Sierpinski triangle/Graphical: Difference between revisions
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An example of Sierpinski's triangle (order = 8) looks like this: <br/><br/>
[[File:Sierpinski_Triangle_Unicon.PNG]]
=={{header|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.
<syntaxhighlight lang="asm"> ;;; 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)</syntaxhighlight>
=={{header|Action!}}==
<syntaxhighlight lang="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</syntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Sierpinski_triangle_graphical.png Screenshot from Atari 8-bit computer]
=={{header|ActionScript}}==
SierpinskiTriangle class:
<syntaxhighlight lang="actionscript3">
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);
}
}
}
</syntaxhighlight>
Document class:
<syntaxhighlight lang="actionscript3">
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);
}
}
}
</syntaxhighlight>
=={{header|ALGOL 68}}==
{{libheader|ALGOL 68-l-system}}
Generates an SVG file containing the curve using the L-System. Very similar to the Algol 68 Sierpinski square curve sample.
Note the Algol 68 L-System library source code is on a separate page on Rosetta Code - follow the above link and then to the Talk page.
<syntaxhighlight lang="algol68">
BEGIN # Sierpinski Triangle Curve in SVG #
# uses the RC Algol 68 L-System library for the L-System evaluation & #
# interpretation #
PR read "lsystem.incl.a68" PR # include L-System utilities #
PROC sierpinski triangle curve = ( STRING fname, INT size, length, order, init x, init y )VOID:
IF FILE svg file;
BOOL open error := IF open( svg file, fname, stand out channel ) = 0
THEN
# opened OK - file already exists and #
# will be overwritten #
FALSE
ELSE
# failed to open the file #
# - try creating a new file #
establish( svg file, fname, stand out channel ) /= 0
FI;
open error
THEN # failed to open the file #
print( ( "Unable to open ", fname, newline ) );
stop
ELSE # file opened OK #
REAL x := init x;
REAL y := init y;
INT angle := 0;
put( svg file, ( "<svg xmlns='http://www.w3.org/2000/svg' width='"
, whole( size, 0 ), "' height='", whole( size, 0 ), "'>"
, newline, "<rect width='100%' height='100%' fill='white'/>"
, newline, "<path stroke-width='1' stroke='black' fill='none' d='"
, newline, "M", whole( x, 0 ), ",", whole( y, 0 ), newline
)
);
LSYSTEM ssc = ( "F-G-G"
, ( "F" -> "F-G+F+G-F"
, "G" -> "GG"
)
);
STRING curve = ssc EVAL order;
curve INTERPRET ( ( CHAR c )VOID:
IF c = "F" OR c = "G" THEN
x +:= length * cos( angle * pi / 180 );
y +:= length * sin( angle * pi / 180 );
put( svg file, ( " L", whole( x, 0 ), ",", whole( y, 0 ), newline ) )
ELIF c = "+" THEN
angle +:= 120 MODAB 360
ELIF c = "-" THEN
angle -:= 120 MODAB 360
FI
);
put( svg file, ( "'/>", newline, "</svg>", newline ) );
close( svg file )
FI # sierpinski square # ;
sierpinski triangle curve( "sierpinski_triangle.svg", 1200, 12, 5, 200, 400 )
END
</syntaxhighlight>
=={{header|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.
