IFS.coco

from math import sqrt
from random import random, choice

data point(x=0, y=0):
    def __add__(self, other):
        return point(self.x + other.x, self.y + other.y)

    def __rmul__(self, other):
        return point(self.x * other, self.y * other)

def chaos_game(n, shape_points):
    p = point(random(), random())

    for _ in range(n):
        p = (1/2) * (p + choice(shape_points))
        yield p


# This will generate a Sierpinski triangle with a chaos game of n points for an
# initial triangle with three points on the vertices of an equilateral triangle:
#     A = (0.0, 0.0)
#     B = (0.5, sqrt(0.75))
#     C = (1.0, 0.0)
# It will output the file sierpinski.dat, which can be plotted after
shape_points = [point(0.0, 0.0),
                point(0.5, sqrt(0.75)),
                point(1.0, 0.0)]
with open("sierpinski.dat", "w") as f:
    for p in chaos_game(10000, shape_points):
        f.write("{0}\t{1}\n".format(p.x, p.y))