Sierpinski triangle/Graphical: Difference between revisions
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if ( level == 1 ) |
if ( level == 1 ) |
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| ⚫ | |||
line to x, y |
line to x, y |
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| ⚫ | |||
line to x+w2, y+h |
line to x+w2, y+h |
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line to x+w, y |
line to x+w, y |
||
line to x, y |
line to x, y |
||
else |
else |
||
| ⚫ | |||
fn SierpinskyTriangle( level-1, x, y, w2, h2 ) |
fn SierpinskyTriangle( level-1, x, y, w2, h2 ) |
||
| ⚫ | |||
fn SierpinskyTriangle( level-1, x+w4, y+h2, w2, h2 ) |
fn SierpinskyTriangle( level-1, x+w4, y+h2, w2, h2 ) |
||
fn SierpinskyTriangle( level-1, x+w2, y, w2, h2 ) |
fn SierpinskyTriangle( level-1, x+w2, y, w2, h2 ) |
||
Revision as of 15:02, 28 June 2023
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:
8086 Assembly
This program will draw a Sierpinski triangle of the given order on a CGA (or EGA/VGA/etc) screen. It uses 320x200 mode, so the maximum order is 7.
;;; Display a Sierpinski triangle on a CGA screen
;;; (order 7 is the maximum that fits in 200 lines)
mode: equ 0Fh ; INT 10H call to get current video mode
puts: equ 9h ; MS-DOS call to print string
cgaseg: equ 0B800h ; Location of CGA video memory
cpu 8086
bits 16
org 100h
section .text
cmp [80h],byte 2 ; Argument length should be 2 (space + digit)
jne eusage
mov al,[82h] ; Get digit
sub al,'0'+2 ; 2->0, 7->5
cmp al,5 ; Then it must be <=5
jbe argok
eusage: mov dx,usage ; Print usage string
estop: mov ah,puts
int 21h
ret ; And stop
argok: add al,2 ; Add 2, setting AL to the order
mov [order],al ; Store the order
mov ah,mode ; Get the current video mode
int 10h
cmp al,7 ; If MDA, we don't have graphics support
mov dx,errcga
je estop
mov [vmode],al ; Otherwise, store the old mode
mov ax,4 ; and switch to mode 4 (320x200 graphics)
int 10h
mov ch,1 ; Size = 2^order
mov cl,[order]
shl ch,cl
xor dh,dh ; Start at coords (0,0)
mov bp,cgaseg ; Point ES at the CGA memory
mkscr: mov es,bp
xor di,di ; Start at the beginning
mkline: xor dl,dl ; Start at coords (0,Y)
mkbyte: xor al,al ; A byte has 4 pixels in it
mov cl,4
mkpx: shl al,1 ; Make room for next pixel
shl al,1
test dl,dh ; X & Y == 0?
jnz nextpx
or al,3 ; X & Y == 0, set pixel on
nextpx: inc dl ; Increment X coordinate
dec cl ; More pixels in this byte?
jnz mkpx ; If so, add them in
stosb ; Otherwise, write it out to CGA memory
cmp dl,ch ; And if the line is not done yet,
jb mkbyte ; do the next byte on this line.
shr dl,1 ; Move ahead to start of next line
shr dl,1
mov ax,80 ; 80 bytes per line
sub al,dl
add di,ax
add dh,2 ; Memory is interlaced so we're 2 lines further
cmp dh,ch ; If we're not done yet,
jb mkline ; Do the next line.
add bp,200h ; Move ahead 8k to the area for the odd lines
cmp bp,0BA00h ; Unless we were already there
mov dh,1 ; We'll have to start at line 1
jbe mkscr
xor ah,ah ; Wait for a keypress to get back to DOS
int 16h
xor ah,ah ; Then, restore the old video mode,
mov al,[vmode]
int 10h
ret ; And exit to DOS
section .data
usage: db 'SIERPCGA [2..7] - display Sierpinski triangle of order N$'
errcga: db 'Need at least CGA.$'
section .bss
order: resb 1 ; Order of Sierpinski triangle
vmode: resb 1 ; Store old video mode (to restore later)
Action!
PROC Draw(INT x0 BYTE y0,depth)
BYTE i,x,y,size
size=1 LSH depth
FOR y=0 TO size-1
DO
FOR x=0 TO size-1
DO
IF (x&y)=0 THEN
Plot(x0+x,y0+y)
FI
OD
OD
RETURN
PROC Main()
BYTE CH=$02FC,COLOR1=$02C5,COLOR2=$02C6
Graphics(8+16)
Color=1
COLOR1=$0C
COLOR2=$02
Draw(96,32,7)
DO UNTIL CH#$FF OD
CH=$FF
RETURN- Output:
Screenshot from Atari 8-bit computer
ActionScript
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
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);
Una versión mas corta:
pair A = (0, 0), B = (1, 0), C = (.5, 1);
void sierpinski(pair p, int d) {
