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Revision b484871ba707ae2f9898e22effcd297c19d4c5ea authored by Łukasz Langa on 09 June 2020, 18:52:10 UTC, committed by Łukasz Langa on 09 June 2020, 18:52:10 UTC
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Tip revision: b484871ba707ae2f9898e22effcd297c19d4c5ea authored by Łukasz Langa on 09 June 2020, 18:52:10 UTC
Python 3.9.0b3
Tip revision: b484871
penrose.py
#!/usr/bin/env python3
"""       xturtle-example-suite:

          xtx_kites_and_darts.py

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

Starting points are the patterns "sun"
consisting of five kites and "star"
consisting of five darts.

For more information see:
 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)
    fd(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)
    inflatedart(fl, n-1)
    fd(l)
    rt(144)
    inflatekite(fl, n-1)
    lt(18)
    fd(l*d)
    rt(162)
    inflatekite(fl, n-1)
    lt(36)
    fd(l)
    rt(180)
    inflatedart(fl, n-1)
    lt(36)

def inflatedart(l, n):
    if n == 0:
        px, py = pos()
        h, x, y = int(heading()), round(px,3), round(py,3)
        tiledict[(h,x,y)] = False
        return
    fl = f * l
    inflatekite(fl, n-1)
    lt(36)
    fd(l)
    rt(180)
    inflatedart(fl, n-1)
    lt(54)
    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 star(l,n):
    for i in range(5):
        inflatedart(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 for x in tiledict if not tiledict[x]])
    print("%d kites 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...",
          align="center", font=('Arial Black', 36, 'bold'))
    test(600, 8, startpos=(70, 117))
    return "Done"

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