<
return
point(p, node) --
Line 26 ⟶ 316:
}
sierpinski((0, 0) -- (5 inch, 1 inch) -- (2 inch, 6 inch) -- cycle, 10);</
Una versión mas corta:
<syntaxhighlight lang="asymptote">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);</syntaxhighlight>
=={{header|ATS}}==
{{libheader|SDL}}
<syntaxhighlight lang="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);
}
%}</syntaxhighlight>
=={{header|AutoHotkey}}==
{{libheader|GDIP}}
<syntaxhighlight lang="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
}</syntaxhighlight>
=={{header|BASIC}}==
{{works with|QBasic}}
<!-- {{works with|QBasic}} codificado por: Kibbee, 12 junio 2012 -->
<syntaxhighlight lang="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
</syntaxhighlight>
[https://www.dropbox.com/s/c3g1ae1i771ox7g/Sierpinski_triangle_QBasic.png?dl=0 Sierpinski triangle QBasic image]
==={{header|BBC BASIC}}===
{{works with|BBC BASIC for Windows}}
<syntaxhighlight lang="bbcbasic"> 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%
</syntaxhighlight>
[[File:sierpinski_triangle_bbc.gif]]
==={{header|FreeBASIC}}===
<syntaxhighlight lang="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
End</syntaxhighlight>
==={{header|IS-BASIC}}===
<syntaxhighlight lang="is-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 DEF</syntaxhighlight>
==={{header|Liberty 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...
<syntaxhighlight lang="lb">
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
</syntaxhighlight>
Up to order 10 displays on a 1080 vertical pixel screen.
==={{header|Run BASIC}}===
[[File : SierpinskiRunBasic.png|thumb|right]]
<syntaxhighlight lang="runbasic">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</syntaxhighlight>
==={{header|SmileBASIC}}===
{{Trans|Action!}}
<syntaxhighlight lang="basic">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</syntaxhighlight>
==={{header|TI-83 BASIC}}===
<syntaxhighlight lang="ti83b">: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</syntaxhighlight>
This could be made faster, but I just wanted to use the DS<( command
==={{header|Yabasic}}===
[http://retrogamecoding.org/board/index.php?action=dlattach;topic=753.0;attach=1800;image Sierpinski Triangle 3D.png]
3D version.
<syntaxhighlight lang="yabasic">// 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 i
</syntaxhighlight>
Simple recursive version
<syntaxhighlight lang="yabasic">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)</syntaxhighlight>
=={{header|Bruijn}}==
Rendered using [https://lambda-screen.marvinborner.de/ lambda screen].
<syntaxhighlight lang="bruijn">y [[1 (0 0)] [1 (0 0)]]
# infinite depth
triangle [y [[0 1 [[0]] 1 1]]]
:import std/Number .
# limited depth
triangle-n [y [[[[1 0 [[0]] 0 0] (=?1 [[1]] (2 --1))]]] (+7)]
</syntaxhighlight>
=={{header|C}}==
[[file:sierp-tri-c.png|thumb|center|128px]]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: <code>gcc -lm stuff.c -o sierp; ./sierp 9 > triangle.pnm</code>. 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 <stdlib.h>
#include <string.h>
Line 67 ⟶ 909:
}
void iter_string(const char * str, int d)
{
long long len;
Line 143 ⟶ 985:
return 0;
}</
=={{header|C++}}==
[[file:STriCpp.png|thumb|right|200px]]
<syntaxhighlight lang="cpp">
#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;
}
</syntaxhighlight>
=={{header|D}}==
The output image is the same as the Go version. This requires the module from the Grayscale image Task.
{{trans|Go}}
<syntaxhighlight lang="d">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");
}</syntaxhighlight>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
[[File:DelphiSierpinskiTriangle.png|frame|none]]
<syntaxhighlight lang="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;
</syntaxhighlight>
{{out}}
<pre>
Elapsed Time: 28.293 ms.
</pre>
=={{header|EasyLang}}==
[https://easylang.dev/show/#cod=fY3BCoMwEETv+Yq5l65RCOghH1PCKoG0kShS+/UmuiAe7O7pzczOjik6zMm/PgMCL/hixeR/DAIpAL7fZQtdKM87LlxSgs4nFxiaalMUDhOLU86eFrXgXlpZNMKXn4/DPl7/CVRockjgLnu2kCIlVguTt9NqAw== Run it]
<syntaxhighlight lang="easylang">
proc triang lev x y size . .
if lev = 0
move x y
circle 0.15
else
lev -= 1
size /= 2
triang lev x + size y size
triang lev x + size / 2 y + size size
triang lev x y size
.
