Sierpinski triangle/Graphical

From Rosetta Code
Task
Sierpinski triangle/Graphical
You are encouraged to solve this task according to the task description, using any language you may know.

Produce a graphical representation of a Sierpinski triangle of order N in any orientation.

An example of Sierpinski's triangle (order = 8) looks like this:

Sierpinski Triangle Unicon.PNG

ActionScript[edit]

SierpinskiTriangle class:

 
package {
 
import flash.display.GraphicsPathCommand;
import flash.display.Sprite;
 
/**
* A Sierpinski triangle.
*/

public class SierpinskiTriangle extends Sprite {
 
/**
* Creates a new SierpinskiTriangle object.
*
* @param n The order of the Sierpinski triangle.
* @param c1 The background colour.
* @param c2 The foreground colour.
* @param width The width of the triangle.
* @param height The height of the triangle.
*/

public function SierpinskiTriangle(n:uint, c1:uint, c2:uint, width:Number, height:Number):void {
_init(n, c1, c2, width, height);
}
 
/**
* Generates the triangle.
*
* @param n The order of the Sierpinski triangle.
* @param c1 The background colour.
* @param c2 The foreground colour.
* @param width The width of the triangle.
* @param height The height of the triangle.
* @private
*/

private function _init(n:uint, c1:uint, c2:uint, width:Number, height:Number):void {
 
if ( n <= 0 )
return;
 
// Draw the outer triangle.
 
graphics.beginFill(c1);
graphics.moveTo(width / 2, 0);
graphics.lineTo(0, height);
graphics.lineTo(width, height);
graphics.lineTo(width / 2, 0);
 
// Draw the inner triangle.
 
graphics.beginFill(c2);
graphics.moveTo(width / 4, height / 2);
graphics.lineTo(width * 3 / 4, height / 2);
graphics.lineTo(width / 2, height);
graphics.lineTo(width / 4, height / 2);
 
if ( n == 1 )
return;
 
// Recursively generate three Sierpinski triangles of half the size and order n - 1 and position them appropriately.
 
var sub1:SierpinskiTriangle = new SierpinskiTriangle(n - 1, c1, c2, width / 2, height / 2);
var sub2:SierpinskiTriangle = new SierpinskiTriangle(n - 1, c1, c2, width / 2, height / 2);
var sub3:SierpinskiTriangle = new SierpinskiTriangle(n - 1, c1, c2, width / 2, height / 2);
 
sub1.x = width / 4;
sub1.y = 0;
sub2.x = 0;
sub2.y = height / 2;
sub3.x = width / 2;
sub3.y = height / 2;
 
addChild(sub1);
addChild(sub2);
addChild(sub3);
 
}
 
}
 
}
 

Document class:

 
package {
 
import flash.display.Sprite;
import flash.events.Event;
 
public class Main extends Sprite {
 
public function Main():void {
if ( stage ) init();
else addEventListener(Event.ADDED_TO_STAGE, init);
}
 
private function init(e:Event = null):void {
var s:SierpinskiTriangle = new SierpinskiTriangle(5, 0x0000FF, 0xFFFF00, 300, 150 * Math.sqrt(3));
// Equilateral triangle (blue and yellow)
s.x = s.y = 20;
addChild(s);
}
 
}
 
}
 

Asymptote[edit]

This simple-minded recursive apporach doesn't scale well to large orders, but neither would your PostScript viewer, so there's nothing to gain from a more efficient algorithm. Thus are the perils of vector graphics.

path subtriangle(path p, real node) {
return
point(p, node) --
point(p, node + 1/2) --
point(p, node - 1/2) --
cycle;
}
 
void sierpinski(path p, int order) {
if (order == 0)
fill(p);
else {
sierpinski(subtriangle(p, 0), order - 1);
sierpinski(subtriangle(p, 1), order - 1);
sierpinski(subtriangle(p, 2), order - 1);
}
}
 
sierpinski((0, 0) -- (5 inch, 1 inch) -- (2 inch, 6 inch) -- cycle, 10);

AutoHotkey[edit]

Library: GDIP
#NoEnv
#SingleInstance, Force
SetBatchLines, -1
 
; Parameters
Width := 512, Height := Width/2*3**0.5, n := 8 ; iterations = 8
 
; Uncomment if Gdip.ahk is not in your standard library
#Include ..\lib\Gdip.ahkl
 
If !pToken := Gdip_Startup() ; Start gdi+
{
MsgBox, 48, gdiplus error!, Gdiplus failed to start. Please ensure you have gdiplus on your system
ExitApp
}
; I've added a simple new function here, just to ensure if anyone is having any problems then to make sure they are using the correct library version
if (Gdip_LibraryVersion() < 1.30)
{
MsgBox, 48, Version error!, Please download the latest version of the gdi+ library
ExitApp
}
OnExit, Exit
 
; Create a layered window (+E0x80000 : must be used for UpdateLayeredWindow to work!) that is always on top (+AlwaysOnTop), has no taskbar entry or caption
Gui, -Caption +E0x80000 +LastFound +OwnDialogs +Owner +AlwaysOnTop
Gui, Show
hwnd1 := WinExist()
OnMessage(0x201, "WM_LBUTTONDOWN")
 
, hbm := CreateDIBSection(Width, Height)
, hdc := CreateCompatibleDC()
, obm := SelectObject(hdc, hbm)
, G := Gdip_GraphicsFromHDC(hdc)
, Gdip_SetSmoothingMode(G, 4)
 
; Sierpinski triangle by subtracting triangles
, pBrushBlack := Gdip_BrushCreateSolid(0xff000000)
, rectangle := 0 "," 0 "|" 0 "," Height "|" Width "," Height "|" Width "," 0
, Gdip_FillPolygon(G, pBrushBlack, rectangle, FillMode=0)
 
, pBrushBlue := Gdip_BrushCreateSolid(0xff0000ff)
, triangle := Width/2 "," 0 "|" 0 "," Height "|" Width "," Height
, Gdip_FillPolygon(G, pBrushBlue, triangle, FillMode=0)
, Gdip_DeleteBrush(pBrushBlue)
 
, UpdateLayeredWindow(hwnd1, hdc, (A_ScreenWidth-Width)/2, (A_ScreenHeight-Height)/2, Width, Height)
 
, k:=2, x:=0, y:=0, i:=1
Loop, % n
{
Sleep 0.5*1000
While x*y<Width*Height
{
triangle := x "," y "|" x+Width/2/k "," y+Height/k "|" x+Width/k "," y
, Gdip_FillPolygon(G, pBrushBlack, triangle, FillMode=0)
, x += Width/k
, (x >= Width) ? (x := i*Width/2/k, y += Height/k, i:=!i) : ""
}
UpdateLayeredWindow(hwnd1, hdc, (A_ScreenWidth-Width)/2, (A_ScreenHeight-Height)/2, Width, Height)
, k*=2, x:=0, y:=0, i:=1
}
 
Gdip_DeleteBrush(pBrushBlack)
 