if (++d < 7) {
p *= 2;
sierpinski(p + A * 2, d);
sierpinski(p + B * 2, d);
sierpinski(p + C * 2, d);
} else {
fill(shift(p / 2) * (A -- B -- C -- cycle));
}
}
sierpinski((0, 0), 0);
ATS
// patscc -O2 -flto -D_GNU_SOURCE -DATS_MEMALLOC_LIBC sierpinski.dats -o sierpinski -latslib -lSDL2
#include "share/atspre_staload.hats"
typedef point = (int, int)
extern fun midpoint(A: point, B: point): point = "mac#"
extern fun sierpinski_draw(n: int, A: point, B: point, C: point): void = "mac#"
extern fun triangle_remove(A: point, B: point, C: point): void = "mac#"
extern fun sdl_drawline(x1: int, y1: int, x2: int, y2: int): void = "ext#sdl_drawline"
extern fun line(A: point, B: point): void
extern fun ats_tredraw(): void = "mac#ats_tredraw"
implement midpoint(A, B) = (xmid, ymid) where {
val xmid = (A.0 + B.0) / 2
val ymid = (A.1 + B.1) / 2
}
implement triangle_remove(A, B, C) = (
line(A, B);
line(B, C);
line(C, A);
)
implement sierpinski_draw(n, A, B, C) =
if n > 0 then
let
val AB = midpoint(A, B)
val BC = midpoint(B, C)
val CA = midpoint(C, A)
in
triangle_remove(AB, BC, CA);
sierpinski_draw(n-1, A, AB, CA);
sierpinski_draw(n-1, B, BC, AB);
sierpinski_draw(n-1, C, CA, BC);
end
implement line(A, B) = sdl_drawline(A.0, A.1, B.0, B.1)
extern fun SDL_Init(): void = "ext#sdl_init"
extern fun SDL_Quit(): void = "ext#sdl_quit"
extern fun SDL_Loop(): void = "ext#sdl_loop"
implement ats_tredraw() = sierpinski_draw(7, (320, 0), (0, 480), (640, 480))
implement main0() = (
SDL_Init();
SDL_Loop();
SDL_Quit();
)
%{
#include <SDL2/SDL.h>
#include <unistd.h>
extern void ats_tredraw();
SDL_Window *sdlwin;
SDL_Renderer *sdlren;
void sdl_init() {
if (SDL_Init(SDL_INIT_VIDEO)) {
exit(1);
}
if ((sdlwin = SDL_CreateWindow("sierpinski triangles", 100, 100, 640, 480, SDL_WINDOW_SHOWN)) == NULL) {
SDL_Quit();
exit(2);
}
if ((sdlren = SDL_CreateRenderer(sdlwin, -1, SDL_RENDERER_ACCELERATED | SDL_RENDERER_PRESENTVSYNC)) == NULL) {
SDL_DestroyWindow(sdlwin);
SDL_Quit();
exit(3);
}
}
void sdl_clear() {
SDL_SetRenderDrawColor(sdlren, 0, 0, 0, SDL_ALPHA_OPAQUE);
SDL_RenderClear(sdlren);
SDL_SetRenderDrawColor(sdlren, 255, 255, 255, SDL_ALPHA_OPAQUE);
}
void sdl_loop() {
SDL_Event event;
while (1) {
sdl_clear();
ats_tredraw();
SDL_RenderPresent(sdlren);
while (SDL_PollEvent(&event)) {
if (event.type == SDL_QUIT) {
return;
}
}
}
}
void sdl_quit() {
SDL_DestroyRenderer(sdlren);
SDL_DestroyWindow(sdlwin);
SDL_Quit();
}
void sdl_drawline(int x1, int y1, int x2, int y2) {
SDL_RenderDrawLine(sdlren, x1, y1, x2, y2);
}
%}AutoHotkey
#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
}
BASIC
SCREEN 9
H=.5
P=300
FOR I=1 TO 9^6
N=RND
IF N > 2/3 THEN
X=H+X*H:Y=Y*H
ELSEIF N > 1/3 THEN
X=H^2+X*H:Y=H+Y*H
ELSE
X=X*H:Y=Y*H
END IF
PSET(P-X*P,P-Y*P)
NEXT
Sierpinski triangle QBasic image
BBC BASIC
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%
FreeBASIC
' 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
EndIS-BASIC
100 PROGRAM "Triangle.bas"
110 SET VIDEO MODE 1:SET VIDEO COLOR 0:SET VIDEO X 40:SET VIDEO Y 27
120 OPEN #101:"video:"
130 DISPLAY #101:AT 1 FROM 1 TO 27
140 CALL SIERP(896,180,50)
150 DEF SIERP(W,X,Y)
160 IF W>28 THEN
170 CALL SIERP(W/2,X,Y)
180 CALL SIERP(W/2,X+W/4,Y+W/2)
190 CALL SIERP(W/2,X+W/2,Y)
200 ELSE
210 PLOT X,Y;X+W/2,Y+W;X+W,Y;X,Y
220 END IF
230 END DEFLiberty BASIC
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 subUp to order 10 displays on a 1080 vertical pixel screen.
Run BASIC
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"
waitSmileBASIC
OPTION STRICT
OPTION DEFINT
DEF DRAW X0, Y0, DEPTH
VAR X, Y, SIZE
SIZE = 1 << DEPTH
FOR Y = 0 TO SIZE - 1
FOR X = 0 TO SIZE - 1
IF (X AND Y) == 0 THEN
GPSET X0 + X, Y0 + Y, RGB(X, 255 - Y, 255)
ENDIF
NEXT
NEXT
END
CALL "DRAW", 96, 32, 7
END
TI-83 BASIC
: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
:EndThis could be made faster, but I just wanted to use the DS<( command
Yabasic
3D version.
