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| #!/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() | |