, UpdateLayeredWindow(hwnd1, hdc, (A_ScreenWidth-Width)/2, (A_ScreenHeight-Height)/2, Width, Height)
Sleep, 1*1000
 
; Bonus: Sierpinski triangle by random dots
Gdip_GraphicsClear(G, 0xff000000)
, pBrushBlue := Gdip_BrushCreateSolid(0xff0000ff)
, x1:=Width/2, y1:=0, x2:=0, y2:=Height, x3:=Width, y3:=Height
, x:= Width/2, y:=Height/2 ; I'm to lazy to pick a random point.
Loop, % n
{
Loop, % 10*10**(A_Index/2)
{
Random, rand, 1, 3
x := abs(x+x%rand%)/2
, y := abs(y+y%rand%)/2
, Gdip_FillEllipse(G, pBrushBlue, x, y, 1, 1)
}
UpdateLayeredWindow(hwnd1, hdc, (A_ScreenWidth-Width)/2, (A_ScreenHeight-Height)/2, Width, Height)
Sleep, 0.5*1000
}
SelectObject(hdc, obm)
, DeleteObject(hbm)
, DeleteDC(hdc)
, Gdip_DeleteGraphics(G)
Return
 
Exit:
Gdip_Shutdown(pToken)
ExitApp
 
WM_LBUTTONDOWN()
{
If (A_Gui = 1)
PostMessage, 0xA1, 2
}

BBC BASIC[edit]

      order% = 8
size% = 2^order%
VDU 23,22,size%;size%;8,8,16,128
FOR Y% = 0 TO size%-1
FOR X% = 0 TO size%-1
IF (X% AND Y%)=0 PLOT X%*2,Y%*2
NEXT
NEXT Y%
 

Sierpinski triangle bbc.gif

C[edit]

Sierp-tri-c.png
Code lifted from Dragon curve. Given a depth n, draws a triangle of size 2^n in a PNM file to the standard output. Usage: gcc -lm stuff.c -o sierp; ./sierp 9 > triangle.pnm. Sample image generated with depth 9. Generated image's size depends on the depth: it plots dots, but does not draw lines, so a large size with low depth is not possible.
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
 
long long x, y, dx, dy, scale, clen, cscale;
typedef struct { double r, g, b; } rgb;
rgb ** pix;
 
void sc_up()
{
scale *= 2; x *= 2; y *= 2;
cscale *= 3;
}
 
void h_rgb(long long x, long long y)
{
rgb *p = &pix[y][x];
 
# define SAT 1
double h = 6.0 * clen / cscale;
double VAL = 1;
double c = SAT * VAL;
double X = c * (1 - fabs(fmod(h, 2) - 1));
 
switch((int)h) {
case 0: p->r += c; p->g += X; return;
case 1: p->r += X; p->g += c; return;
case 2: p->g += c; p->b += X; return;
case 3: p->g += X; p->b += c; return;
case 4: p->r += X; p->b += c; return;
default:
p->r += c; p->b += X;
}
}
 
void iter_string(const char * str, int d)
{
long long len;
while (*str != '\0') {
switch(*(str++)) {
case 'X':
if (d) iter_string("XHXVX", d - 1);
else{
clen ++;
h_rgb(x/scale, y/scale);
x += dx;
y -= dy;
}
continue;
case 'V':
len = 1LLU << d;
while (len--) {
clen ++;
h_rgb(x/scale, y/scale);
y += dy;
}
continue;
case 'H':
len = 1LLU << d;
while(len --) {
clen ++;
h_rgb(x/scale, y/scale);
x -= dx;
}
continue;
}
}
}
 
void sierp(long leng, int depth)
{
long i;
long h = leng + 20, w = leng + 20;
 
/* allocate pixel buffer */
rgb *buf = malloc(sizeof(rgb) * w * h);
pix = malloc(sizeof(rgb *) * h);
for (i = 0; i < h; i++)
pix[i] = buf + w * i;
memset(buf, 0, sizeof(rgb) * w * h);
 
/* init coords; scale up to desired; exec string */
x = y = 10; dx = leng; dy = leng; scale = 1; clen = 0; cscale = 3;
for (i = 0; i < depth; i++) sc_up();
iter_string("VXH", depth);
 
/* write color PNM file */
unsigned char *fpix = malloc(w * h * 3);
double maxv = 0, *dbuf = (double*)buf;
 
for (i = 3 * w * h - 1; i >= 0; i--)
if (dbuf[i] > maxv) maxv = dbuf[i];
for (i = 3 * h * w - 1; i >= 0; i--)
fpix[i] = 255 * dbuf[i] / maxv;
 
printf("P6\n%ld %ld\n255\n", w, h);
fflush(stdout); /* printf and fwrite may treat buffer differently */
fwrite(fpix, h * w * 3, 1, stdout);
}
 
int main(int c, char ** v)
{
int size, depth;
 
depth = (c > 1) ? atoi(v[1]) : 10;
size = 1 << depth;
 
fprintf(stderr, "size: %d depth: %d\n", size, depth);
sierp(size, depth + 2);
 
return 0;
}

C++[edit]

STriCpp.png
 
#include <windows.h>
#include <string>
#include <iostream>
 
const int BMP_SIZE = 612;
 
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 sierpinski {
public:
void draw( int o ) {
colors[0] = 0xff0000; colors[1] = 0x00ff33; colors[2] = 0x0033ff;
colors[3] = 0xffff00; colors[4] = 0x00ffff; colors[5] = 0xffffff;
bmp.create( BMP_SIZE, BMP_SIZE ); HDC dc = bmp.getDC();
drawTri( dc, 0, 0, ( float )BMP_SIZE, ( float )BMP_SIZE, o / 2 );
bmp.setPenColor( colors[0] ); MoveToEx( dc, BMP_SIZE >> 1, 0, NULL );
LineTo( dc, 0, BMP_SIZE - 1 ); LineTo( dc, BMP_SIZE - 1, BMP_SIZE - 1 );
LineTo( dc, BMP_SIZE >> 1, 0 ); bmp.saveBitmap( "./st.bmp" );
}
private:
void drawTri( HDC dc, float l, float t, float r, float b, int i ) {
float w = r - l, h = b - t, hh = h / 2.f, ww = w / 4.f;
if( i ) {
drawTri( dc, l + ww, t, l + ww * 3.f, t + hh, i - 1 );
drawTri( dc, l, t + hh, l + w / 2.f, t + h, i - 1 );
drawTri( dc, l + w / 2.f, t + hh, l + w, t + h, i - 1 );
}
bmp.setPenColor( colors[i % 6] );
MoveToEx( dc, ( int )( l + ww ), ( int )( t + hh ), NULL );
LineTo ( dc, ( int )( l + ww * 3.f ), ( int )( t + hh ) );
LineTo ( dc, ( int )( l + ( w / 2.f ) ), ( int )( t + h ) );
LineTo ( dc, ( int )( l + ww ), ( int )( t + hh ) );
}
myBitmap bmp;
DWORD colors[6];
};
int main(int argc, char* argv[]) {
sierpinski s; s.draw( 12 );
return 0;
}
 

D[edit]

The output image is the same as the Go version. This requires the module from the Grayscale image Task.

