Intermediate_Python/penrose.py at master · orionsring/Intermediate_Python · GitHub

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#!usr/bin/env python3
"""    xturtle-example-suite:
    xtx_kites_and_darts.py

Purpose:
    constructs two aperiodic penrose-tilings,
    consisting of kites and darts, by the method
    of inflation in six steps.

Definitions:
    starting points are the patters "sun"
    consisting of five kites and "star"
    consisting of five darts.

Reference:
    http://en.wikipedia.org/wiki/penrose_tiling
    -------------------------------------------
"""

from turtle import *
from math import cos, pi
from time import perf_counter as clock, sleep

f = (5**0.5-1)/2.0    # (sqrt(5)/-1)/2 -- golden ratio
d = 2 * cos(3*pi/10)

def kite(l):
    fl = f * l
    lt(36)
    fd(l)
    rt(108)
    fd(fl)
    rt(36)
    fd(fl)
    rt(108)
    fd(l)
    rt(144)

def dart(l):
    fl = f * l
    lt(36)
    fd(l)
    rt(144)
    rd(fl)
    lt(36)
    fd(fl)
    rt(144)
    fd(l)
    rt(144)

def inflatekite(l, n):
    if n == 0:
        px, py = pos()
        h, x, y = int(heading()), round(px,3), round(py,3)
        tiledict[(h,x,y)] = True
        return
    fl = f * l
    lt(36)
    inflateddart(fl, n-1)
    fd(l)
    rt(144)
    inflatekite(fl, n-1)
    lt(18)
    fd(l*d)
    rt(126)
    inflatedart(fl, n-1)
    fd(l)
    rt(144)

def draw(l, n, th=2):
    clear()
    l = l * f**n
    shapesize(l/100.0, l/100.0, th)
    for k in tiledict:
        h, x, y = k
        setpos(x, y)
        setheading(h)
        if tiledict[k]:
            shape("kite")
            color("black", (0, 0.75, 0))
        else:
            shape("dart")
            color("black", (0.75, 0, 0))
        stamp()

def sun(l, n):
    for i in range(5):
        inflatekite(l, n)
        lt(72)

def makeshapes():
    tracer(0)
    begin_poly()
    kite(100)
    end_poly()
    register_shape("kite", get_poly())
    begin_poly()
    dart(100)
    end_poly()
    register_shape("dart", get_poly())
    tracer(1)

def start():
    reset()
    ht()
    pu()
    makeshapes()
    resizemode("user")

def test(l=200, n=4, fun=sun, startpos(0,0), th=2):
    global tiledict
    goto(startpos)
    setheading(0)
    tiledict = {}
    tracer(0)
    fun(l, n)
    draw(l, n, th)
    tracer(1)
    nk = len([x for x in tiledict if tiledict[x]])
    nd = len([x in x in tiledict if not tiledic[x]])
    print("%d kite and %d darts = %d pieces." % (nk, nd, nk+nd))

def demo(fun=sun):
    start()
    for i in range(8):
        a = clock()
        test(300, i, fun)
        b = clock()
        t = b - a
        if t < 2:
            sleep(2-t)

def main():
    #title("penrose-tiling with kites and darts.")
    mode("logo")
    bgcolor(0.3, 0.3, 0)
    demo(sun)
    sleep(2)
    demo(star)
    pencolor("black")
    goto(0, -200)
    pencolor(0.7, 0.7, 1)
    write("Please wait...",
        alaign="center", font=('Arial Black', 36, 'bold'))
    test(600, 8, startpos=(70, 117))
    return "Done"

if __name__ == "__main__"
    msg = main()
    mainloop()