.
triang 8 5 5 90
</syntaxhighlight>
=={{header|Erlang}}==
<syntaxhighlight lang="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).
</syntaxhighlight>
=={{header|ERRE}}==
<syntaxhighlight lang="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 PROGRAM
</syntaxhighlight>
=={{header|Evaldraw}}==
This makes use of sleep(millis); and refresh(); in the middle of a function to do the slow animation of triangles.
[[File:Evaldraw sierpinski.gif|thumb|alt=refresh allows for drawing outside the main () function|With sleep() we wait 1 milli before redraw any pixels with refresh()]]
<syntaxhighlight lang="c">
static calls=0;
() {
setcol(255,255,255);
if (numframes==0) {
cls(0);
calls = 0;
sierpinski(xres/2,yres*0.1,xres*.8,xres*.8);
}
moveto(0,0); printf("%g recursions", calls);
}
sierpinski(x,y,w,h) {
calls++;
triangle(x,y,w,h);
if(w < 10 || h < 10) return;
sleep(1); refresh();
halfH = h/2;
halfW = w/2;
sierpinski(x,y,halfW,halfH); // left
sierpinski(x+halfW/2,y+halfH,halfW,halfH);
sierpinski(x-halfW/2,y+halfH,halfW,halfH);
}
triangle(x,y,w,h) {
moveto(x,y);
lineto(x+w/2, y+h);
lineto(x-w/2, y+h);
lineto(x,y);
}</syntaxhighlight>
=={{header|Factor}}==
<syntaxhighlight lang="factor">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</syntaxhighlight>
{{out}}
[https://i.imgur.com/wjwCrvL.png]
=={{header|Forth}}==
{{works with|4tH v3.62}}
<syntaxhighlight lang="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</syntaxhighlight>
{{Out}}''Because Rosetta code doesn't allow file uploads, the output can't be shown.''
=={{header|FutureBasic}}==
<syntaxhighlight lang="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
</syntaxhighlight>
{{output}}
[[File:Sierpinski_triangle_in_FutureBasic.png]]
=={{header|Fōrmulæ}}==
{{FormulaeEntry|page=https://formulae.org/?script=examples/L-system}}
'''Solution'''
=== By L-system ===
There are generic functions written in Fōrmulæ to compute an L-system in the page [[L-system#Fōrmulæ | L-system]].
The script that creates a Sierpiński triangle is:
[[File:Fōrmulæ - L-system - Sierpiński triangle 01.png]]
[[File:Fōrmulæ - L-system - Sierpiński triangle 02.png]]
=== By chaos game ===
There is a function written in Fōrmulæ to generate fractals by chaos game in the page [[Chaos game#Fōrmulæ | chaos game]].
The script that creates a Sierpiński triangle is:
[[File:Fōrmulæ - Chaos game 05.png]]
[[File:Fōrmulæ - Chaos game 06.png]]
=== By Kronecker product ===
There is a function written in Fōrmulæ to create generic Kronecker product based fractal in the page [[Kronecker product based fractals#Fōrmulæ | Kronecker product based fractals]].
The script that creates a Sierpiński triangle is:
[[File:Fōrmulæ - Kronecker product based fractals 08.png]]
[[File:Fōrmulæ - Kronecker product based fractals 09.png]]
=== By elementary cellular automaton ===
There is a function written in Fōrmulæ to create images for the elementary cellular automaton in the page [[Elementary cellular automaton#Fōrmulæ | Elementary cellular automaton]].
All the rules 18, 22 , 23, 60, 82, 90, 102, 126, 129, 146, 153, 154, 161, 165, 167, 181, 182, 195, 210 and 218 produce Sierpiński triangles:
[[File:Fōrmulæ - Elementary cellular automaton - Sierpiński triangle 01.png]]
[[File:Fōrmulæ - Elementary cellular automaton - Sierpiński triangle 02.png]]
=={{header|gnuplot}}==
Generating X,Y coordinates by the ternary digits of parameter t.