// Adpated from non recursive sierpinsky.bas for SmallBASIC 0.12.6 [B+=MGA] 2016-05-19 with demo mod 2016-05-29
//Sierpinski triangle gasket drawn with lines from any 3 given points
// WITHOUT RECURSIVE Calls
//first a sub, given 3 points of a triangle draw the traiangle within
//from the midpoints of each line forming the outer triangle
//this is the basic Sierpinski Unit that is repeated at greater depths
//3 points is 6 arguments to function plus a depth level
xmax=800:ymax=600
open window xmax,ymax
backcolor 0,0,0
color 255,0,0
clear window
sub SierLineTri(x1, y1, x2, y2, x3, y3, maxDepth)
local mx1, mx2, mx3, my1, my2, my3, ptcount, depth, i, X, Y
Y = 1
//load given set of 3 points into oa = outer triangles array, ia = inner triangles array
ptCount = 3
depth = 1
dim oa(ptCount - 1, 1) //the outer points array
oa(0, X) = x1
oa(0, Y) = y1
oa(1, X) = x2
oa(1, Y) = y2
oa(2, X) = x3
oa(2, Y) = y3
dim ia(3 * ptCount - 1, 1) //the inner points array
iaIndex = 0
while(depth <= maxDepth)
for i=0 to ptCount-1 step 3 //draw outer triangles at this level
if depth = 1 then
line oa(i,X), oa(i,Y), oa(i+1,X), oa(i+1,Y)
line oa(i+1,X), oa(i+1,Y), oa(i+2,X), oa(i+2,Y)
line oa(i,X), oa(i,Y), oa(i+2,X), oa(i+2,Y)
end if
if oa(i+1,X) < oa(i,X) then mx1 = (oa(i,X) - oa(i+1,X))/2 + oa(i+1,X) else mx1 = (oa(i+1,X) - oa(i,X))/2 + oa(i,X) endif
if oa(i+1,Y) < oa(i,Y) then my1 = (oa(i,Y) - oa(i+1,Y))/2 + oa(i+1,Y) else my1 = (oa(i+1,Y) - oa(i,Y))/2 + oa(i,Y) endif
if oa(i+2,X) < oa(i+1,X) then mx2 = (oa(i+1,X)-oa(i+2,X))/2 + oa(i+2,X) else mx2 = (oa(i+2,X)-oa(i+1,X))/2 + oa(i+1,X) endif
if oa(i+2,Y) < oa(i+1,Y) then my2 = (oa(i+1,Y)-oa(i+2,Y))/2 + oa(i+2,Y) else my2 = (oa(i+2,Y)-oa(i+1,Y))/2 + oa(i+1,Y) endif
if oa(i+2,X) < oa(i,X) then mx3 = (oa(i,X) - oa(i+2,X))/2 + oa(i+2,X) else mx3 = (oa(i+2,X) - oa(i,X))/2 + oa(i,X) endif
if oa(i+2,Y) < oa(i,Y) then my3 = (oa(i,Y) - oa(i+2,Y))/2 + oa(i+2,Y) else my3 = (oa(i+2,Y) - oa(i,Y))/2 + oa(i,Y) endif
//color 9 //testing
//draw all inner triangles
line mx1, my1, mx2, my2
line mx2, my2, mx3, my3
line mx1, my1, mx3, my3
//x1, y1 with mx1, my1 and mx3, my3
ia(iaIndex,X) = oa(i,X)
ia(iaIndex,Y) = oa(i,Y) : iaIndex = iaIndex + 1
ia(iaIndex,X) = mx1
ia(iaIndex,Y) = my1 : iaIndex = iaIndex + 1
ia(iaIndex,X) = mx3
ia(iaIndex,Y) = my3 : iaIndex = iaIndex + 1
//x2, y2 with mx1, my1 and mx2, my2
ia(iaIndex,X) = oa(i+1,X)
ia(iaIndex,Y) = oa(i+1,Y) : iaIndex = iaIndex + 1
ia(iaIndex,X) = mx1
ia(iaIndex,Y) = my1 : iaIndex = iaIndex + 1
ia(iaIndex,X) = mx2
ia(iaIndex,Y) = my2 : iaIndex = iaIndex + 1
//x3, y3 with mx3, my3 and mx2, my2
ia(iaIndex,X) = oa(i+2,X)
ia(iaIndex,Y) = oa(i+2,Y) : iaIndex = iaIndex + 1
ia(iaIndex,X) = mx2
ia(iaIndex,Y) = my2 : iaIndex = iaIndex + 1
ia(iaIndex,X) = mx3
ia(iaIndex,Y) = my3 : iaIndex = iaIndex + 1
next i
//update and prepare for next level
ptCount = ptCount * 3
depth = depth + 1
redim oa(ptCount - 1, 1 )
for i = 0 to ptCount - 1
oa(i, X) = ia(i, X)
oa(i, Y) = ia(i, Y)
next i
redim ia(3 * ptCount - 1, 1)
iaIndex = 0
wend
end sub
//Test Demo for the sub (NEW as 2016 - 05 - 29 !!!!!)
cx=xmax/2
cy=ymax/2
r=cy - 20
N=3
for i = 0 to 2
color 64+42*i,64+42*i,64+42*i
SierLineTri(cx, cy, cx+r*cos(2*pi/N*i), cy +r*sin(2*pi/N*i), cx + r*cos(2*pi/N*(i+1)), cy + r*sin(2*pi/N*(i+1)), 5)
next iSimple recursive version
w = 800 : h = 600
open window w, h
window origin "lb"
sub SierpinskyTriangle(level, x, y, w, h)
local w2, w4, h2
w2 = w/2 : w4 = w/4 : h2 = h/2
if level=1 then
new curve
line to x, y
line to x+w2, y+h
line to x+w, y
line to x, y
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 sub
SierpinskyTriangle(7, w*0.05, h*0.05, w*0.9, h*0.9)C
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++
#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
The output image is the same as the Go version. This requires the module from the Grayscale image Task.
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");
}
Delphi
const DepthColors24: array [0..23] of TColor =(
0 or (0 shl 8) or (0 shl 16),
255 or (0 shl 8) or (0 shl 16),
255 or (63 shl 8) or (0 shl 16),
255 or (127 shl 8) or (0 shl 16),
255 or (191 shl 8) or (0 shl 16),
255 or (255 shl 8) or (0 shl 16),
191 or (255 shl 8) or (0 shl 16),
127 or (255 shl 8) or (0 shl 16),
63 or (255 shl 8) or (0 shl 16),
0 or (255 shl 8) or (0 shl 16),
0 or (255 shl 8) or (63 shl 16),
0 or (255 shl 8) or (127 shl 16),
0 or (255 shl 8) or (191 shl 16),
0 or (255 shl 8) or (255 shl 16),
0 or (191 shl 8) or (255 shl 16),
0 or (127 shl 8) or (255 shl 16),
0 or (63 shl 8) or (255 shl 16),
0 or (0 shl 8) or (255 shl 16),
63 or (0 shl 8) or (255 shl 16),
127 or (0 shl 8) or (255 shl 16),
191 or (0 shl 8) or (255 shl 16),
255 or (0 shl 8) or (255 shl 16),
255 or (0 shl 8) or (191 shl 16),
255 or (0 shl 8) or (127 shl 16));
procedure DrawSerpTriangle(Image: TImage; StartX,StartY, Depth: integer);
var I,X,Y,Size,Inx: integer;
var C: TColor;
begin
Size:=1 shl Depth;
for Y:=0 to Size-1 do
for X:=0 to Size-1 do
begin
{Calculate new color index}
Inx:=MulDiv(Length(DepthColors24),X+Y,Size+Size)+1;
if (X and Y)=0 then
begin
Image.Canvas.Pixels[StartX+X,StartY+Y]:=DepthColors24[Inx];
end;
end;
end;
procedure ShowSierpinskiTriangle(Image: TImage);
begin
ClearImage(Image,clBlack);
DrawSerpTriangle(Image,50,32,8);
Image.Invalidate;
end;
- Output:
Elapsed Time: 28.293 ms.
