Drawing Sierpinski Pentagon with Chaos Game and Python Turtle (with Solution)

Draw the Sierpinski Pentagon with Chaos Game. Work on this Sierpinski Triangle with Chaos Game first if you haven’t done so already.

Hint: Try jump less than half way to the target.

Solution:

import turtle
import random
import math

screen = turtle.Screen()
screen.title('Sierpinski Pentagon with Chaos Game - PythonTurtle.Academy')
screen.setup(1000,1000)
screen.setworldcoordinates(-250,-250,250,250)
screen.tracer(0,0)
turtle.hideturtle()
turtle.speed(0)
turtle.up()

m=5
angle = math.pi/2
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('red')

n = 100000 # number of points to draw
p = V[0] # start from first vertex
t = turtle.Turtle()
t.up()
t.hideturtle()
for i in range(n):
    t.goto(p)
    t.dot(2,'orange')
    q = V[random.randrange(len(V))] # pick a random vertex
    p = ((q[0]+p[0])/2.6,(q[1]+p[1])/2.6) # 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()