<syntaxhighlight lang="gnuplot"># 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</syntaxhighlight>
=={{header|Go}}==
[[file:GoSierpinski.png|right|thumb|Output png]]
{{trans|Icon and Unicon}}
<
import (
Line 186 ⟶ 1,508:
fmt.Println(err)
}
}</
=={{header|Haskell}}==
Line 196 ⟶ 1,518:
[[File:Sierpinski-Haskell.svg|thumb|Sierpinski Triangle]]
<
import Diagrams.Backend.Cairo.CmdLine
Line 208 ⟶ 1,530:
main = defaultMain $ sierpinski !! 7
</syntaxhighlight>
=={{header|Icon}} and {{header|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-
[[File:Sierpinski_Triangle_Unicon.PNG|thumb|Sample Output for order=8]]
<
procedure main(A)
Line 229 ⟶ 1,551:
Event()
end</
{{libheader|Icon Programming Library}}
[http://www.cs.arizona.edu/icon/library/src/gprogs/sier1.icn Original source IPL Graphics/sier1.]
Line 235 ⟶ 1,557:
=={{header|J}}==
'''Solution:'''
<
'rgb'viewmat--. |. (~:_1&|.)^:(<@#) (2^8){.1</syntaxhighlight>
This looks almost exactly (except for OS specific decorations) like the [[:File:Sierpinski_Triangle_Unicon.PNG|task example image]]
Other approaches are possible
<syntaxhighlight lang="j">load'viewmat'
viewmat(,~,.~)^:4,1</syntaxhighlight> generates a [[j:File:Sier1.jpg|"smaller" image]] and is white on black instead of black on white.
Similarly, <syntaxhighlight lang="j">viewmat #:(~:/&.#:@, +:)^:(<32) 1</syntaxhighlight> presents the [[j:File:Sierpinksi.png|image]] in a different orientation.
And, of course, other approaches are [[j:File:Triangle.png|viable]].
=={{header|Java}}==
'''Solution:'''
<syntaxhighlight lang="java">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);
}
}</syntaxhighlight>
===Animated version===
{{works with|Java|8}}
<syntaxhighlight lang="java">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);
});
}
}</syntaxhighlight>
=={{header|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".
<br>
{{trans|PARI/GP}}
{{Works with|Chrome}}
[[File:SierpTRjs.png|200px|right|thumb|Output SierpTRjs.png]]
<syntaxhighlight lang="html">
<!-- 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>
</syntaxhighlight>
{{Output}}
<pre>
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.
</pre>
=={{header|jq}}==
{{works with|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.
<syntaxhighlight lang="jq">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)
| svg
</syntaxhighlight>
=={{header|Julia}}==
Produces a png graphic on a transparent background. The brushstroke used for fill might need to be modified for a white background.
<syntaxhighlight lang="julia">
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()
</syntaxhighlight>
=={{header|Kotlin}}==
'''From Java code:'''
<syntaxhighlight lang="scala">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)
}
}</syntaxhighlight>
=={{header|Logo}}==
This will draw a graphical Sierpinski gasket using turtle graphics.
<syntaxhighlight lang="logo">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</syntaxhighlight>
=={{header|Lua}}==
{{libheader|LÖVE}}
<syntaxhighlight lang="lua">-- 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</syntaxhighlight>
[[File:Love2D-Sierpinski.jpg]]
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">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]}]</syntaxhighlight>
Another faster version
<syntaxhighlight lang="mathematica">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]</syntaxhighlight>
[[File:MmaSierpinski.png]]
=={{header|MATLAB}}==
===Basic Version===
<syntaxhighlight lang="matlab">[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(:,:)')</syntaxhighlight>
{{out}}
Fail to upload output image, use the one of PostScript:
[[File:Sierpinski-PS.png]]
===Bit Operator Version===
<syntaxhighlight lang="matlab">t = 0 : 2^16 - 1;
plot(t, bitand(t, bitshift(t, -8)), 'k.')</syntaxhighlight>
=={{header|Nim}}==
{{trans|Julia}}
{{libheader|imageman}}
Our triangle is ref on a black background.