EasyLang
proc triang lev x y size . .
if lev = 0
move x y
circle 0.15
else
lev -= 1
size /= 2
call triang lev x + size y size
call triang lev x + size / 2 y + size size
call triang lev x y size
.
.
call triang 8 5 5 90
Erlang
-module(sierpinski).
-author("zduchac").
-export([start/0]).
sierpinski(DC, Order) ->
Size = 1 bsl Order,
sierpinski(DC, Order, Size, 0, 0).
sierpinski(_, _, Size, _, Y) when Y =:= Size ->
ok;
sierpinski(DC, Order, Size, X, Y) when X =:= Size ->
sierpinski(DC, Order, Size, 0, Y + 1);
sierpinski(DC, Order, Size, X, Y) when X band Y =:= 0 ->
wxDC:drawPoint(DC, {X, Y}),
sierpinski(DC, Order, Size, X + 1, Y);
sierpinski(DC, Order, Size, X, Y) ->
sierpinski(DC, Order, Size, X + 1, Y).
start() ->
Wx = wx:new(),
Frame = wxFrame:new(Wx, -1, "Raytracer", []),
wxFrame:connect(Frame, paint, [{callback,
fun(_Evt, _Obj) ->
DC = wxPaintDC:new(Frame),
sierpinski(DC, 8),
wxPaintDC:destroy(DC)
end
}]),
wxFrame:show(Frame).
ERRE
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 PROGRAMFactor
USING: accessors images images.loader kernel literals math
math.bits math.functions make sequences ;
IN: rosetta-code.sierpinski-triangle-graphical
CONSTANT: black B{ 33 33 33 255 }
CONSTANT: white B{ 255 255 255 255 }
CONSTANT: size $[ 2 8 ^ ] ! edit 8 to change order
! Generate Sierpinksi's triangle sequence. This is sequence
! A001317 in OEIS.
: sierpinski ( n -- seq )
[ [ 1 ] dip [ dup , dup 2 * bitxor ] times ] { } make nip ;
! Convert a number to binary, then append a black pixel for each
! set bit or a white pixel for each unset bit to the image being
! built by make.
: expand ( n -- ) make-bits [ black white ? % ] each ;
! Append white pixels until the end of the row in the image
! being built by make.
: pad ( n -- ) [ size ] dip 1 + - [ white % ] times ;
! Generate the image data for a sierpinski triangle of a given
! size in pixels. The image is square so its dimensions are
! n x n.
: sierpinski-img ( n -- seq )
sierpinski [ [ [ expand ] dip pad ] each-index ] B{ } make ;
: main ( -- )
<image>
${ size size } >>dim
BGRA >>component-order
ubyte-components >>component-type
size sierpinski-img >>bitmap
"sierpinski-triangle.png" save-graphic-image ;
MAIN: main
- Output:
![[1]](https://i.imgur.com/wjwCrvL.png){kind=link}
Forth
include lib/graphics.4th \ graphics support is needed
520 pic_width ! \ width of the image
520 pic_height ! \ height of the image
9 constant order \ Sierpinski's triangle order
black 255 whiteout \ black ink, white background
grayscale_image \ we're making a gray scale image
\ do we set a pixel or not?
: ?pixel over over and if drop drop else set_pixel then ;
: triangle 1 order lshift dup 0 do dup 0 do i j ?pixel loop loop drop ;
triangle s" triangle.ppm" save_image \ done, save the image
- Output:
Because Rosetta code doesn't allow file uploads, the output can't be shown.
FutureBasic
_window = 1
_width = 600
_height = 500
local fn SierpinskyTriangle( level as NSUInteger, x as NSUInteger, y as NSUInteger, w as NSUInteger, h as NSUInteger )
NSUInteger w2 = w/2, w4 = w/4, h2 = h/2
if ( level == 1 )
pen -1.0
line to x, y
pen 1.0, fn ColorYellow
line to x+w2, y+h
line to x+w, y
line to x, y
else
fn SierpinskyTriangle( level-1, x, y, w2, h2 )
fn SierpinskyTriangle( level-1, x+w4, y+h2, w2, h2 )
fn SierpinskyTriangle( level-1, x+w2, y, w2, h2 )
end if
end fn
window _window, @"Sierpinsky Triangle", ( 0, 0, _width, _height )
WindowSetBackgroundColor( 1, fn ColorBlack )
fn SierpinskyTriangle( 9, _width * 0.05, _height * 0.05, _width * 0.9, _height * 0.9 )
HandleEvents- Output:
gnuplot
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
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
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.
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
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.
Original source IPL Graphics/sier1.
J
Solution:
load 'viewmat'
'rgb'viewmat--. |. (~:_1&|.)^:(<@#) (2^8){.1
This looks almost exactly (except for OS specific decorations) like the task example image
Other approaches are possible
load'viewmat'
viewmat(,~,.~)^:4,1
generates a "smaller" image and is white on black instead of black on white. Similarly,
viewmat #:(~:/&.#:@, +:)^:(<32) 1
presents the image in a different orientation.
And, of course, other approaches are viable.
Java
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
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
- 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".
<!-- 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();">
<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.
jq
Works with gojq, the Go implementation of jq
This entry uses an L-system and turtle graphics to generate an SVG file, which can be viewed using a web browser, at least if the file type is `.svg`.
