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176 lines
3.3 KiB
176 lines
3.3 KiB
#!/usr/bin/env python3
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""" xturtle-example-suite:
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xtx_kites_and_darts.py
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Constructs two aperiodic penrose-tilings,
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consisting of kites and darts, by the method
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of inflation in six steps.
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Starting points are the patterns "sun"
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consisting of five kites and "star"
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consisting of five darts.
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For more information see:
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http://en.wikipedia.org/wiki/Penrose_tiling
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-------------------------------------------
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"""
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from turtle import *
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from math import cos, pi
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from time import perf_counter as clock, sleep
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f = (5**0.5-1)/2.0 # (sqrt(5)-1)/2 -- golden ratio
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d = 2 * cos(3*pi/10)
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def kite(l):
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fl = f * l
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lt(36)
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fd(l)
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rt(108)
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fd(fl)
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rt(36)
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fd(fl)
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rt(108)
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fd(l)
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rt(144)
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def dart(l):
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fl = f * l
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lt(36)
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fd(l)
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rt(144)
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fd(fl)
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lt(36)
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fd(fl)
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rt(144)
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fd(l)
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rt(144)
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def inflatekite(l, n):
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if n == 0:
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px, py = pos()
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h, x, y = int(heading()), round(px,3), round(py,3)
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tiledict[(h,x,y)] = True
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return
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fl = f * l
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lt(36)
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inflatedart(fl, n-1)
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fd(l)
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rt(144)
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inflatekite(fl, n-1)
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lt(18)
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fd(l*d)
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rt(162)
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inflatekite(fl, n-1)
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lt(36)
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fd(l)
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rt(180)
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inflatedart(fl, n-1)
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lt(36)
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def inflatedart(l, n):
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if n == 0:
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px, py = pos()
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h, x, y = int(heading()), round(px,3), round(py,3)
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tiledict[(h,x,y)] = False
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return
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fl = f * l
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inflatekite(fl, n-1)
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lt(36)
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fd(l)
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rt(180)
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inflatedart(fl, n-1)
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lt(54)
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fd(l*d)
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rt(126)
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inflatedart(fl, n-1)
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fd(l)
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rt(144)
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def draw(l, n, th=2):
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clear()
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l = l * f**n
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shapesize(l/100.0, l/100.0, th)
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for k in tiledict:
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h, x, y = k
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setpos(x, y)
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setheading(h)
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if tiledict[k]:
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shape("kite")
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color("black", (0, 0.75, 0))
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else:
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shape("dart")
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color("black", (0.75, 0, 0))
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stamp()
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def sun(l, n):
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for i in range(5):
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inflatekite(l, n)
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lt(72)
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def star(l,n):
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for i in range(5):
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inflatedart(l, n)
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lt(72)
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def makeshapes():
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tracer(0)
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begin_poly()
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kite(100)
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end_poly()
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register_shape("kite", get_poly())
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begin_poly()
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dart(100)
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end_poly()
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register_shape("dart", get_poly())
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tracer(1)
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def start():
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reset()
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ht()
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pu()
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makeshapes()
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resizemode("user")
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def test(l=200, n=4, fun=sun, startpos=(0,0), th=2):
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global tiledict
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goto(startpos)
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setheading(0)
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tiledict = {}
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tracer(0)
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fun(l, n)
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draw(l, n, th)
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tracer(1)
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nk = len([x for x in tiledict if tiledict[x]])
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nd = len([x for x in tiledict if not tiledict[x]])
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print("%d kites and %d darts = %d pieces." % (nk, nd, nk+nd))
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def demo(fun=sun):
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start()
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for i in range(8):
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a = clock()
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test(300, i, fun)
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b = clock()
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t = b - a
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if t < 2:
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sleep(2 - t)
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def main():
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#title("Penrose-tiling with kites and darts.")
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mode("logo")
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bgcolor(0.3, 0.3, 0)
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demo(sun)
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sleep(2)
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demo(star)
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pencolor("black")
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goto(0,-200)
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pencolor(0.7,0.7,1)
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write("Please wait...",
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align="center", font=('Arial Black', 36, 'bold'))
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test(600, 8, startpos=(70, 117))
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return "Done"
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if __name__ == "__main__":
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msg = main()
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mainloop()
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