<syntaxhighlight lang="nim">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)</syntaxhighlight>
=={{header|Objeck}}==
<syntaxhighlight lang="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
}
</syntaxhighlight>
=={{header|OCaml}}==
<
let round v =
Line 340 ⟶ 2,123:
let res = loop 6 [ initial_triangle ] in
List.iter draw_triangle res;
ignore (read_key ())</
run with:
ocaml graphics.cma sierpinski.ml
=={{header|
{{Works with|PARI/GP|2.7.4 and above}}
[[File:SierpT9.png|right|thumb|Output SierpT9.png]]
<syntaxhighlight lang="parigp">
\\ 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
}
</syntaxhighlight>
{{Output}}
<pre>
> pSierpinskiT(9); \\ SierpT9.png
*** matrix(512x512) 19682 DOTS
</pre>
=={{header|Perl
{{trans|Raku}}
<syntaxhighlight lang="perl">my $levels = 6;
my $height = get_height($side);
sub get_height { my($side)
sub triangle
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
}
sub fractal
my
my $side = abs($x3 - $x2) / 2;
my $height = get_height($side);
$svg .= fractal( $
$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">
Line 419 ⟶ 2,196:
<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' )
fractal( $side/2, $height, $side*3/4, $height/2, $side/4, $height/2, $levels )
[https://github.com/SqrtNegInf/Rosettacode-Perl5-Smoke/blob/master/ref/sierpinski_triangle.svg See sierpinski_triangle] (offsite .svg image)
=={{header|Phix}}==
Can resize, and change the level from 1 to 12 (press +/-).
{{libheader|Phix/pGUI}}
<!--<syntaxhighlight lang="phix">-->
<span style="color: #000080;font-style:italic;">-- demo\rosetta\SierpinskyTriangle.exw</span>
<span style="color: #008080;">include</span> <span style="color: #000000;">pGUI</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #004080;">Ihandle</span> <span style="color: #000000;">dlg</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">canvas</span>
<span style="color: #004080;">cdCanvas</span> <span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cdcanvas</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">SierpinskyTriangle</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">level</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">w2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">w4</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">/</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">level</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">cdCanvasBegin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span><span style="color: #000000;">CD_CLOSED_LINES</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">cdCanvasVertex</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">cdCanvasVertex</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">w2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">+</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">cdCanvasVertex</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">w</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">cdCanvasEnd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">SierpinskyTriangle</span><span style="color: #0000FF;">(</span><span style="color: #000000;">level</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">w2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h2</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">SierpinskyTriangle</span><span style="color: #0000FF;">(</span><span style="color: #000000;">level</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">w4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">+</span><span style="color: #000000;">h2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">w2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h2</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">SierpinskyTriangle</span><span style="color: #0000FF;">(</span><span style="color: #000000;">level</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">w2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">w2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">level</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">7</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">redraw_cb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000080;font-style:italic;">/*ih*/</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000080;font-style:italic;">/*posx*/</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000080;font-style:italic;">/*posy*/</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">w</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupGetIntInt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"DRAWSIZE"</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">cdCanvasActivate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">cdCanvasClear</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">SierpinskyTriangle</span><span style="color: #0000FF;">(</span><span style="color: #000000;">level</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">*</span><span style="color: #000000;">0.05</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">*</span><span style="color: #000000;">0.05</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">*</span><span style="color: #000000;">0.