This is a function I worked on with a student at the Vancouver Ladies Learning Code workshop in Vancouver on May 11th, 2013. I added the docstring, and cleaned up a few things, but most of the work was done by June Yakavonis.

draw_srpk_tri.py

import random as rn
from ipythonblocks import BlockGrid
 
def draw_srpk_tri(dim = 100, iterations = 1000, background_color = (255,255,255), triangle_color = (0,0,0) ,block_size = 3):
    '''
    Draws a Sierpinski triangle using the chaos game approach (http://en.wikipedia.org/wiki/Chaos_game)
    
    Parameters:
        dim -- integer, the dimensions of the square to draw the triangle in, default is 100
        iterations -- integer, the number of points to create the triangle with, the higher the value, the more resolution, default is 1000
        background_color -- tuple of integers, the RGB values of the background color of the square, default is black
        triangle_color -- tuple of integers, the RGB values of the triangle color of the square, default is white
        block_size -- integer, the number of pixels that make up a block, bigger is easier to see, but more coarse, default is 3
    
    Authors:
        June Yakavonis <jwyframed@gmail.com>
        Ted Hart <edmund.m.hart@gmail.com>
    '''
    srpnskgrid = BlockGrid(dim, dim, background_color, block_size = block_size, lines_on = 0)
    vertices = [[(dim - 1),0],[0,int(dim / 2)],[(dim - 1),(dim - 1)]]
    for i in vertices:
        srpnskgrid[i[0],i[1]].rgb = triangle_color
   
    point_x = rn.randint(0,dim)
    point_y = rn.randint(0,int(point_x * .5))
    i = 0
    points = []
 
    while i < iterations:
        r_vert = rn.randint(0,2)
        point_x = int((vertices[r_vert][0] + point_x) * 0.5)
        point_y = int((vertices[r_vert][1] + point_y) * 0.5)
        points.append([point_x,point_y])
        i += 1
   
    #stored as a list for the possibility of animating later.
    for x in points:
        srpnskgrid[x[0],x[1]].rgb = triangle_color
 
    return srpnskgrid