang"|> ]
nc = NewConfig[{-0.5, 0.0}, {0.5, 0.0}]; config = <|"quads" -> {nc["quad"]}, "triangs" -> {nc["triang"]}|>; config = NestList[NextConfigs, config, n - 1]; Graphics[MapThread[{EdgeForm[Black], FaceForm[#2], #1["quads"], #1["triangs"]} &, {config, colors}]]</lang>
Nim
Using Perl algorithm with some changes: background is black and there is no color variation according to depth. <lang Nim>import imageman
const
Width = 1920 Height = 1080 MaxDepth = 10 Color = ColorRGBU([byte 0, 255, 0])
proc drawTree(img: var Image; x1, y1, x2, y2: int; depth: Natural) =
if depth == 0: return
let dx = x2 - x1 dy = y1 - y2 x3 = x2 - dy y3 = y2 - dx x4 = x1 - dy y4 = y1 - dx x5 = x4 + (dx - dy) div 2 y5 = y4 - (dx + dy) div 2
# Draw square. img.drawPolyline(true, Color, (x1, y1), (x2, y2), (x3, y3), (x4, y4))
# Draw triangle. img.drawPolyline(true, Color, (x3, y3), (x4, y4), (x5, y5))
# Next level. img.drawTree(x4, y4, x5, y5, depth - 1) img.drawTree(x5, y5, x3, y3, depth - 1)
var image = initImage[ColorRGBU](Width, Height)
image.drawTree(int(Width / 2.3), Height - 1, int(Width / 1.8), Height - 1, MaxDepth)
image.savePNG("pythagoras_tree.png", compression = 9)</lang>
Ol
<lang scheme> (import (lib gl)) (import (OpenGL version-1-0)) (gl:set-window-size 700 600) (gl:set-window-title "http://rosettacode.org/wiki/Pythagoras_tree")
(glLineWidth 2) (gl:set-renderer (lambda (mouse)
(glClear GL_COLOR_BUFFER_BIT) (glLoadIdentity) (glOrtho -3 4 -1 5 0 1)
(let loop ((a '(0 . 0)) (b '(1 . 0)) (n 7))
(unless (zero? n)
(define dx (- (car b) (car a)))
(define dy (- (cdr b) (cdr a)))
(define c (cons
(- (car b) dy)
(+ (cdr b) dx)))
(define d (cons
(- (car a) dy)
(+ (cdr a) dx)))
(define e (cons
(- (/ (+ (car c) (car d)) 2) (/ dy 2))
(+ (/ (+ (cdr c) (cdr d)) 2) (/ dx 2))))
(glColor3f 0 (+ 1/3 (/ 2/3 n)) 0)
(glBegin GL_QUADS)
(glVertex2f (car a) (cdr a))
(glVertex2f (car b) (cdr b))
(glVertex2f (car c) (cdr c))
(glVertex2f (car d) (cdr d))
(glEnd)
(glColor3f 1 0 0)
(glBegin GL_TRIANGLES)
(glVertex2f (car c) (cdr c))
(glVertex2f (car e) (cdr e))
(glVertex2f (car d) (cdr d))
(glEnd)
(loop d e (- n 1))
(loop e c (- n 1))
))
)) </lang>
PARI/GP
This version with recursion, in general, is a translation of zkl version. Almost "as is", so, outputting upside-down tree.
<lang parigp>\\ 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 }</lang>
- Output:
*** Pythagoras Tree, depth 9, size 640 *** Start: 275,500,375,500
Perl
<lang perl>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');</lang>
Phix
You can run this online here.