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">*</span><span style="color: #000000;">0.9</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">cdCanvasFlush</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetStrAttribute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"TITLE"</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"Sierpinsky Triangle (level %d)"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">level</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">IUP_DEFAULT</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">map_cb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000000;">ih</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">cdcanvas</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">cdCreateCanvas</span><span style="color: #0000FF;">(</span><span style="color: #004600;">CD_IUP</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ih</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">cddbuffer</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">cdCreateCanvas</span><span style="color: #0000FF;">(</span><span style="color: #004600;">CD_DBUFFER</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cdcanvas</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">cdCanvasSetBackground</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span> <span style="color: #004600;">CD_WHITE</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">cdCanvasSetForeground</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">CD_GRAY</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">IUP_DEFAULT</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">esc_close</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000080;font-style:italic;">/*ih*/</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #004600;">K_ESC</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">IUP_CLOSE</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+-"</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">level</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">level</span><span style="color: #0000FF;">+</span><span style="color: #008000;">','</span><span style="color: #0000FF;">-</span><span style="color: #000000;">c</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">IupRedraw</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">IUP_CONTINUE</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">IupOpen</span><span style="color: #0000FF;">()</span>
<span style="color: #000000;">canvas</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupCanvas</span><span style="color: #0000FF;">(</span><span style="color: #004600;">NULL</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetAttribute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"RASTERSIZE"</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"640x640"</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetCallback</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"MAP_CB"</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">Icallback</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"map_cb"</span><span style="color: #0000FF;">))</span>
<span style="color: #7060A8;">IupSetCallback</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"ACTION"</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">Icallback</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"redraw_cb"</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">dlg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupDialog</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetAttribute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"TITLE"</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"Sierpinsky Triangle"</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetCallback</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"K_ANY"</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">Icallback</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"esc_close"</span><span style="color: #0000FF;">))</span>
<span style="color: #7060A8;">IupShow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetAttribute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"RASTERSIZE"</span><span style="color: #0000FF;">,</span> <span style="color: #004600;">NULL</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">IupMainLoop</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">IupClose</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<!--</syntaxhighlight>-->
=={{header|PicoLisp}}==
[[File:Pil_sierpinski.png|thumb|right]]
Slight modification of the [[Sierpinski_triangle#PicoLisp|text version]], requires ImageMagick's display:
<
(let (D '("1") S "0")
(do N
Line 445 ⟶ 2,300:
(prinl (length (car Img)) " " (length Img))
(mapc prinl Img) ) )
</syntaxhighlight>
=={{header|PostScript}}==
[[File:Sierpinski-PS.png|thumb|right]]
<syntaxhighlight lang="postscript">%!PS
/sierp { % level ax ay bx by cx cy
Line 478 ⟶ 2,334:
} bind def
6
showpage</
=={{header|Processing}}==
{{works with|Processing|3.5.4}}
Should work with most versions of Processing
Recursive Sierpinski triangles
===Pixel based===
<syntaxhighlight lang="processing">
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);
}
}
</syntaxhighlight>
===Animated===
<syntaxhighlight lang="processing">
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);
}
}
</syntaxhighlight>
===3D version===
<syntaxhighlight lang="processing">
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);
}
}
</syntaxhighlight>
=={{header|Prolog}}==
Line 491 ⟶ 2,499:
Works up to sierpinski(13).
<
sformat(A, 'Sierpinski order ~w', [N]),
new(D, picture(A)),
Line 520 ⟶ 2,528:
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===
<
sierpinski_iterate(N) :-
Line 562 ⟶ 2,570:
; Lst2 = [point(X2, Y1)|Lst1]),
assert(top(Lst2)).</
=={{header|Python}}==
{{libheader|Turtle}}
<syntaxhighlight lang="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)
</syntaxhighlight>
{{libheader|PyLab}}
[https://www.dropbox.com/s/gxnl8r8z0kbwi5v/Sierpinski_triangle_Phyton.png?dl=0 Sierpinski triangle image]
<syntaxhighlight lang="python">
# otra versión muy simple
from pylab import*
x=[[1,1],[1,0]]
for i in'123':x=kron(x,x)
imsave('a',x)
</syntaxhighlight>
{{libheader|NumPy}}
{{libheader|Turtle}}
[[File:SierpinskiTriangle-turtle.png|thumb|right]]
<syntaxhighlight lang="python">#!/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]
</syntaxhighlight>
<syntaxhighlight lang="python">##########################################################################################
# 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)
</syntaxhighlight>
=={{header|Quackery}}==
<syntaxhighlight lang="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</syntaxhighlight>
{{output}}
[[File:Quackery Sierpinski triangle.png|500px]]
=={{header|R}}==
Note: Find plotmat() here on RC [[User:AnatolV/Helper_Functions| R Helper Functions page]].
