jpayne@68: #!/usr/bin/env python3
jpayne@68: """       xturtle-example-suite:
jpayne@68: 
jpayne@68:           xtx_kites_and_darts.py
jpayne@68: 
jpayne@68: Constructs two aperiodic penrose-tilings,
jpayne@68: consisting of kites and darts, by the method
jpayne@68: of inflation in six steps.
jpayne@68: 
jpayne@68: Starting points are the patterns "sun"
jpayne@68: consisting of five kites and "star"
jpayne@68: consisting of five darts.
jpayne@68: 
jpayne@68: For more information see:
jpayne@68:  http://en.wikipedia.org/wiki/Penrose_tiling
jpayne@68:  -------------------------------------------
jpayne@68: """
jpayne@68: from turtle import *
jpayne@68: from math import cos, pi
jpayne@68: from time import perf_counter as clock, sleep
jpayne@68: 
jpayne@68: f = (5**0.5-1)/2.0   # (sqrt(5)-1)/2 -- golden ratio
jpayne@68: d = 2 * cos(3*pi/10)
jpayne@68: 
jpayne@68: def kite(l):
jpayne@68:     fl = f * l
jpayne@68:     lt(36)
jpayne@68:     fd(l)
jpayne@68:     rt(108)
jpayne@68:     fd(fl)
jpayne@68:     rt(36)
jpayne@68:     fd(fl)
jpayne@68:     rt(108)
jpayne@68:     fd(l)
jpayne@68:     rt(144)
jpayne@68: 
jpayne@68: def dart(l):
jpayne@68:     fl = f * l
jpayne@68:     lt(36)
jpayne@68:     fd(l)
jpayne@68:     rt(144)
jpayne@68:     fd(fl)
jpayne@68:     lt(36)
jpayne@68:     fd(fl)
jpayne@68:     rt(144)
jpayne@68:     fd(l)
jpayne@68:     rt(144)
jpayne@68: 
jpayne@68: def inflatekite(l, n):
jpayne@68:     if n == 0:
jpayne@68:         px, py = pos()
jpayne@68:         h, x, y = int(heading()), round(px,3), round(py,3)
jpayne@68:         tiledict[(h,x,y)] = True
jpayne@68:         return
jpayne@68:     fl = f * l
jpayne@68:     lt(36)
jpayne@68:     inflatedart(fl, n-1)
jpayne@68:     fd(l)
jpayne@68:     rt(144)
jpayne@68:     inflatekite(fl, n-1)
jpayne@68:     lt(18)
jpayne@68:     fd(l*d)
jpayne@68:     rt(162)
jpayne@68:     inflatekite(fl, n-1)
jpayne@68:     lt(36)
jpayne@68:     fd(l)
jpayne@68:     rt(180)
jpayne@68:     inflatedart(fl, n-1)
jpayne@68:     lt(36)
jpayne@68: 
jpayne@68: def inflatedart(l, n):
jpayne@68:     if n == 0:
jpayne@68:         px, py = pos()
jpayne@68:         h, x, y = int(heading()), round(px,3), round(py,3)
jpayne@68:         tiledict[(h,x,y)] = False
jpayne@68:         return
jpayne@68:     fl = f * l
jpayne@68:     inflatekite(fl, n-1)
jpayne@68:     lt(36)
jpayne@68:     fd(l)
jpayne@68:     rt(180)
jpayne@68:     inflatedart(fl, n-1)
jpayne@68:     lt(54)
jpayne@68:     fd(l*d)
jpayne@68:     rt(126)
jpayne@68:     inflatedart(fl, n-1)
jpayne@68:     fd(l)
jpayne@68:     rt(144)
jpayne@68: 
jpayne@68: def draw(l, n, th=2):
jpayne@68:     clear()
jpayne@68:     l = l * f**n
jpayne@68:     shapesize(l/100.0, l/100.0, th)
jpayne@68:     for k in tiledict:
jpayne@68:         h, x, y = k
jpayne@68:         setpos(x, y)
jpayne@68:         setheading(h)
jpayne@68:         if tiledict[k]:
jpayne@68:             shape("kite")
jpayne@68:             color("black", (0, 0.75, 0))
jpayne@68:         else:
jpayne@68:             shape("dart")
jpayne@68:             color("black", (0.75, 0, 0))
jpayne@68:         stamp()
jpayne@68: 
jpayne@68: def sun(l, n):
jpayne@68:     for i in range(5):
jpayne@68:         inflatekite(l, n)
jpayne@68:         lt(72)
jpayne@68: 
jpayne@68: def star(l,n):
jpayne@68:     for i in range(5):
jpayne@68:         inflatedart(l, n)
jpayne@68:         lt(72)
jpayne@68: 
jpayne@68: def makeshapes():
jpayne@68:     tracer(0)
jpayne@68:     begin_poly()
jpayne@68:     kite(100)
jpayne@68:     end_poly()
jpayne@68:     register_shape("kite", get_poly())
jpayne@68:     begin_poly()
jpayne@68:     dart(100)
jpayne@68:     end_poly()
jpayne@68:     register_shape("dart", get_poly())
jpayne@68:     tracer(1)
jpayne@68: 
jpayne@68: def start():
jpayne@68:     reset()
jpayne@68:     ht()
jpayne@68:     pu()
jpayne@68:     makeshapes()
jpayne@68:     resizemode("user")
jpayne@68: 
jpayne@68: def test(l=200, n=4, fun=sun, startpos=(0,0), th=2):
jpayne@68:     global tiledict
jpayne@68:     goto(startpos)
jpayne@68:     setheading(0)
jpayne@68:     tiledict = {}
jpayne@68:     tracer(0)
jpayne@68:     fun(l, n)
jpayne@68:     draw(l, n, th)
jpayne@68:     tracer(1)
jpayne@68:     nk = len([x for x in tiledict if tiledict[x]])
jpayne@68:     nd = len([x for x in tiledict if not tiledict[x]])
jpayne@68:     print("%d kites and %d darts = %d pieces." % (nk, nd, nk+nd))
jpayne@68: 
jpayne@68: def demo(fun=sun):
jpayne@68:     start()
jpayne@68:     for i in range(8):
jpayne@68:         a = clock()
jpayne@68:         test(300, i, fun)
jpayne@68:         b = clock()
jpayne@68:         t = b - a
jpayne@68:         if t < 2:
jpayne@68:             sleep(2 - t)
jpayne@68: 
jpayne@68: def main():
jpayne@68:     #title("Penrose-tiling with kites and darts.")
jpayne@68:     mode("logo")
jpayne@68:     bgcolor(0.3, 0.3, 0)
jpayne@68:     demo(sun)
jpayne@68:     sleep(2)
jpayne@68:     demo(star)
jpayne@68:     pencolor("black")
jpayne@68:     goto(0,-200)
jpayne@68:     pencolor(0.7,0.7,1)
jpayne@68:     write("Please wait...",
jpayne@68:           align="center", font=('Arial Black', 36, 'bold'))
jpayne@68:     test(600, 8, startpos=(70, 117))
jpayne@68:     return "Done"
jpayne@68: 
jpayne@68: if __name__ == "__main__":
jpayne@68:     msg = main()
jpayne@68:     mainloop()