Translation of: Go
void main() {
import grayscale_image;
 
enum order = 8,
margin = 10,
width = 2 ^^ order;
 
auto im = new Image!Gray(width + 2 * margin, width + 2 * margin);
im.clear(Gray.white);
 
foreach (immutable y; 0 .. width)
foreach (immutable x; 0 .. width)
if ((x & y) == 0)
im[x + margin, y + margin] = Gray.black;
im.savePGM("sierpinski.pgm");
}

ERRE[edit]

 
PROGRAM SIERPINSKY
 
!$INCLUDE="PC.LIB"
 
BEGIN
ORDER%=8
SIZE%=2^ORDER%
SCREEN(9)
GR_WINDOW(0,0,520,520)
FOR Y%=0 TO SIZE%-1 DO
FOR X%=0 TO SIZE%-1 DO
IF (X% AND Y%)=0 THEN PSET(X%*2,Y%*2,2) END IF
END FOR
END FOR
GET(K$)
END PROGRAM
 

FreeBASIC[edit]

' version 06-07-2015
' compile with: fbc -s console or with: fbc -s gui
 
#Define black 0
#Define white RGB(255,255,255)
 
Dim As Integer x, y
Dim As Integer order = 9
Dim As Integer size = 2 ^ order
 
ScreenRes size, size, 32
Line (0,0) - (size -1, size -1), black, bf
 
For y = 0 To size -1
For x = 0 To size -1
If (x And y) = 0 Then PSet(x, y) ' ,white
Next
Next
 
' empty keyboard buffer
While Inkey <> "" : Wend
WindowTitle "Hit any key to end program"
Sleep
End

gnuplot[edit]

Generating X,Y coordinates by the ternary digits of parameter t.

# triangle_x(n) and triangle_y(n) return X,Y coordinates for the
# Sierpinski triangle point number n, for integer n.
triangle_x(n) = (n > 0 ? 2*triangle_x(int(n/3)) + digit_to_x(int(n)%3) : 0)
triangle_y(n) = (n > 0 ? 2*triangle_y(int(n/3)) + digit_to_y(int(n)%3) : 0)
digit_to_x(d) = (d==0 ? 0 : d==1 ? -1 : 1)
digit_to_y(d) = (d==0 ? 0 : 1)
 
# Plot the Sierpinski triangle to "level" many replications.
# "trange" and "samples" are chosen so the parameter t runs through
# integers t=0 to 3**level-1, inclusive.
#
level=6
set trange [0:3**level-1]
set samples 3**level
set parametric
set key off
plot triangle_x(t), triangle_y(t) with points

Go[edit]

Output png
Translation of: Icon and Unicon
package main
 
import (
"fmt"
"image"
"image/color"
"image/draw"
"image/png"
"os"
)
 
func main() {
const order = 8
const width = 1 << order
const margin = 10
bounds := image.Rect(-margin, -margin, width+2*margin, width+2*margin)
im := image.NewGray(bounds)
gBlack := color.Gray{0}
gWhite := color.Gray{255}
draw.Draw(im, bounds, image.NewUniform(gWhite), image.ZP, draw.Src)
 
for y := 0; y < width; y++ {
for x := 0; x < width; x++ {
if x&y == 0 {
im.SetGray(x, y, gBlack)
}
}
}
f, err := os.Create("sierpinski.png")
if err != nil {
fmt.Println(err)
return
}
if err = png.Encode(f, im); err != nil {
fmt.Println(err)
}
if err = f.Close(); err != nil {
fmt.Println(err)
}
}

Haskell[edit]

This program uses the diagrams package to produce the Sierpinski triangle. The package implements an embedded DSL for producing vector graphics. Depending on the command-line arguments, the program can generate SVG, PNG, PDF or PostScript output.

For fun, we take advantage of Haskell's layout rules, and the operators provided by the diagrams package, to give the reduce function the shape of a triangle. It could also be written as reduce t = t === (t ||| t).

The command to produce the SVG output is sierpinski -o Sierpinski-Haskell.svg.

Sierpinski Triangle
import Diagrams.Prelude
import Diagrams.Backend.Cairo.CmdLine
 
triangle = eqTriangle # fc black # lw 0
 
reduce t = t
===
(t ||| t)
 
sierpinski = iterate reduce triangle
 
main = defaultMain $ sierpinski !! 7
 

Icon and Unicon[edit]

The following code is adapted from a program by Ralph Griswold that demonstrates an interesting way to draw the Sierpinski Triangle. Given an argument of the order it will calculate the canvas size needed with margin. It will not stop you from asking for a triangle larger than you display. For an explanation, see "Chaos and Fractals", Heinz-Otto Peitgen, Harmut Jurgens, and Dietmar Saupe, Springer-Verlag, 1992, pp. 132-134.

Sample Output for order=8
link wopen
 
procedure main(A)
local width, margin, x, y
 
width := 2 ^ (order := (0 < integer(\A[1])) | 8)
wsize := width + 2 * (margin := 30 )
WOpen("label=Sierpinski", "size="||wsize||","||wsize) |
stop("*** cannot open window")
 
every y := 0 to width - 1 do
every x := 0 to width - 1 do
if iand(x, y) = 0 then DrawPoint(x + margin, y + margin)
 
Event()
end

Original source IPL Graphics/sier1.

J[edit]

Solution:

   load 'viewmat'
'rgb'viewmat--. |. (~:_1&|.)^:(<@#) (2^8){.1
 

or

 
load'viewmat'
viewmat(,~,.~)^:8,1
 

Java[edit]

Solution:

import javax.swing.*;
import java.awt.*;
 
/**
* SierpinskyTriangle.java
* Draws a SierpinskyTriangle in a JFrame
* The order of complexity is given from command line, but
* defaults to 3
*
* @author Istarnion
*/

 
class SierpinskyTriangle {
 
public static void main(String[] args) {
int i = 3; // Default to 3
if(args.length >= 1) {
try {
i = Integer.parseInt(args[0]);
}
catch(NumberFormatException e) {
System.out.println("Usage: 'java SierpinskyTriangle [level]'\nNow setting level to "+i);
}
}
final int level = i;
 
JFrame frame = new JFrame("Sierpinsky Triangle - Java");
frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
 
JPanel panel = new JPanel() {
@Override
public void paintComponent(Graphics g) {
g.setColor(Color.BLACK);
drawSierpinskyTriangle(level, 20, 20, 360, (Graphics2D)g);
}
};
 
panel.setPreferredSize(new Dimension(400, 400));
 
frame.add(panel);
frame.pack();
frame.setResizable(false);
frame.setLocationRelativeTo(null);
frame.setVisible(true);
}
 
private static void drawSierpinskyTriangle(int level, int x, int y, int size, Graphics2D g) {
if(level <= 0) return;
 
g.drawLine(x, y, x+size, y);
g.drawLine(x, y, x, y+size);
g.drawLine(x+size, y, x, y+size);
 
drawSierpinskyTriangle(level-1, x, y, size/2, g);
drawSierpinskyTriangle(level-1, x+size/2, y, size/2, g);
drawSierpinskyTriangle(level-1, x, y+size/2, size/2, g);
}
}