-- demo\rosetta\PythagorasTree.exw with javascript_semantics include pGUI.e Ihandle dlg, canvas cdCanvas cddbuffer, cdcanvas enum FILL, BORDER procedure drawTree(atom x1, y1, x2, y2, integer depth, dd) atom dx = x2 - x1, dy = y1 - y2, x3 = x2 - dy, y3 = y2 - dx, x4 = x1 - dy, y4 = y1 - dx, x5 = x4 + 0.5 * (dx - dy), y5 = y4 - 0.5 * (dx + dy) if depth=dd then integer r = 250-depth*20 for draw=FILL to BORDER do -- one square... cdCanvasSetForeground(cddbuffer, iff(draw=FILL?rgb(r,#FF,0):CD_GRAY)) integer mode = iff(draw=FILL?CD_FILL:CD_CLOSED_LINES) cdCanvasBegin(cddbuffer,mode) cdCanvasVertex(cddbuffer, x1, 640-y1) cdCanvasVertex(cddbuffer, x2, 640-y2) cdCanvasVertex(cddbuffer, x3, 640-y3) cdCanvasVertex(cddbuffer, x4, 640-y4) cdCanvasEnd(cddbuffer) -- ...and the attached triangle if draw=FILL then cdCanvasSetForeground(cddbuffer, rgb(r-depth*10,#FF,0)) end if cdCanvasBegin(cddbuffer,mode) cdCanvasVertex(cddbuffer, x3, 640-y3) cdCanvasVertex(cddbuffer, x4, 640-y4) cdCanvasVertex(cddbuffer, x5, 640-y5) cdCanvasEnd(cddbuffer) end for elsif depth<dd then drawTree(x4, y4, x5, y5, depth + 1, dd) drawTree(x5, y5, x3, y3, depth + 1, dd) end if end procedure function redraw_cb(Ihandle /*ih*/, integer /*posx*/, /*posy*/) cdCanvasActivate(cddbuffer) for i=0 to 7 do -- (draw leaves last) drawTree(275, 500, 375, 500, 0, i) end for 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 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") IupShow(dlg) if platform()!=JS then IupMainLoop() IupClose() end if end procedure main()
Processing
<lang java>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);
}</lang>
Processing Python mode
<lang python>def setup():
size(800, 400) background(255) stroke(0, 255, 0) tree(width / 2.3, height, width / 1.8, height, 10)
def tree(x1, y1, x2, y2, depth):
if depth <= 0: return dx = (x2 - x1) dy = (y1 - y2)
x3 = (x2 - dy) y3 = (y2 - dx) x4 = (x1 - dy) y4 = (y1 - dx) x5 = (x4 + 0.5 * (dx - dy)) 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)</lang>
PureBasic
<lang PureBasic>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</lang>
Python
Using turtle graphics and the Zkl example for the calculations. <lang python>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()</lang>
R
<lang r>## 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)</lang>
- 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
QB64
<lang qb64>_Title "Pythagoras Tree"
Dim As Integer sw, sh sw = 640 sh = 480
Screen _NewImage(sw, sh, 32)
Call pythTree(sw / 2 - sw / 12, sh - 30, sw / 2 + sw / 12, sh - 30, 0)
Sleep System
Sub pythTree (ax As Integer, ay As Integer, bx As Integer, by As Integer, depth As Integer)
Dim As Single cx, cy, dx, dy, ex, ey Dim As Integer c
cx = ax - ay + by
cy = ax + ay - bx
dx = bx + by - ay
dy = ax - bx + by
ex = (cx - cy + dx + dy) * 0.5
ey = (cx + cy - dx + dy) * 0.5
c = depth * 15
Color _RGB(c Mod 256, Abs((255 - c)) Mod 256, (144 + c) Mod 256)
Line (cx, cy)-(ax, ay)
Line (ax, ay)-(bx, by)
Line (bx, by)-(dx, dy)
Line (dx, dy)-(cx, cy)
Line (cx, cy)-(ex, ey)
Line (ex, ey)-(dx, dy)
If depth < 12 Then
Call pythTree(cx, cy, ex, ey, depth + 1)
Call pythTree(ex, ey, dx, dy, depth + 1)
End If
End Sub</lang>
Racket
<lang 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)</lang>
Raku
(formerly Perl 6) We'll generate a SVG image. <lang perl6>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);</lang>
Ring
<lang 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)</lang>
Output: https://www.dropbox.com/s/a1gtue7tvmaj2je/PythagorasTree.jpg?dl=0
Ruby
A clone of processing version <lang ruby>
- frozen_string_literal: true
def setup
sketch_title 'Pythagoras Tree' background(255) stroke(0, 255, 0) tree(width / 2.3, height, width / 1.8, height, 10)
end
def tree(x1, y1, x2, y2, depth)
return if depth <= 0
dx = (x2 - x1) dy = (y1 - y2)