See Category_talk:Jq-turtle for the turtle.jq module used here. Please note that the `include` directive may need to be modified depending on the location of the included file, and the command-line options used.
include "turtle" {search: "."};
# Compute the curve using a Lindenmayer system of rules
def rules:
# "H" signfies Horizontal motion
{X: "XX",
H: "H--X++H++X--H",
"": "H--X--X"};
def sierpinski($count):
rules as $rules
| def repeat($count):
if $count == 0 then .
else gsub("X"; $rules["X"]) | gsub("H"; $rules["H"])
| repeat($count-1)
end;
$rules[""] | repeat($count) ;
def interpret($x):
if $x == "+" then turtleRotate(-60)
elif $x == "-" then turtleRotate(60)
else turtleForward(20)
end;
def sierpinski_curve($n):
sierpinski($n)
| split("")
| reduce .[] as $action (
turtle([200,-200]) | turtleDown;
interpret($action) ) ;
# viewBox = <min-x> <min-y> <width> <height>
# Input: {svg, minx, miny, maxx, maxy}
def svg:
"<svg viewBox='\(.minx|floor) \(.miny - 4 |floor) \(.maxx - .minx|ceil) \(6 + .maxy - .miny|ceil)'",
" preserveAspectRatio='xMinYmin meet'",
" xmlns='http://www.w3.org/2000/svg' >",
path("none"; "red"; 1),
"</svg>";
sierpinski_curve(5)
| svgJulia
Produces a png graphic on a transparent background. The brushstroke used for fill might need to be modified for a white background.
using Luxor
function sierpinski(txy, levelsyet)
nxy = zeros(6)
if levelsyet > 0
for i in 1:6
pos = i < 5 ? i + 2 : i - 4
nxy[i] = (txy[i] + txy[pos]) / 2.0
end
sierpinski([txy[1],txy[2],nxy[1],nxy[2],nxy[5],nxy[6]], levelsyet-1)
sierpinski([nxy[1],nxy[2],txy[3],txy[4],nxy[3],nxy[4]], levelsyet-1)
sierpinski([nxy[5],nxy[6],nxy[3],nxy[4],txy[5],txy[6]], levelsyet-1)
else
poly([Point(txy[1],txy[2]),Point(txy[3],txy[4]),Point(txy[5],txy[6])], :fill ,close=true)
end
end
Drawing(800, 800)
sierpinski([400., 100., 700., 500., 100., 500.], 7)
finish()
preview()
Kotlin
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)
}
}
Logo
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 200Lua
-- 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
Mathematica/Wolfram Language
Sierpinski[n_] :=
Nest[Join @@ Table[With[{a = #[[i, 1]], b = #[[i, 2]], c = #[[i, 3]]},
{{a, (a + b)/2, (c + a)/2}, {(a + b)/2, b, (b + c)/2}, {(c + a)/2, (b + c)/2, c}}],
{i, Length[#]}] &, {{{0, 0}, {1/2, 1}, {1, 0}}}, n]
Graphics[{Black, Polygon /@ Sierpinski[8]}]
Another faster version
cf = Compile[{{A, _Real, 2}},
With[{a = A[[1]], b = A[[2]], c = A[[3]]},
With[{ab = (a + b)/2, bc = (b + c)/2, ca = (a + c)/2},
{{a, ab, ca}, {ab, b, bc}, {ca, bc, c}}]],
RuntimeAttributes -> {Listable}
];
n = 3;
pts = Flatten[Nest[cf, N@{{{0, 0}, {1, 0}, {1/2, √3/2}}}, n], n];
Graphics[Polygon /@ pts]
MATLAB
Basic Version
[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:
Bit Operator Version
t = 0 : 2^16 - 1;
plot(t, bitand(t, bitshift(t, -8)), 'k.')
Nim
Our triangle is ref on a black background.
import imageman
const
Black = ColorRGBU [byte 0, 0, 0] # For background.
Red = ColorRGBU [byte 255, 0, 0] # For triangle.
proc drawSierpinski(img: var Image; txy: array[1..6, float]; levelsYet: Natural) =
var nxy: array[1..6, float]
if levelsYet > 0:
for i in 1..6:
let pos = if i < 5: i + 2 else: i - 4
nxy[i] = (txy[i] + txy[pos]) / 2
img.drawSierpinski([txy[1], txy[2], nxy[1], nxy[2], nxy[5], nxy[6]], levelsYet - 1)
img.drawSierpinski([nxy[1], nxy[2], txy[3], txy[4], nxy[3], nxy[4]], levelsyet - 1)
img.drawSierpinski([nxy[5], nxy[6], nxy[3], nxy[4], txy[5], txy[6]], levelsyet - 1)
else:
img.drawPolyline(closed = true, Red,
(txy[1].toInt, txy[2].toInt), (txy[3].toInt, txy[4].toInt),(txy[5].toInt, txy[6].toInt))
var image = initImage[ColorRGBU](800, 800)
image.fill(Black)
image.drawSierpinski([400.0, 100.0, 700.0, 500.0, 100.0, 500.0], 7)
image.savePNG("sierpinski_triangle.png", compression = 9)
Objeck
use Game.SDL2;
use Game.Framework;
class Test {
@framework : GameFramework;
@colors : Color[];
@step : Int;
function : Main(args : String[]) ~ Nil {
Test->New()->Run();
}
New() {
@framework := GameFramework->New(GameConsts->SCREEN_WIDTH, GameConsts->SCREEN_HEIGHT, "Sierpinski Triangle");
@framework->SetClearColor(Color->New(0,0,0));
@colors := Color->New[1];
@colors[0] := Color->New(178,34,34);
}
method : Run() ~ Nil {
if(@framework->IsOk()) {
e := @framework->GetEvent();
quit := false;
while(<>quit) {
# process input
while(e->Poll() <> 0) {
if(e->GetType() = EventType->SDL_QUIT) {
quit := true;
};
};
@framework->FrameStart();
@framework->Clear();
Render(8, 20, 20, 450);
@framework->Show();
@framework->FrameEnd();
};
}
else {
"--- Error Initializing Environment ---"->ErrorLine();
return;
};
leaving {
@framework->Quit();
};
}
method : Render(level : Int, x : Int, y : Int, size : Int) ~ Nil {
if(level > -1) {
renderer := @framework->GetRenderer();
