Demo/turtle/tdemo_penrose.py

   1 #!/usr/bin/env python
   2 """       xturtle-example-suite:
   3
   4           xtx_kites_and_darts.py
   5
   6 Constructs two aperiodic penrose-tilings,
   7 consisting of kites and darts, by the method
   8 of inflation in six steps.
   9
  10 Starting points are the patterns "sun"
  11 consisting of five kites and "star"
  12 consisting of five darts.
  13
  14 For more information see:
  15  http://en.wikipedia.org/wiki/Penrose_tiling
  16  -------------------------------------------
  17 """
  18 from turtle import *
  19 from math import cos, pi
  20 from time import clock, sleep
  21
  22 f = (5**0.5-1)/2.0   # (sqrt(5)-1)/2 -- golden ratio
  23 d = 2 * cos(3*pi/10)
  24
  25 def kite(l):
  26     fl = f * l
  27     lt(36)
  28     fd(l)
  29     rt(108)
  30     fd(fl)
  31     rt(36)
  32     fd(fl)
  33     rt(108)
  34     fd(l)
  35     rt(144)
  36
  37 def dart(l):
  38     fl = f * l
  39     lt(36)
  40     fd(l)
  41     rt(144)
  42     fd(fl)
  43     lt(36)
  44     fd(fl)
  45     rt(144)
  46     fd(l)
  47     rt(144)
  48
  49 def inflatekite(l, n):
  50     if n == 0:
  51         px, py = pos()
  52         h, x, y = int(heading()), round(px,3), round(py,3)
  53         tiledict[(h,x,y)] = True
  54         return
  55     fl = f * l
  56     lt(36)
  57     inflatedart(fl, n-1)
  58     fd(l)
  59     rt(144)
  60     inflatekite(fl, n-1)
  61     lt(18)
  62     fd(l*d)
  63     rt(162)
  64     inflatekite(fl, n-1)
  65     lt(36)
  66     fd(l)
  67     rt(180)
  68     inflatedart(fl, n-1)
  69     lt(36)
  70
  71 def inflatedart(l, n):
  72     if n == 0:
  73         px, py = pos()
  74         h, x, y = int(heading()), round(px,3), round(py,3)
  75         tiledict[(h,x,y)] = False
  76         return
  77     fl = f * l
  78     inflatekite(fl, n-1)
  79     lt(36)
  80     fd(l)
  81     rt(180)
  82     inflatedart(fl, n-1)
  83     lt(54)
  84     fd(l*d)
  85     rt(126)
  86     inflatedart(fl, n-1)
  87     fd(l)
  88     rt(144)
  89
  90 def draw(l, n, th=2):
  91     clear()
  92     l = l * f**n
  93     shapesize(l/100.0, l/100.0, th)
  94     for k in tiledict:
  95         h, x, y = k
  96         setpos(x, y)
  97         setheading(h)
  98         if tiledict[k]:
  99             shape("kite")
 100             color("black", (0, 0.75, 0))
 101         else:
 102             shape("dart")
 103             color("black", (0.75, 0, 0))
 104         stamp()
 105
 106 def sun(l, n):
 107     for i in range(5):
 108         inflatekite(l, n)
 109         lt(72)
 110
 111 def star(l,n):
 112     for i in range(5):
 113         inflatedart(l, n)
 114         lt(72)
 115
 116 def makeshapes():
 117     tracer(0)
 118     begin_poly()
 119     kite(100)
 120     end_poly()
 121     register_shape("kite", get_poly())
 122     begin_poly()
 123     dart(100)
 124     end_poly()
 125     register_shape("dart", get_poly())
 126     tracer(1)
 127
 128 def start():
 129     reset()
 130     ht()
 131     pu()
 132     makeshapes()
 133     resizemode("user")
 134
 135 def test(l=200, n=4, fun=sun, startpos=(0,0), th=2):
 136     global tiledict
 137     goto(startpos)
 138     setheading(0)
 139     tiledict = {}
 140     a = clock()
 141     tracer(0)
 142     fun(l, n)
 143     b = clock()
 144     draw(l, n, th)
 145     tracer(1)
 146     c = clock()
 147     print "Calculation:   %7.4f s" % (b - a)
 148     print "Drawing:  %7.4f s" % (c - b)
 149     print "Together: %7.4f s" % (c - a)
 150     nk = len([x for x in tiledict if tiledict[x]])
 151     nd = len([x for x in tiledict if not tiledict[x]])
 152     print "%d kites and %d darts = %d pieces." % (nk, nd, nk+nd)
 153
 154 def demo(fun=sun):
 155     start()
 156     for i in range(8):
 157         a = clock()
 158         test(300, i, fun)
 159         b = clock()
 160         t = b - a
 161         if t < 2:
 162             sleep(2 - t)
 163
 164 def main():
 165     #title("Penrose-tiling with kites and darts.")
 166     mode("logo")
 167     bgcolor(0.3, 0.3, 0)
 168     demo(sun)
 169     sleep(2)
 170     demo(star)
 171     pencolor("black")
 172     goto(0,-200)
 173     pencolor(0.7,0.7,1)
 174     write("Please wait...",
 175           align="center", font=('Arial Black', 36, 'bold'))
 176     test(600, 8, startpos=(70, 117))
 177     return "Done"
 178
 179 if __name__ == "__main__":
 180     msg = main()
 181     mainloop()