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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 |
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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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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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