Chaos Game – Sierpinski Triangle with Python Turtle (with Solution)

Draw three points to form a triangle. Draw the fourth point in a random position. In each of the following step, this point will move halfway towards one of the three randomly chosen points of the original triangle. Repeat the above step 1000, 10,000, and 100,000 times. You will see a Sierpinski Triangle! This process is an example of Chaos Game.

Solution:

import turtle
import random

screen = turtle.Screen()
screen.title('Triangle Chaos Game with Python Turtle')
screen.setup(1000,1000)
screen.tracer(0,0)
turtle.hideturtle()
turtle.speed(0)
turtle.up()

A = (0,350)
B = (-300,-200)
C = (300,-200)
V = (A,B,C) # list of three vertices
for v in V:
    turtle.goto(v)
    turtle.dot('red')

n = 10000 # number of points to draw
p = (random.uniform(-200,200),random.uniform(-200,200)) # random starting point
t = turtle.Turtle()
t.up()
t.hideturtle()
for i in range(n):
    t.goto(p)
    t.dot(2,'blue')
    r = random.randrange(len(V)) # pick a random vertex
    p = ((V[r][0]+p[0])/2,(V[r][1]+p[1])/2) # go to mid point between the random vertex and point   
    if i % 1000 == 0: # update for every 1000 moves, this part is for performance reason only
        t = turtle.Turtle() # use new turutle
        t.up()
        t.hideturtle()
        screen.update()