x3 = (x2 - dy) y3 = (y2 - dx) x4 = (x1 - dy) y4 = (y1 - dx) x5 = (x4 + 0.5 * (dx - dy)) y5 = (y4 - 0.5 * (dx + dy)) # square begin_shape fill(0.0, 255.0 / depth, 0.0) vertex(x1, y1) vertex(x2, y2) vertex(x3, y3) vertex(x4, y4) vertex(x1, y1) end_shape # triangle begin_shape fill(0.0, 255.0 / depth, 0.0) vertex(x3, y3) vertex(x4, y4) vertex(x5, y5) vertex(x3, y3) end_shape tree(x4, y4, x5, y5, depth - 1) tree(x5, y5, x3, y3, depth - 1)
end
def settings
size(800, 400)
end
</lang>
Rust
Creates a pythagoras_tree.svg file (12 levels) that can be opened in a browser <lang fsharp>/* add to file Cargo.toml: [dependencies] svg = "0.10.0"
- /
use svg::node::element::{Group, Polygon};
fn main() {
let mut doc = svg::Document::new().set("stroke", "white");
let mut base: Vec<[(f64, f64); 2]> = vec!(-200.0, 0.0), (200.0, 0.0);
for lvl in 0..12u8 {
let rg = |step| lvl.wrapping_mul(step).wrapping_add(80 - step * 2);
let mut group = Group::new().set("fill", format!("#{:02X}{:02X}18", rg(20), rg(30))); // level color
let mut next_base = Vec::new();
for [a, b] in base {
let v = (b.0 - a.0, b.1 - a.1);
let c = (a.0 + v.1, a.1 - v.0);
let d = (c.0 + v.0, c.1 + v.1);
let e = (c.0 + 0.5 * (v.0 + v.1), c.1 + 0.5 * (v.1 - v.0));
group = group.add(Polygon::new().set("points", vec![a, c, e, d, c, d, b]));
next_base.extend([[c, e], [e, d]]);
}
base = next_base;
doc = doc.add(group);
}
let (x0, y0) = (base.iter()).fold((0.0, 0.0), |(x0, y0), [(x, y), _]| (x.min(x0), y.min(y0)));
let file = "pythagoras_tree.svg";
match svg::save(file, &doc.set("viewBox", (x0, y0, -x0 * 2.0, -y0))) {
Ok(_) => println!("{file} file written successfully!"),
Err(e) => println!("failed to write {file}: {e}"),
}
}</lang>
Scala
Java Swing Interoperability
<lang Scala>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)
}
})
}</lang>
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.
<lang>side = 1; //side length of the square
depth = 8; //final number of branch levels
//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']);</lang>
Recursive approach
A minor change was made so that the final depth of the tree is an argument of fcn, and not a condition set within itself.
<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']);</lang>
Sidef
<lang ruby>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')</lang> Output image: Pythagoras tree
Wren
<lang ecmascript>import "graphics" for Canvas, Color import "dome" for Window import "./polygon" for Polygon
var DepthLimit = 7 var Hue = 0.15
class PythagorasTree {
construct new(width, height) {
Window.title = "Pythagoras Tree"
Window.resize(width, height)
Canvas.resize(width, height)
}
init() {
Canvas.cls(Color.white)
drawTree(275, 500, 375, 500, 0)
}
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)
// draw a square
var col = Color.hsv((Hue + depth * 0.02) * 360, 1, 1)
var square = Polygon.quick([[x1, y1], [x2, y2], [x3, y3], [x4, y4]])
square.drawfill(col)
square.draw(Color.lightgray)
// draw a triangle
col = Color.hsv((Hue + depth * 0.035) * 360, 1, 1)
var triangle = Polygon.quick([[x3, y3], [x4, y4], [x5, y5]])
triangle.drawfill(col)
triangle.draw(Color.lightgray)
drawTree(x4, y4, x5, y5, depth + 1)
drawTree(x5, y5, x3, y3, depth + 1)
}
update() {}
draw(alpha) {}
}
var Game = PythagorasTree.new(640, 640)</lang>
Yabasic
<lang Yabasic>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)</lang>
zkl
I added green crosses at three of the vertexes of the new square to simulate leaves on the tree.
Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl
<lang zkl>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);
}();</lang>
- Programming Tasks
- Solutions by Programming Task
- Ada
- SDLAda
- AutoHotkey
- BASIC256
- C
- C++
- EasyLang
- F Sharp
- FreeBASIC
- Go
- Haskell
- Gloss
- Easyplot
- IS-BASIC
- J
- Java
- JavaScript
- Jq
- Julia
- Kotlin
- M2000 Interpreter
- Mathematica
- Wolfram Language
- Nim
- Imageman
- Ol
- PARI/GP
- Perl
- Phix
- Phix/pGUI
- Phix/online
- Processing
- Processing Python mode
- PureBasic
- Python
- R
- Pages with broken file links
- QB64
- Racket
- Raku
- Ring
- Ruby
- RubyGems
- JRubyArt
- Rust
- Scala
- Scilab
- Sidef
- Wren
- DOME
- Wren-polygon
- Yabasic
- Zkl