#!/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()