A program that explores the Koch snowflake and the Thule-Morse sequence.

koch.py

"""
koch.py

Description:

A program that explores the Koch snowflake and the Thue-Morse sequence.

Author: Mahesh Venkitachalam
Website: electronut.in
"""

import time
import turtle
import math
import sys, argparse

# generate the Thue-Morse sequence
def genThueMorse():
    # initialize
    tms = '0'
    curr = 0
    while True:
        # generate next sequence
        if curr == len(tms):
            tmp = ''
            for i in range(len(tms)):
                if tms[i] is '0':
                    tmp += '1'
                else:
                    tmp += '0'
            tms += tmp
        yield tms[curr]
        curr +=1

# turtle graphics using Thue-Morse sequence
def drawTM(x, y):
    t = turtle.Turtle()
    t.hideturtle()
    t.up()
    t.setpos(x, y)
    t.down()
    tms = genThueMorse()
    delta = 4
    while True:
        a = next(tms)
        if a is '0':
            t.fd(delta)
        else:
            t.left(60)

# recursive koch snow flake
def kochSF(x1, y1, x2, y2, t):
    d = math.sqrt((x1-x2)*(x1-x2) + (y1-y2)*(y1-y2))
    r = d/3.0
    h = r*math.sqrt(3)/2.0
    p3 = ((x1 + 2*x2)/3.0, (y1 + 2*y2)/3.0)
    p1 = ((2*x1 + x2)/3.0, (2*y1 + y2)/3.0)
    c = (0.5*(x1+x2), 0.5*(y1+y2))
    n = ((y1-y2)/d, (x2-x1)/d)
    p2 = (c[0]+h*n[0], c[1]+h*n[1])     
    if d > 10:
        # flake #1
        kochSF(x1, y1, p1[0], p1[1], t)
        # flake #2
        kochSF(p1[0], p1[1], p2[0], p2[1], t)
        # flake #3
        kochSF(p2[0], p2[1], p3[0], p3[1], t)
        # flake #4
        kochSF(p3[0], p3[1], x2, y2, t)
    else:
        # draw cone
        t.up()
        t.setpos(p1[0], p1[1])
        t.down()
        t.setpos(p2[0], p2[1])
        t.setpos(p3[0], p3[1])
        # draw sides
        t.up()
        t.setpos(x1, y1)
        t.down()
        t.setpos(p1[0], p1[1])
        t.up()
        t.setpos(p3[0], p3[1])
        t.down()
        t.setpos(x2, y2) 

# draw a koch snowflake
def drawKochSF(x1, y1, x2, y2):
    t = turtle.Turtle()
    t.hideturtle()
    kochSF(x1, y1, x2, y2, t)

# main() function
def main():
    print('Exploring the Koch Snowflake...')

    parser = argparse.ArgumentParser(description="Koch Snowflake")
    # add arguments
    parser.add_argument('--thue', action='store_true', required=False)
    args = parser.parse_args()

    if args.thue:
        drawTM(200, 200)
    else:
        drawKochSF(-100, 0, 100, 0)
        drawKochSF(0, -173.2, -100, 0)
        drawKochSF(100, 0, 0, -173.2)
        win = turtle.Screen()
        win.exitonclick()

# call main
if __name__ == '__main__':
    main()

I just completed your Spirograph chapter in 'Python Playground' and loved that exercise. Thank you for this wonderful addition. I'm still new to all this and recursion in particular still stumps me, but this is a lovely turtle draw script.
-Cory