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Tip revision: fbd7518a412b162a0b749f6df71b3105140ab253 authored by Georg Brandl on 09 March 2014, 08:37:14 UTC
Bump to 3.3.5 final.
Tip revision: fbd7518
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 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 = {}
    a = clock()
    tracer(0)
    fun(l, n)
    b = clock()
    draw(l, n, th)
    tracer(1)
    c = clock()
    print("Calculation:   %7.4f s" % (b - a))
    print("Drawing:  %7.4f s" % (c - b))
    print("Together: %7.4f s" % (c - a))
    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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