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