import random

from OpenGL.GL import *

from OpenGL.GLUT import *

from OpenGL.GLU import *

"""

Sierpinski's triangle.

Sierpinski's triangle∞ is an image which has always fascinated me. The technique

used here is the so called Chaos game∞ here we generate a constellation of points

which ends up being Sierpinski's triangle. The algorithm is as follows:

Pick three points which form the outer boundaries of the triangle

Pick a midpoint of one of the lines which make up an edge

Until we're happy with the amount of detail a new dot is formed by the midpoint of

the current midpoint and one of the three points of the triangle

http://en.wikipedia.org/wiki/Sierpinski_triangle

http://en.wikipedia.org/wiki/Chaos_game

"""

def initFun():

glClearColor(1.0, 1.0, 1.0, 0.0)

glColor3f(0.0, 0.0, 0.0)

glPointSize(1.0)

glMatrixMode(GL_PROJECTION)

glLoadIdentity()

gluOrtho2D(0.0, 640.0, 0.0, 480.0)

def displayFun():

glClear(GL_COLOR_BUFFER_BIT)

glBegin(GL_POINTS)

x = [0.0, 640.0, 320.0]

y = [0.0, 0.0, 480.0]

curx = 0

cury = 320

glVertex2f(curx, cury)

for i in range(0, 500000):

idx = random.randint(0, 2)

curx = (curx + x[idx]) / 2.0

cury = (cury + y[idx]) / 2.0

glVertex2f(curx, cury)

glEnd()

glFlush()

if __name__ == "__main__":

# This is the current implementation, note that all points are recalculated on

# a window update, for any other purpose than showing off with how simply it is

# to create this eyecode you'd probably want to precalculate the dots and put them

# in a display list.

glutInit()

glutInitWindowSize(640, 480)

glutCreateWindow(b"Sierpinski")

glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB)

glutDisplayFunc(displayFun)

initFun()

glutMainLoop()