{{trans|PARI/GP}}
{{Works with|R|3.3.3 and above}}
[[File:SierpTRo6.png|200px|right|thumb|Output SierpTRo6.png]]
[[File:SierpTRo8.png|200px|right|thumb|Output SierpTRo8.png]]
<syntaxhighlight lang="r">
## 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);
</syntaxhighlight>
{{Output}}
<pre>
> 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
</pre>
=={{header|Racket}}==
[[File : RacketSierpinski.png|thumb|right]]
<syntaxhighlight lang="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))))))
</syntaxhighlight>
Test:
<syntaxhighlight lang="racket">
;; 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")
</syntaxhighlight>
=={{header|Raku}}==
(formerly Perl 6)
[[File:Sierpinski-perl6.svg|thumb]]
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.
<syntaxhighlight lang="raku" line>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>';</syntaxhighlight>
=={{header|Ring}}==
<syntaxhighlight lang="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() }
</syntaxhighlight>
Output:
[[File:CalmoSoftSierpinski.jpg]]
=={{header|Ruby}}==
{{libheader|Shoes}}
[[File : sierpinski.shoes.png|thumb|right]]
<
def triangle(slot, tri, color)
x, y, len = tri
Line 607 ⟶ 2,936:
end
end
end</
{{libheader|RubyGems}}
{{libheader|JRubyArt}}
JRubyArt is a port of processing to ruby
<syntaxhighlight lang="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
</syntaxhighlight>
=={{header|Rust}}==
Output is an SVG file.
<syntaxhighlight lang="rust">// [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();
}</syntaxhighlight>
{{out}}
[[Media:Sierpinski_triangle_rust.svg]]
=={{header|Seed7}}==
[[File : SierpinskiSeed7.png|thumb|right]]
<syntaxhighlight lang="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;</syntaxhighlight>
Original source: [http://seed7.sourceforge.net/algorith/graphic.htm#sierpinski]
=={{header|Sidef}}==
[[File:Sierpinski_triangle_sidef.png|200px|thumb|right]]
<syntaxhighlight lang="ruby">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)</syntaxhighlight>
=={{header|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.
{{libheader|Tk}}
<
package require Tk
Line 636 ⟶ 3,152:
pack [canvas .c -width 400 -height 400 -background white]
update; # So we can see progress
sierpinski .c {200 10 390 390 10 390} 7</
=={{header|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.
<syntaxhighlight lang="vb">
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
</syntaxhighlight>
=={{out}}==
[[File:Sierpinski triengle vbs.png]]
=={{header|Wren}}==
{{trans|Kotlin}}
{{libheader|DOME}}
<syntaxhighlight lang="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)
}
}
}</syntaxhighlight>
{{out}}
[[File:Wren-Sierpinski_triangle_Graphical.png|400px]]
=={{header|XPL0}}==
[[File:TriangXPL0.gif|right]]
<syntaxhighlight lang="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
]</syntaxhighlight>
=={{header|zkl}}==
[[File:SierpinskiTriangle.zkl.jpg|150px|thumb|right]]
Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl
{{trans|XPL0}}
<syntaxhighlight lang="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"));</syntaxhighlight>
{{omit from|ACL2}}
{{omit from|GUISS}}
[[Category:Geometry]]
| |||