Animated version[edit]

Works with: Java version 8
import java.awt.*;
import java.awt.event.ActionEvent;
import java.awt.geom.Path2D;
import javax.swing.*;
 
public class SierpinskiTriangle extends JPanel {
private final int dim = 512;
private final int margin = 20;
 
private int limit = dim;
 
public SierpinskiTriangle() {
setPreferredSize(new Dimension(dim + 2 * margin, dim + 2 * margin));
setBackground(Color.white);
setForeground(Color.green.darker());
 
new Timer(2000, (ActionEvent e) -> {
limit /= 2;
if (limit <= 2)
limit = dim;
repaint();
}).start();
}
 
void drawTriangle(Graphics2D g, int x, int y, int size) {
if (size <= limit) {
Path2D p = new Path2D.Float();
p.moveTo(x, y);
p.lineTo(x + size / 2, y + size);
p.lineTo(x - size / 2, y + size);
g.fill(p);
} else {
size /= 2;
drawTriangle(g, x, y, size);
drawTriangle(g, x + size / 2, y + size, size);
drawTriangle(g, x - size / 2, y + size, size);
}
}
 
@Override
public void paintComponent(Graphics gg) {
super.paintComponent(gg);
Graphics2D g = (Graphics2D) gg;
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);
g.translate(margin, margin);
drawTriangle(g, dim / 2, 0, dim);
}
 
public static void main(String[] args) {
SwingUtilities.invokeLater(() -> {
JFrame f = new JFrame();
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.setTitle("Sierpinski Triangle");
f.setResizable(false);
f.add(new SierpinskiTriangle(), BorderLayout.CENTER);
f.pack();
f.setLocationRelativeTo(null);
f.setVisible(true);
});
}
}

JavaScript[edit]

Note
  • "Order" to calculate a size of resulting plot/matrix is not used in this algorithm, Instead, construction is done in accordance to a square   m x m matrix. In our case it should be equal to a size of the square canvas.
  • Change canvas setting from size "640" to "1280". You will discover that density of dots in plotted triangle is stable for this algorithm. Size of the plotted figure is constantly increasing in the S-E direction. Also, the number of all triangles in N-W triangular part of the canvas is always the same.
  • So, in this case it could be called: "Sierpinski ever-expanding field of triangles".


Translation of: PARI/GP
Works with: Chrome
File:SierpTRjs.png
Output SierpTRjs.png
 
<!-- SierpinskiTriangle.html -->
<html>
<head><title>Sierpinski Triangle Fractal</title>
<script>
// HF#1 Like in PARI/GP: return random number 0..max-1
function randgp(max) {return Math.floor(Math.random()*max)}
// HF#2 Random hex color
function randhclr() {
return "#"+
("00"+randgp(256).toString(16)).slice(-2)+
("00"+randgp(256).toString(16)).slice(-2)+
("00"+randgp(256).toString(16)).slice(-2)
}
// HFJS#3: Plot any matrix mat (filled with 0,1)
function pmat01(mat, color) {
// DCLs
var cvs = document.getElementById('cvsId');
var ctx = cvs.getContext("2d");
var w = cvs.width; var h = cvs.height;
var m = mat[0].length; var n = mat.length;
// Cleaning canvas and setting plotting color
ctx.fillStyle="white"; ctx.fillRect(0,0,w,h);
ctx.fillStyle=color;
// MAIN LOOP
for(var i=0; i<m; i++) {
for(var j=0; j<n; j++) {
if(mat[i][j]==1) { ctx.fillRect(i,j,1,1)};
}//fend j
}//fend i
}//func end
 
// Prime function
// Plotting Sierpinski triangle. aev 4/9/17
// ord - order, fn - file name, ttl - plot title, clr - color
function pSierpinskiT() {
var cvs=document.getElementById("cvsId");
var ctx=cvs.getContext("2d");
var w=cvs.width, h=cvs.height;
var R=new Array(w);
for (var i=0; i<w; i++) {R[i]=new Array(w)
for (var j=0; j<w; j++) {R[i][j]=0}
}
ctx.fillStyle="white"; ctx.fillRect(0,0,w,h);
for (var y=0; y<w; y++) {
for (var x=0; x<w; x++) {
if((x & y) == 0 ) {R[x][y]=1}
}}
pmat01(R, randhclr());
}
</script></head>
<body style="font-family: arial, helvatica, sans-serif;">
<b>Please click to start and/or change color: </b>
<input type="button" value=" Plot it! " onclick="pSierpinskiT();">&nbsp;&nbsp;
<h3>Sierpinski triangle fractal</h3>
<canvas id="cvsId" width="640" height="640" style="border: 2px inset;"></canvas>
<!--canvas id="cvsId" width="1280" height="1280" style="border: 2px inset;"></canvas-->
</body></html>
 
Output:
Page with Sierpinski triangle fractal. Plotting color is changing randomly.
Right clicking on canvas with image allows you to save it as png-file, for example.

Kotlin[edit]

From Java code:

import java.awt.*
import javax.swing.JFrame
import javax.swing.JPanel
 
fun main(args: Array<String>) {
var i = 8 // Default
if (args.any()) {
try {
i = args.first().toInt()
} catch (e: NumberFormatException) {
i = 8
println("Usage: 'java SierpinskyTriangle [level]'\nNow setting level to $i")
}
}
 
object : JFrame("Sierpinsky Triangle - Kotlin") {
val panel = object : JPanel() {
val size = 800
 
init {
preferredSize = Dimension(size, size)
}
 
public override fun paintComponent(g: Graphics) {
g.color = Color.BLACK
if (g is Graphics2D) {
g.drawSierpinskyTriangle(i, 20, 20, size - 40)
}
}
}
 
init {
defaultCloseOperation = JFrame.EXIT_ON_CLOSE
add(panel)
pack()
isResizable = false
setLocationRelativeTo(null)
isVisible = true
}
}
}
 
internal fun Graphics2D.drawSierpinskyTriangle(level: Int, x: Int, y: Int, size: Int) {
if (level > 0) {
drawLine(x, y, x + size, y)
drawLine(x, y, x, y + size)
drawLine(x + size, y, x, y + size)
 
drawSierpinskyTriangle(level - 1, x, y, size / 2)
drawSierpinskyTriangle(level - 1, x + size / 2, y, size / 2)
drawSierpinskyTriangle(level - 1, x, y + size / 2, size / 2)
}
}

Liberty BASIC[edit]

The ability of LB to handle very large integers makes the Pascal triangle method very attractive. If you alter the rem'd line you can ask it to print the last, central term...

 
nomainwin
 
open "test" for graphics_nsb_fs as #gr
 
#gr "trapclose quit"
#gr "down; home"
#gr "posxy cx cy"
 
order =10
 
w =cx *2: h =cy *2
 
dim a( h, h) 'line, col
 
#gr "trapclose quit"
#gr "down; home"
 
a( 1, 1) =1
 
for i = 2 to 2^order -1
scan
a( i, 1) =1
a( i, i) =1
for j = 2 to i -1
'a(i,j)=a(i-1,j-1)+a(i-1,j) 'LB is quite capable for crunching BIG numbers
a( i, j) =(a( i -1, j -1) +a( i -1, j)) mod 2 'but for this task, last bit is enough (and it much faster)
next
for j = 1 to i
if a( i, j) mod 2 then #gr "set "; cx +j -i /2; " "; i
next
next
#gr "flush"
 
wait
 
sub quit handle$
close #handle$
end
end sub
 

Up to order 10 displays on a 1080 vertical pixel screen.