renderer->LineColor(x, y, x+size, y, @colors[0]);
renderer->LineColor(x, y, x, y+size, @colors[0]);
renderer->LineColor(x+size, y, x, y+size, @colors[0]);
Render(level-1, x, y, size/2);
Render(level-1, x+size/2, y, size/2);
Render(level-1, x, y+size/2, size/2);
};
}
}
consts GameConsts {
SCREEN_WIDTH := 640,
SCREEN_HEIGHT := 480
}OCaml
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
\\ 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
my $levels = 6;
my $side = 512;
my $height = get_height($side);
sub get_height { my($side) = @_; $side * sqrt(3) / 2 }
sub triangle {
my($x1, $y1, $x2, $y2, $x3, $y3, $fill, $animate) = @_;
my $svg;
$svg .= qq{<polygon points="$x1,$y1 $x2,$y2 $x3,$y3"};
$svg .= qq{ style="fill: $fill; stroke-width: 0;"} if $fill;
$svg .= $animate
? qq{>\n <animate attributeType="CSS" attributeName="opacity"\n values="1;0;1" keyTimes="0;.5;1" dur="20s" repeatCount="indefinite" />\n</polygon>\n}
: ' />';
return $svg;
}
sub fractal {
my( $x1, $y1, $x2, $y2, $x3, $y3, $r ) = @_;
my $svg;
$svg .= triangle( $x1, $y1, $x2, $y2, $x3, $y3 );
return $svg unless --$r;
my $side = abs($x3 - $x2) / 2;
my $height = get_height($side);
$svg .= fractal( $x1, $y1-$height*2, $x1-$side/2, $y1-3*$height, $x1+$side/2, $y1-3*$height, $r);
$svg .= fractal( $x2, $y1, $x2-$side/2, $y1-$height, $x2+$side/2, $y1-$height, $r);
$svg .= fractal( $x3, $y1, $x3-$side/2, $y1-$height, $x3+$side/2, $y1-$height, $r);
}
open my $fh, '>', 'run/sierpinski_triangle.svg';
print $fh <<'EOD',
<?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>
EOD
triangle( $side/2, 0, 0, $height, $side, $height, 'url(#basegradient)' ),
triangle( $side/2, 0, 0, $height, $side, $height, '#000', 'animate' ),
'<g style="fill: #fff; stroke-width: 0;">',
fractal( $side/2, $height, $side*3/4, $height/2, $side/4, $height/2, $levels ),
'</g></svg>';
See sierpinski_triangle (offsite .svg image)
Phix
Can resize, and change the level from 1 to 12 (press +/-).
-- 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) if platform()!=JS then IupMainLoop() IupClose() end if end procedure main()
PicoLisp
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
%!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
Processing
Should work with most versions of Processing
Recursive Sierpinski triangles
Pixel based
PVector [] coord = {new PVector(0, 0), new PVector(150, 300), new PVector(300, 0)};
void setup()
{
size(400,400);
background(32);
sierpinski(new PVector(150,150), 8);
noLoop();
}
void sierpinski(PVector cPoint, int cDepth)
{
if (cDepth == 0) {
set(50+int(cPoint.x), (height-50)-int(cPoint.y), color(192));
return;
}
for (int v=0; v<3; v++) {
sierpinski(new PVector((cPoint.x+coord[v].x)/2, (cPoint.y+coord[v].y)/2), cDepth-1);
}
}Animated
int depth = 5;
int interval = 50;
int currentTime;
int lastTime;
int progress = 0;
int lastProgress = 0;
//int finished = int(pow(3,depth));
boolean intervalExpired = false;
void setup() {
size(410, 230);
background(255);
fill(0);
lastTime = millis();
}
void draw() {
currentTime = millis();
triangle (10, 25, 100, depth);
}
void triangle (int x, int y, int l, int n) {
if (n == 0) {
checkIfIntervalExpired();
if (intervalExpired && progress == lastProgress) {
text("*", x, y);
lastProgress++;
intervalExpired = false;
}
progress++;
} else {
triangle(x, y+l, l/2, n-1);
triangle(x+l, y, l/2, n-1);
triangle(x+l*2, y+l, l/2, n-1);
}
}
void checkIfIntervalExpired() {
if (currentTime-lastTime > interval) {
lastTime = currentTime;
progress = 0;
intervalExpired = true;
}
}
void keyReleased() {
if (key==' ') { // reset
progress = 0;
lastProgress = 0;
background(255);
}
}3D version
import peasy.*;
int depth = 6; // recursion depth
int dWidth = 600;
int dHeight = 600;
color pyramidColor = color( 0 );
color bgColor = color( 255 );
// 3D Sierpinski tetrahedron vertices
PVector [] coord = {
new PVector( 0, 0, 0),
new PVector( 300, 0, 0),
new PVector( 150, 0, -260),
new PVector( 150, -245, -86.6)
};
int verts = coord.length;
float boxSize = 600/pow(3, depth);
// "random" start point (mid point)
PVector startPoint = new PVector(150, 183.7, 173.2);
PeasyCam cam;
void settings()
{
size(dWidth, dHeight, P3D);
}
void setup()
{
cam = new PeasyCam(this, startPoint.x, startPoint.y, startPoint.z, 400);
cam.setMaximumDistance(3000);
fill(pyramidColor);
stroke(pyramidColor);
}
void draw()
{
background(bgColor);
sierpinski(startPoint, depth);
}
void sierpinski(PVector currentPoint, int currentDepth)
{
if (currentDepth == 0) {
pushMatrix();
translate(currentPoint.x, 245+currentPoint.y, 260+currentPoint.z);
box(boxSize);
popMatrix();
return;
}
for (int v=0; v<verts; v++) {
sierpinski(new PVector(
(currentPoint.x+coord[v].x)/2,
(currentPoint.y+coord[v].y)/2,
(currentPoint.z+coord[v].z)/2),
currentDepth-1);
}
}Prolog
Works with SWI-Prolog and XPCE.
