Let’s do a Koch snowflake

Good friend Dimitris, after reading my previous post pointed me to Koch snowflakes. How cool is a line of infinite length that covers a finite surface! A Koch snowflake turns out to be easily constructed with turtle as suggested by the Wikipedia article. Well, you also get to learn about Thue-Morse sequences and evil numbers in the process. To be honest, this is also a good toy case, using a real sequence, to learn how to use yield.

import turtle
import functools

# Compute the next digit of the Thue-Morse sequence
# https://oeis.org/A010060
# Learn about evil and oddium numbers in the process.

def thue_morse_seq(n=0):
  while True:
    yield functools.reduce(lambda x, y: x + y, map(int, bin(n)[2:])) % 2
    n += 1

if __name__ == "__main__":

  window = turtle.Screen()
  window.bgcolor('light gray')

  pen = turtle.Turtle()
  pen.speed(20)
  pen.color('dark blue')
  pen.pensize(1)
  pen.shape('classic')
  pen.penup()
  pen.setpos(0, 0)
  pen.pendown()

  n = thue_morse_seq(0)
  while True:
    if next(n) == 0:
      pen.forward(2)
    else:
      pen.left(60)

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