[edit]

This will draw a graphical Sierpinski gasket using turtle graphics.

to sierpinski :n :length
if :n = 0 [stop]
repeat 3 [sierpinski :n-1 :length/2 fd :length rt 120]
end
seth 30 sierpinski 5 200

Lua[edit]

Library: LÖVE
-- The argument 'tri' is a list of co-ords: {x1, y1, x2, y2, x3, y3}
function sierpinski (tri, order)
local new, p, t = {}
if order > 0 then
for i = 1, #tri do
p = i + 2
if p > #tri then p = p - #tri end
new[i] = (tri[i] + tri[p]) / 2
end
sierpinski({tri[1],tri[2],new[1],new[2],new[5],new[6]}, order-1)
sierpinski({new[1],new[2],tri[3],tri[4],new[3],new[4]}, order-1)
sierpinski({new[5],new[6],new[3],new[4],tri[5],tri[6]}, order-1)
else
love.graphics.polygon("fill", tri)
end
end
 
-- Callback function used to draw on the screen every frame
function love.draw ()
sierpinski({400, 100, 700, 500, 100, 500}, 7)
end

Love2D-Sierpinski.jpg

Mathematica[edit]

Sierpinski[n_] :=Nest[Flatten[Table[{{
#[[i, 1]], (#[[i, 1]] + #[[i, 2]])/2, (#[[i, 1]] + #[[i, 3]])/
2}, {(#[[i, 1]] + #[[i, 2]])/2, #[[i,
2]], (#[[i, 2]] + #[[i, 3]])/2}, {(#[[i, 1]] + #[[i, 3]])/
2, (#[[i, 2]] + #[[i, 3]])/2, #[[i, 3]]}}, {i, Length[#]}],
1] &, {{{0, 0}, {1/2, 1}, {1, 0}}}, n]
 
Show[Graphics[{Opacity[1], Black, Map[Polygon, Sierpinski[8], 1]}, AspectRatio -> 1]]
sierpinski[v_, 0] := [email protected];
sierpinski[v_, n_] := sierpinski[#, n - 1] & /@ (Mean /@ # & /@ v~Tuples~2~Partition~3);
[email protected][[email protected]{{0, 0}, {1, 0}, {.5, .8}}, 3]
sierpinski = Map[Mean, Partition[Tuples[#, 2], 3], {2}] &;
p = Nest[Join @@ sierpinski /@ # &, {{{0, 0}, {1, 0}, {.5, .8}}}, 3];
Graphics[[email protected]]

MmaSierpinski.png

MATLAB[edit]

Basic Version[edit]

[x, x0] = deal(cat(3, [1 0]', [-1 0]', [0 sqrt(3)]'));
for k = 1 : 6
x = x(:,:) + x0 * 2 ^ k / 2;
end
patch('Faces', reshape(1 : 3 * 3 ^ k, 3, '')', 'Vertices', x(:,:)')
Output:

Fail to upload output image, use the one of PostScript:

Sierpinski-PS.png

Bit Operator Version[edit]

t = 0 : 2^16 - 1;
plot(t, bitand(t, bitshift(t, -8)), 'k.')

OCaml[edit]

open Graphics
 
let round v =
int_of_float (floor (v +. 0.5))
 
let middle (x1, y1) (x2, y2) =
((x1 +. x2) /. 2.0,
(y1 +. y2) /. 2.0)
 
let draw_line (x1, y1) (x2, y2) =
moveto (round x1) (round y1);
lineto (round x2) (round y2);
;;
 
let draw_triangle (p1, p2, p3) =
draw_line p1 p2;
draw_line p2 p3;
draw_line p3 p1;
;;
 
let () =
open_graph "";
let width = float (size_x ()) in
let height = float (size_y ()) in
let pad = 20.0 in
let initial_triangle =
( (pad, pad),
(width -. pad, pad),
(width /. 2.0, height -. pad) )
in
let rec loop step tris =
if step <= 0 then tris else
loop (pred step) (
List.fold_left (fun acc (p1, p2, p3) ->
let m1 = middle p1 p2
and m2 = middle p2 p3
and m3 = middle p3 p1 in
let tri1 = (p1, m1, m3)
and tri2 = (p2, m2, m1)
and tri3 = (p3, m3, m2) in
tri1 :: tri2 :: tri3 :: acc
) [] tris
)
in
let res = loop 6 [ initial_triangle ] in
List.iter draw_triangle res;
ignore (read_key ())

run with:

ocaml graphics.cma sierpinski.ml

PARI/GP[edit]

Works with: PARI/GP version 2.7.4 and above
File:SierpT9.png
Output SierpT9.png
 
\\ Sierpinski triangle fractal
\\ Note: plotmat() can be found here on
\\ http://rosettacode.org/wiki/Brownian_tree#PARI.2FGP page.
\\ 6/3/16 aev
pSierpinskiT(n)={
my(sz=2^n,M=matrix(sz,sz),x,y);
for(y=1,sz, for(x=1,sz, if(!bitand(x,y),M[x,y]=1);));\\fends
plotmat(M);
}
{\\ Test:
pSierpinskiT(9); \\ SierpT9.png
}
 
Output:
> pSierpinskiT(9); \\ SierpT9.png
 *** matrix(512x512) 19682 DOTS

Perl[edit]

Writes out an EPS given an arbitrary triangle. The perl code only calculates the bounding box, while real work is done in postscript.

use List::Util qw'min max sum';
 
sub write_eps {
my @x = @_[0, 2, 4];
my @y = @_[1, 3, 5];
my $sx = sum(@x) / 3;
my $sy = sum(@y) / 3;
@x = map { $_ - $sx } @x;
@y = map { $_ - $sy } @y;
 
print <<"HEAD";
%!PS-Adobe-3.0
%%BoundingBox: @{[min(@x) - 10]} @{[min(@y) - 10]} @{[max(@x) + 10]} @{[max(@y) + 10]}
/v1 { $x[0] $y[0] } def /v2 { $x[1] $y[1] } def /v3 { $x[2] $y[2] } def
/t { translate } def
/r { .5 .5 scale 2 copy t 2 index sierp pop neg exch neg exch t 2 2 scale } def
 
/sierp { dup 1 sub dup 0 ne
{ v1 r v2 r v3 r }
{ v1 moveto v2 lineto v3 lineto} ifelse
pop
} def
 