Recursive version
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
:- 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
# a very simple version
import turtle as t
def sier(n,length):
if n == 0:
return
for i in range(3):
sier(n - 1, length / 2)
t.fd(length)
t.rt(120)
# otra versión muy simple
from pylab import*
x=[[1,1],[1,0]]
for i in'123':x=kron(x,x)
imsave('a',x)
#!/usr/bin/env python
##########################################################################################
# a very complicated version
# 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)
Quackery
[ $ "turtleduck.qky" loadfile ] now!
[ 1 & ] is odd ( n --> b )
[ 4 times
[ 2dup walk
1 4 turn ]
2drop ] is square ( n/d --> )
[ dup
witheach
[ odd if
[ ' [ 0 0 0 ] fill
[ 2 1 square ] ]
2 1 fly ]
size -2 * 1 fly
1 4 turn
2 1 fly
-1 4 turn ] is showline ( [ --> )
[ [] 0 rot 0 join
witheach
[ tuck +
rot join swap ]
drop ] is nextline ( [ --> [ )
[ ' [ 1 ] swap
bit
1 - times
[ dup showline
nextline ]
showline ] is sierpinski ( n --> )
turtle
100 frames
5 8 turn
400 1 fly
3 8 turn
8 sierpinski
1 frame- Output:
R
Note: Find plotmat() here on RC R Helper Functions page.
## 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
#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")
Raku
(formerly Perl 6)
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 $levels = 8;
my $side = 512;
my $height = get_height($side);
sub get_height ($side) { $side * 3.sqrt / 2 }
sub triangle ( $x1, $y1, $x2, $y2, $x3, $y3, $fill?, $animate? ) {
my $svg;
$svg ~= qq{<polygon points="$x1,$y1 $x2,$y2 $x3,$y3"};
$svg ~= qq{ style="fill: $fill; stroke-width: 0;"} if $fill;
$svg ~= $animate
?? qq{>\n <animate attributeType="CSS" attributeName="opacity"\n values="1;0;1" keyTimes="0;.5;1" dur="20s" repeatCount="indefinite" />\n</polygon>}
!! ' />';
return $svg;
}
sub fractal ( $x1, $y1, $x2, $y2, $x3, $y3, $r is copy ) {
my $svg;
$svg ~= triangle( $x1, $y1, $x2, $y2, $x3, $y3 );
return $svg unless --$r;
my $side = abs($x3 - $x2) / 2;
my $height = get_height($side);
$svg ~= fractal( $x1, $y1-$height*2, $x1-$side/2, $y1-3*$height, $x1+$side/2, $y1-3*$height, $r);
$svg ~= fractal( $x2, $y1, $x2-$side/2, $y1-$height, $x2+$side/2, $y1-$height, $r);
$svg ~= fractal( $x3, $y1, $x3-$side/2, $y1-$height, $x3+$side/2, $y1-$height, $r);
}
my $fh = open('sierpinski_triangle.svg', :w) orelse .die;
$fh.print: qq:to/EOD/,
<?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>
EOD
triangle( $side/2, 0, 0, $height, $side, $height, 'url(#basegradient)' ),
triangle( $side/2, 0, 0, $height, $side, $height, '#000', 'animate' ),
'<g style="fill: #fff; stroke-width: 0;">',
fractal( $side/2, $height, $side*3/4, $height/2, $side/4, $height/2, $levels ),
'</g></svg>';
Ring
load "guilib.ring"
new qapp
{
win1 = new qwidget() {
setwindowtitle("drawing using qpainter")
setgeometry(100,100,500,500)
label1 = new qlabel(win1) {
setgeometry(10,10,400,400)
settext("")
}
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:
Ruby
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
JRubyArt is a port of processing to ruby
T_HEIGHT = sqrt(3) / 2
TOP_Y = 1 / sqrt(3)
BOT_Y = sqrt(3) / 6
TRIANGLE_SIZE = 800
def settings
size(TRIANGLE_SIZE, (T_HEIGHT * TRIANGLE_SIZE))
smooth
end
def setup
sketch_title 'Sierpinski Triangle'
fill(255)
background(0)
no_stroke
draw_sierpinski(width / 2, height / 1.5, TRIANGLE_SIZE)
end
def draw_sierpinski(cx, cy, sz)
if sz < 5 # Limit no of recursions on size
draw_triangle(cx, cy, sz) # Only draw terminals
else
cx0 = cx
cy0 = cy - BOT_Y * sz
cx1 = cx - sz / 4
cy1 = cy + (BOT_Y / 2) * sz
cx2 = cx + sz / 4
cy2 = cy + (BOT_Y / 2) * sz
draw_sierpinski(cx0, cy0, sz / 2)
draw_sierpinski(cx1, cy1, sz / 2)
draw_sierpinski(cx2, cy2, sz / 2)
end
end
def draw_triangle(cx, cy, sz)
cx0 = cx
cy0 = cy - TOP_Y * sz
cx1 = cx - sz / 2
cy1 = cy + BOT_Y * sz
cx2 = cx + sz / 2
cy2 = cy + BOT_Y * sz
triangle(cx0, cy0, cx1, cy1, cx2, cy2)
end
Rust
Output is an SVG file.
