sierpinski.py

import math
import turtle
from random import randint

def draw_list(turtle, coords, color):
  for coord in coords:
    draw_circle(turtle, color, 3, coord[0], coord[1])

def draw_circle(turtle, color, size, x, y):
  turtle.penup()
  turtle.color(color)
  turtle.fillcolor(color)
  turtle.goto(x,y)
  turtle.begin_fill()
  turtle.pendown()
  turtle.circle(size)
  turtle.penup()
  turtle.end_fill()
  turtle.pendown()

# random starting point in an Isosceles Triangle
def get_st_point(t):
  while True:
    p = [randint(t[2][0], t[1][0]), randint(t[1][1],t[0][1])]
    yn = t[0][1] - p[1]
    h = t[0][1] - t[1][1]
    if (abs(p[0]) / abs(yn)) < (abs(t[1][0]) / h):
      return p

tommy = turtle.Turtle()
tommy.speed('fastest')
i = 0
iteration = 1000
t = [[0, 150], [150,-100], [-150,-100]] # triangle

# black point to the corners
draw_list(tommy, t, "black")

# find a random starting point
st = get_st_point(t)
draw_circle(tommy, "red", 0.5, st[0], st[1])

lp = st # last point
while True:
  c = randint(0, 2) # random corner
  np = [(t[c][0] + lp[0])/2, (t[c][1] + lp[1])/2]
  draw_circle(tommy, "green", 0.5, np[0], np[1])
  lp = np
  if i > iteration:
    break
  i += 1