9 sierp fill pop showpage
%%EOF
HEAD

}
 
write_eps 0, 0, 300, 215, -25, 200;

Perl 6[edit]

Sierpinski-perl6.svg

This is a recursive solution. It is not really practical for more than 8 levels of recursion, but anything more than 7 is barely visible anyway.

my $side = 512;
my $height = get_height($side);
my $levels = 8;
 
sub get_height ($side) { $side * 3.sqrt / 2 }
 
sub triangle ( $x1, $y1, $x2, $y2, $x3, $y3, $fill?, $animate? ) {
print "<polygon points=\"$x1,$y1 $x2,$y2 $x3,$y3\"";
if $fill { print " style=\"fill: $fill; stroke-width: 0;\"" };
if $animate
{
say ">\n <animate attributeType=\"CSS\" attributeName=\"opacity\"\n values=\"1;0;1\""
~ " keyTimes=\"0;.5;1\" dur=\"20s\" repeatCount=\"indefinite\" />\n</polygon>"
}
else
{
say ' />';
}
}
 
sub fractal ( $x1, $y1, $x2, $y2, $x3, $y3, $r is copy ) {
triangle( $x1, $y1, $x2, $y2, $x3, $y3 );
return unless --$r;
my $side = abs($x3 - $x2) / 2;
my $height = get_height($side);
fractal( $x1, $y1-$height*2, $x1-$side/2, $y1-3*$height, $x1+$side/2, $y1-3*$height, $r);
fractal( $x2, $y1, $x2-$side/2, $y1-$height, $x2+$side/2, $y1-$height, $r);
fractal( $x3, $y1, $x3-$side/2, $y1-$height, $x3+$side/2, $y1-$height, $r);
}
 
say '<?xml version="1.0" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg width="100%" height="100%" version="1.1" xmlns="http://www.w3.org/2000/svg">
<defs>
<radialGradient id="basegradient" cx="50%" cy="65%" r="50%" fx="50%" fy="65%">
<stop offset="10%" stop-color="#ff0" />
<stop offset="60%" stop-color="#f00" />
<stop offset="99%" stop-color="#00f" />
</radialGradient>
</defs>'
;
 
triangle( $side/2, 0, 0, $height, $side, $height, 'url(#basegradient)' );
triangle( $side/2, 0, 0, $height, $side, $height, '#000', 'animate' );
say '<g style="fill: #fff; stroke-width: 0;">';
fractal( $side/2, $height, $side*3/4, $height/2, $side/4, $height/2, $levels );
say '</g></svg>';

Phix[edit]

Can resize, and change the level from 1 to 12 (press +/-).

Library: pGUI
--
-- demo\rosetta\SierpinskyTriangle.exw
--
include pGUI.e
 
Ihandle dlg, canvas
cdCanvas cddbuffer, cdcanvas
 
procedure SierpinskyTriangle(integer level, atom x, atom y, atom w, atom h)
atom w2 = w/2, w4 = w/4, h2 = h/2
if level=1 then
cdCanvasBegin(cddbuffer,CD_CLOSED_LINES)
cdCanvasVertex(cddbuffer, x, y)
cdCanvasVertex(cddbuffer, x+w2, y+h)
cdCanvasVertex(cddbuffer, x+w, y)
cdCanvasEnd(cddbuffer)
else
SierpinskyTriangle(level-1, x, y, w2, h2)
SierpinskyTriangle(level-1, x+w4, y+h2, w2, h2)
SierpinskyTriangle(level-1, x+w2, y, w2, h2)
end if
end procedure
 
integer level = 7
 
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
integer {w, h} = IupGetIntInt(canvas, "DRAWSIZE")
cdCanvasActivate(cddbuffer)
cdCanvasClear(cddbuffer)
SierpinskyTriangle(level, w*0.05, h*0.05, w*0.9, h*0.9)
cdCanvasFlush(cddbuffer)
IupSetStrAttribute(dlg, "TITLE", "Sierpinsky Triangle (level %d)",{level})
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_GRAY)
return IUP_DEFAULT
end function
 
function esc_close(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if
if find(c,"+-") then
level = max(1,min(12,level+','-c))
IupRedraw(canvas)
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)
IupSetAttribute(dlg, "TITLE", "Sierpinsky Triangle")
IupSetCallback(dlg, "K_ANY", Icallback("esc_close"))
 
IupShow(dlg)
IupSetAttribute(canvas, "RASTERSIZE", NULL)
IupMainLoop()
IupClose()
end procedure
main()

PicoLisp[edit]

Pil sierpinski.png

Slight modification of the text version, requires ImageMagick's display:

(de sierpinski (N)
(let (D '("1") S "0")
(do N
(setq
D (conc
(mapcar '((X) (pack S X S)) D)
(mapcar '((X) (pack X "0" X)) D) )
S (pack S S) ) )
D ) )
 
(out '(display -)
(let Img (sierpinski 7)
(prinl "P1")
(prinl (length (car Img)) " " (length Img))
(mapc prinl Img) ) )
 

PostScript[edit]

Sierpinski-PS.png
%!PS
 
/sierp { % level ax ay bx by cx cy
6 cpy triangle
sierpr
} bind def
 
/sierpr {
12 cpy
10 -4 2 {
5 1 roll exch 4 -1 roll
add 0.5 mul 3 1 roll
add 0.5 mul 3 -1 roll
2 roll
} for  % l a b c bc ac ab
13 -1 roll dup 0 gt {
1 sub
dup 4 cpy 18 -2 roll sierpr
dup 7 index 7 index 2 cpy 16 -2 roll sierpr
9 3 roll 1 index 1 index 2 cpy 13 4 roll sierpr
} { 13 -6 roll 7 { pop } repeat } ifelse
triangle
} bind def
 
/cpy { { 5 index } repeat } bind def
 
/triangle {
newpath moveto lineto lineto closepath stroke
} bind def
 
6 50 100 550 100 300 533 sierp
showpage

Prolog[edit]

Works with SWI-Prolog and XPCE.

Recursive version[edit]

Prolog sierpinski 3.png
Prolog sierpinski 8.png

Works up to sierpinski(13).

sierpinski(N) :-
sformat(A, 'Sierpinski order ~w', [N]),
new(D, picture(A)),
draw_Sierpinski(D, N, point(350,50), 600),
send(D, size, size(690,690)),
send(D, open).
 
draw_Sierpinski(Window, 1, point(X, Y), Len) :-
X1 is X - round(Len/2),
X2 is X + round(Len/2),
Y1 is Y + Len * sqrt(3) / 2,
send(Window, display, new(Pa, path)),
(
send(Pa, append, point(X, Y)),
send(Pa, append, point(X1, Y1)),
send(Pa, append, point(X2, Y1)),
send(Pa, closed, @on),
send(Pa, fill_pattern, colour(@default, 0, 0, 0))
).
 
 
draw_Sierpinski(Window, N, point(X, Y), Len) :-
Len1 is round(Len/2),
X1 is X - round(Len/4),
X2 is X + round(Len/4),
Y1 is Y + Len * sqrt(3) / 4,
N1 is N - 1,
draw_Sierpinski(Window, N1, point(X, Y), Len1),
draw_Sierpinski(Window, N1, point(X1, Y1), Len1),
draw_Sierpinski(Window, N1, point(X2, Y1), Len1).