// [dependencies]
// svg = "0.8.0"
const SQRT3_2: f64 = 0.86602540378444;
fn sierpinski_triangle(
mut document: svg::Document,
mut x: f64,
mut y: f64,
mut side: f64,
order: usize,
) -> svg::Document {
use svg::node::element::Polygon;
if order == 1 {
let mut points = Vec::new();
points.push((x, y));
y += side * SQRT3_2;
x -= side * 0.5;
points.push((x, y));
x += side;
points.push((x, y));
let polygon = Polygon::new()
.set("fill", "black")
.set("stroke", "none")
.set("points", points);
document = document.add(polygon);
} else {
side *= 0.5;
document = sierpinski_triangle(document, x, y, side, order - 1);
y += side * SQRT3_2;
x -= side * 0.5;
document = sierpinski_triangle(document, x, y, side, order - 1);
x += side;
document = sierpinski_triangle(document, x, y, side, order - 1);
}
document
}
fn write_sierpinski_triangle(file: &str, size: usize, order: usize) -> std::io::Result<()> {
use svg::node::element::Rectangle;
let margin = 20.0;
let side = (size as f64) - 2.0 * margin;
let y = 0.5 * ((size as f64) - SQRT3_2 * side);
let x = margin + side * 0.5;
let rect = Rectangle::new()
.set("width", "100%")
.set("height", "100%")
.set("fill", "white");
let mut document = svg::Document::new()
.set("width", size)
.set("height", size)
.add(rect);
document = sierpinski_triangle(document, x, y, side, order);
svg::save(file, &document)
}
fn main() {
write_sierpinski_triangle("sierpinski_triangle.svg", 600, 8).unwrap();
}
- Output:
Media:Sierpinski_triangle_rust.svg
Seed7
$ include "seed7_05.s7i";
include "draw.s7i";
include "keybd.s7i";
include "bin64.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 bin64(x) & bin64(y) = bin64(0) then
point(margin + x, margin + y, black);
end if;
end for;
end for;
ignore(getc(KEYBOARD));
end func;Original source: [2]
Sidef
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
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.
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
VBScript
VBScript does'nt have access to windows graphics. To achieve this i had to implement turtle graphics wtiting SVG commands to an HTML file. At the end the program opens the graphics in the default browser.
option explicit
'outputs turtle graphics to svg file and opens it
const pi180= 0.01745329251994329576923690768489 ' pi/180
const pi=3.1415926535897932384626433832795 'pi
class turtle
dim fso
dim fn
dim svg
dim iang 'radians
dim ori 'radians
dim incr
dim pdown
dim clr
dim x
dim y
public property let orient(n):ori = n*pi180 :end property
public property let iangle(n):iang= n*pi180 :end property
public sub pd() : pdown=true: end sub
public sub pu() :pdown=FALSE :end sub
public sub rt(i)
ori=ori - i*iang:
'if ori<0 then ori = ori+pi*2
end sub
public sub lt(i):
ori=(ori + i*iang)
'if ori>(pi*2) then ori=ori-pi*2
end sub
public sub bw(l)
x= x+ cos(ori+pi)*l*incr
y= y+ sin(ori+pi)*l*incr
' ori=ori+pi '?????
end sub
public sub fw(l)
dim x1,y1
x1=x + cos(ori)*l*incr
y1=y + sin(ori)*l*incr
if pdown then line x,y,x1,y1
x=x1:y=y1
end sub
Private Sub Class_Initialize()
setlocale "us"
initsvg
x=400:y=400:incr=100
ori=90*pi180
iang=90*pi180
clr=0
pdown=true
end sub
Private Sub Class_Terminate()
disply
end sub
private sub line (x,y,x1,y1)
svg.WriteLine "<line x1=""" & x & """ y1= """& y & """ x2=""" & x1& """ y2=""" & y1 & """/>"
end sub
private sub disply()
dim shell
svg.WriteLine "</svg></body></html>"
svg.close
Set shell = CreateObject("Shell.Application")
shell.ShellExecute fn,1,False
end sub
private sub initsvg()
dim scriptpath
Set fso = CreateObject ("Scripting.Filesystemobject")
ScriptPath= Left(WScript.ScriptFullName, InStrRev(WScript.ScriptFullName, "\"))
fn=Scriptpath & "SIERP.HTML"
Set svg = fso.CreateTextFile(fn,True)
if SVG IS nothing then wscript.echo "Can't create svg file" :vscript.quit
svg.WriteLine "<!DOCTYPE html>" &vbcrlf & "<html>" &vbcrlf & "<head>"
svg.writeline "<style>" & vbcrlf & "line {stroke:rgb(255,0,0);stroke-width:.5}" &vbcrlf &"</style>"
svg.writeline "</head>"&vbcrlf & "<body>"
svg.WriteLine "<svg xmlns=""http://www.w3.org/2000/svg"" width=""800"" height=""800"" viewBox=""0 0 800 800"">"
end sub
end class
sub sier(lev,lgth)
dim i
'wscript.echo lev,lgth
if lev=1 then
for i=1 to 3
x.fw lgth
x.lt 2
next
else
sier lev-1,lgth\2
x.fw lgth\2
sier lev-1,lgth\2
x.bw lgth\2
x.lt 1
x.fw lgth\2
x.rt 1
sier lev-1,lgth\2
x.lt 1
x.bw lgth\2
x.rt 1
end if
end sub
dim x
set x=new turtle
x.iangle=60
x.orient=0
x.incr=10
x.x=100:x.y=100
'star5
sier 7,64
set x=nothing 'outputs html file to browser==
- Output:
==
Wren
import "graphics" for Canvas, Color
import "dome" for Window
class Game {
static init() {
Window.title = "Sierpinski Triangle"
var size = 800
Window.resize(size, size)
Canvas.resize(size, size)
Canvas.cls(Color.white)
var level = 8
sierpinskiTriangle(level, 20, 20, size - 40)
}
static update() {}
static draw(alpha) {}
static sierpinskiTriangle(level, x, y, size) {
if (level > 0) {
var col = Color.black
Canvas.line(x, y, x + size, y, col)
Canvas.line(x, y, x, y + size, col)
Canvas.line(x + size, y, x, y + size, col)
var size2 = (size/2).floor
sierpinskiTriangle(level - 1, x, y, size2)
sierpinskiTriangle(level - 1, x + size/2, y, size2)
sierpinskiTriangle(level - 1, x, y + size/2, size2)
}
}
}XPL0
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
Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl
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"));Categories:
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