Drawing Sierpinski Carpet with Chaos Game (with Solution)

You can draw a Sierpinski Carpet with Chaos Game too. Read the first Chaos Game project first to understand what Chaos Game is.

In this project, you start with a square. The moving point will toward a randomly chosen corner of the square as well as the center of the four edges of the square. Therefore, there are total eight points that the moving point will move toward. In addition, it will only 1/3 of the way towards the target.

Solution:

import turtle
import random
import math

screen = turtle.Screen()
screen.title('Sierpinski Carpet with Chaos Game - PythonTurtle.Academy')
screen.setup(1000,1000)
screen.setworldcoordinates(-200,-200,200,200)
screen.tracer(0,0)
turtle.hideturtle()
turtle.speed(0)
turtle.up()

m=4
angle = math.pi/4
V = []
for i in range(m):
    p = (400*math.cos(angle),400*math.sin(angle))
    V.append(p)
    angle += math.pi*2/m

for v in V:
    turtle.goto(v)
    turtle.dot('blue')

n = 100000 # number of points to draw
p = V[0] # start from the first vertex
t = turtle.Turtle()
t.up()
t.hideturtle()
for i in range(n):
    t.goto(p)
    t.dot(2,'red')
    r = random.randrange(len(V)) # pick a random vertex
    if random.randint(0,1) == 0: # randomly decide to use edge or vertex
        q = V[r] # vertex
    else:
        q = ((V[r][0]+V[(r+1)%len(V)][0])/2,(V[r][1]+V[(r+1)%len(V)][1])/2) # go to mid point between two vertices   
    p = ((q[0]+p[0])/3,(q[1]+p[1])/3) # go 1/3 towards target   
    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()