Iterative version[edit]

:- dynamic top/1.
 
sierpinski_iterate(N) :-
retractall(top(_)),
sformat(A, 'Sierpinski order ~w', [N]),
new(D, picture(A)),
draw_Sierpinski_iterate(D, N, point(550, 50)),
send(D, open).
 
draw_Sierpinski_iterate(Window, N, point(X,Y)) :-
assert(top([point(X,Y)])),
NbTours is 2 ** (N - 1),
% Size is given here to preserve the "small" triangles when N is big
Len is 10,
forall(between(1, NbTours, _I),
( retract(top(Lst)),
assert(top([])),
forall(member(P, Lst),
draw_Sierpinski(Window, P, Len)))).
 
draw_Sierpinski(Window, point(X, Y), Len) :-
X1 is X - round(Len/2),
X2 is X + round(Len/2),
Y1 is Y + round(Len * sqrt(3) / 2),
send(Window, display, new(Pa, path)),
(
send(Pa, append, point(X, Y)),
send(Pa, append, point(X1, Y1)),
send(Pa, append, point(X2, Y1)),
send(Pa, closed, @on),
send(Pa, fill_pattern, colour(@default, 0, 0, 0))
),
retract(top(Lst)),
( member(point(X1, Y1), Lst) -> select(point(X1,Y1), Lst, Lst1)
; Lst1 = [point(X1, Y1)|Lst]),
 
( member(point(X2, Y1), Lst1) -> select(point(X2,Y1), Lst1, Lst2)
; Lst2 = [point(X2, Y1)|Lst1]),
 
assert(top(Lst2)).

Python[edit]

Library: Numpy
Library: Turtle
SierpinskiTriangle-turtle.png
#!/usr/bin/env python
##########################################################################################
# import necessary modules
# ------------------------
from numpy import *
import turtle
 
##########################################################################################
# Functions defining the drawing actions
# (used by the function DrawSierpinskiTriangle).
# ----------------------------------------------
def Left(turn, point, fwd, angle, turt):
turt.left(angle)
return [turn, point, fwd, angle, turt]
def Right(turn, point, fwd, angle, turt):
turt.right(angle)
return [turn, point, fwd, angle, turt]
def Forward(turn, point, fwd, angle, turt):
turt.forward(fwd)
return [turn, point, fwd, angle, turt]
 
##########################################################################################
# The drawing function
# --------------------
#
# level level of Sierpinski triangle (minimum value = 1)
# ss screensize (Draws on a screen of size ss x ss. Default value = 400.)
#-----------------------------------------------------------------------------------------
def DrawSierpinskiTriangle(level, ss=400):
# typical values
turn = 0 # initial turn (0 to start horizontally)
angle=60.0 # in degrees
 
# Initialize the turtle
turtle.hideturtle()
turtle.screensize(ss,ss)
turtle.penup()
turtle.degrees()
 
# The starting point on the canvas
fwd0 = float(ss)
point=array([-fwd0/2.0, -fwd0/2.0])
 
# Setting up the Lindenmayer system
# Assuming that the triangle will be drawn in the following way:
# 1.) Start at a point
# 2.) Draw a straight line - the horizontal line (H)
# 3.) Bend twice by 60 degrees to the left (--)
# 4.) Draw a straight line - the slanted line (X)
# 5.) Bend twice by 60 degrees to the left (--)
# 6.) Draw a straight line - another slanted line (X)
# This produces the triangle in the first level. (so the axiom to begin with is H--X--X)
# 7.) For the next level replace each horizontal line using
# X->XX
# H -> H--X++H++X--H
# The lengths will be halved.
 
 
decode = {'-':Left, '+':Right, 'X':Forward, 'H':Forward}
axiom = 'H--X--X'
 
# Start the drawing
turtle.goto(point[0], point[1])
turtle.pendown()
turtle.hideturtle()
turt=turtle.getpen()
startposition=turt.clone()
 
# Get the triangle in the Lindenmayer system
fwd = fwd0/(2.0**level)
path = axiom
for i in range(0,level):
path=path.replace('X','XX')
path=path.replace('H','H--X++H++X--H')
 
# Draw it.
for i in path:
[turn, point, fwd, angle, turt]=decode[i](turn, point, fwd, angle, turt)
##########################################################################################
 
DrawSierpinskiTriangle(5)
 

R[edit]

Note: Find plotmat() here on RC R Helper Functions page.

Translation of: PARI/GP
Works with: R version 3.3.3 and above
File:SierpTRo6.png
Output SierpTRo6.png
File:SierpTRo8.png
Output SierpTRo8.png
 
## Plotting Sierpinski triangle. aev 4/1/17
## ord - order, fn - file name, ttl - plot title, clr - color
pSierpinskiT <- function(ord, fn="", ttl="", clr="navy") {
m=640; abbr="STR"; dftt="Sierpinski triangle";
n=2^ord; M <- matrix(c(0), ncol=n, nrow=n, byrow=TRUE);
cat(" *** START", abbr, date(), "\n");
if(fn=="") {pf=paste0(abbr,"o", ord)} else {pf=paste0(fn, ".png")};
if(ttl!="") {dftt=ttl}; ttl=paste0(dftt,", order ", ord);
cat(" *** Plot file:", pf,".png", "title:", ttl, "\n");
for(y in 1:n) {
for(x in 1:n) {
if(bitwAnd(x, y)==0) {M[x,y]=1}
##if(bitwAnd(x, y)>0) {M[x,y]=1} ## Try this for "reversed" ST
}}
plotmat(M, pf, clr, ttl);
cat(" *** END", abbr, date(), "\n");
}
## Executing:
pSierpinskiT(6,,,"red");
pSierpinskiT(8);
 
Output:
> pSierpinskiT(6,,,"red");
 *** START STR Sat Apr 01 21:45:23 2017 
 *** Plot file: STRo6 .png title: Sierpinski triangle, order 6 
 *** Matrix( 64 x 64 ) 728 DOTS
 *** END STR Sat Apr 01 21:45:23 2017 
> pSierpinskiT(8)
 *** START STR Sat Apr 01 21:59:06 2017 
 *** Plot file: STRo8 .png title: Sierpinski triangle, order 8 
 *** Matrix( 256 x 256 ) 6560 DOTS
 *** END STR Sat Apr 01 21:59:07 2017 

Racket[edit]

RacketSierpinski.png
 
#lang racket
(require 2htdp/image)
(define (sierpinski n)
(if (zero? n)
(triangle 2 'solid 'red)
(let ([t (sierpinski (- n 1))])
(freeze (above t (beside t t))))))
 

Test:

 
;; the following will show the graphics if run in DrRacket
(sierpinski 8)
;; or use this to dump the image into a file, shown on the right
(require file/convertible)
(display-to-file (convert (sierpinski 8) 'png-bytes) "sierpinski.png")
 

Ring[edit]

 
load "guilib.ring"
 
new qapp
{
win1 = new qwidget() {
setwindowtitle("drawing using qpainter")
setgeometry(100,100,500,500)
label1 = new qlabel(win1) {
setgeometry(10,10,400,400)
settext("")
}
new qpushbutton(win1) {
setgeometry(200,400,100,30)
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)
}
new qpainter() {
begin(p1)
setpen(pen)
 
order = 7
size = pow(2,order)
for y = 0 to size-1
for x = 0 to size-1
if (x & y)=0 drawpoint(x*2,y*2) ok
next
next
endpaint()
}
label1 { setpicture(p1) show() }
 

Output:

CalmoSoftSierpinski.jpg

Ruby[edit]

Library: Shoes
Sierpinski.shoes.png
Shoes.app(:height=>540,:width=>540, :title=>"Sierpinski Triangle") do
def triangle(slot, tri, color)
x, y, len = tri
slot.append do
fill color
shape do
move_to(x,y)
dx = len * Math::cos(Math::PI/3)
dy = len * Math::sin(Math::PI/3)
line_to(x-dx, y+dy)
line_to(x+dx, y+dy)
line_to(x,y)
end
end
end
@s = stack(:width => 520, :height => 520) {}
@s.move(10,10)
 
length = 512
@triangles = [[length/2,0,length]]
triangle(@s, @triangles[0], rgb(0,0,0))
 
@n = 1
animate(1) do
if @n <= 7
@triangles = @triangles.inject([]) do |sum, (x, y, len)|
dx = len/2 * Math::cos(Math::PI/3)
dy = len/2 * Math::sin(Math::PI/3)
triangle(@s, [x, y+2*dy, -len/2], rgb(255,255,255))
sum += [[x, y, len/2], [x-dx, y+dy, len/2], [x+dx, y+dy, len/2]]
end
end
@n += 1
end
 
keypress do |key|
case key
when :control_q, "\x11" then exit
end
end
end

Run BASIC[edit]

SierpinskiRunBasic.png
graphic #g, 300,300
order = 8
width = 100
w = width * 11
dim canvas(w,w)
canvas(1,1) = 1
 
for x = 2 to 2^order -1
canvas(x,1) = 1
canvas(x,x) = 1
for y = 2 to x -1
canvas( x, y) = (canvas(x -1,y -1) + canvas(x -1, y)) mod 2
if canvas(x,y) mod 2 then #g "set "; width + (order*3) + y - x / 2;" "; x
next y
next x
render #g
#g "flush"
wait

Seed7[edit]

SierpinskiSeed7.png
$ include "seed7_05.s7i";
include "draw.s7i";
include "keybd.s7i";
 
const proc: main is func
local
const integer: order is 8;
const integer: width is 1 << order;
const integer: margin is 10;
var integer: x is 0;
var integer: y is 0;
begin
screen(width + 2 * margin, width + 2 * margin);
clear(curr_win, white);
KEYBOARD := GRAPH_KEYBOARD;
for y range 0 to pred(width) do
for x range 0 to pred(width) do
if bitset conv x & bitset conv y = bitset.value then
point(margin + x, margin + y, black);
end if;
end for;
end for;
ignore(getc(KEYBOARD));
end func;

Original source: [1]

Sidef[edit]

Sierpinski triangle sidef.png
func sierpinski_triangle(n) -> Array {
var triangle = ['*']
{ |i|
var sp = (' ' * 2**i)
triangle = (triangle.map {|x| sp + x + sp} +
triangle.map {|x| x + ' ' + x})
} * n
triangle
}
 
class Array {
method to_png(scale=1, bgcolor='white', fgcolor='black') {
 
static gd = require('GD::Simple')
var width = self.max_by{.len}.len
self.map!{|r| "%-#{width}s" % r}
 
var img = gd.new(width * scale, self.len * scale)
 
for i in ^self {
for j in RangeNum(i*scale, i*scale + scale) {
img.moveTo(0, j)
for line in (self[i].scan(/(\s+|\S+)/)) {
img.fgcolor(line.contains(/\S/) ? fgcolor : bgcolor)
img.line(scale * line.len)
}
}
}
img.png
}
}
 
var triangle = sierpinski_triangle(8)
var raw_png = triangle.to_png(bgcolor:'black', fgcolor:'red')
File('triangle.png').write(raw_png, :raw)

Tcl[edit]

This code maintains a queue of triangles to cut out; though a stack works just as well, the observed progress is more visually pleasing when a queue is used.

Library: Tk
package require Tcl 8.5
package require Tk
 
proc mean args {expr {[::tcl::mathop::+ {*}$args] / [llength $args]}}
proc sierpinski {canv coords order} {
$canv create poly $coords -fill black -outline {}
set queue [list [list {*}$coords $order]]
while {[llength $queue]} {
lassign [lindex $queue 0] x1 y1 x2 y2 x3 y3 order
set queue [lrange $queue 1 end]
if {[incr order -1] < 0} continue
set x12 [mean $x1 $x2]; set y12 [mean $y1 $y2]
set x23 [mean $x2 $x3]; set y23 [mean $y2 $y3]
set x31 [mean $x3 $x1]; set y31 [mean $y3 $y1]
$canv create poly $x12 $y12 $x23 $y23 $x31 $y31 -fill white -outline {}
update idletasks; # So we can see progress
lappend queue [list $x1 $y1 $x12 $y12 $x31 $y31 $order] \
[list $x12 $y12 $x2 $y2 $x23 $y23 $order] \
[list $x31 $y31 $x23 $y23 $x3 $y3 $order]
}
}
 
pack [canvas .c -width 400 -height 400 -background white]
update; # So we can see progress
sierpinski .c {200 10 390 390 10 390} 7

TI-83 BASIC[edit]

:1→X:1→Y
:Zdecimal
:Horizontal 3.1
:Vertical -4.5
:While 1
:X+1→X
:DS<(Y,1
:While 0
:X→Y
:1→X
:End
:If pxl-Test(Y-1,X) xor (pxl-Test(Y,X-1
:PxlOn(Y,X
:End

This could be made faster, but I just wanted to use the DS<( command

XPL0[edit]

TriangXPL0.gif
include c:\cxpl\codes;          \intrinsic 'code' declarations
def Order=7, Size=1<<Order;
int X, Y;
[SetVid($13); \set 320x200 graphics video mode
for Y:= 0 to Size-1 do
for X:= 0 to Size-1 do
if (X&Y)=0 then Point(X, Y, 4\red\);
X:= ChIn(1); \wait for keystroke
SetVid(3); \restore normal text display
]

zkl[edit]

SierpinskiTriangle.zkl.jpg

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

Translation of: XPL0
const Order=8, Size=(1).shiftLeft(Order);
img:=PPM(300,300);
foreach y,x in (Size,Size){ if(x.bitAnd(y)==0) img[x,y]=0xff0000 }
img.write(File("sierpinskiTriangle.ppm","wb"));