| 1 | n/a | #!/usr/bin/env python3 |
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| 2 | n/a | """ xturtle-example-suite: |
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| 3 | n/a | |
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| 4 | n/a | xtx_kites_and_darts.py |
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| 5 | n/a | |
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| 6 | n/a | Constructs two aperiodic penrose-tilings, |
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| 7 | n/a | consisting of kites and darts, by the method |
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| 8 | n/a | of inflation in six steps. |
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| 9 | n/a | |
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| 10 | n/a | Starting points are the patterns "sun" |
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| 11 | n/a | consisting of five kites and "star" |
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| 12 | n/a | consisting of five darts. |
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| 13 | n/a | |
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| 14 | n/a | For more information see: |
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| 15 | n/a | http://en.wikipedia.org/wiki/Penrose_tiling |
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| 16 | n/a | ------------------------------------------- |
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| 17 | n/a | """ |
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| 18 | n/a | from turtle import * |
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| 19 | n/a | from math import cos, pi |
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| 20 | n/a | from time import clock, sleep |
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| 21 | n/a | |
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| 22 | n/a | f = (5**0.5-1)/2.0 # (sqrt(5)-1)/2 -- golden ratio |
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| 23 | n/a | d = 2 * cos(3*pi/10) |
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| 24 | n/a | |
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| 25 | n/a | def kite(l): |
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| 26 | n/a | fl = f * l |
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| 27 | n/a | lt(36) |
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| 28 | n/a | fd(l) |
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| 29 | n/a | rt(108) |
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| 30 | n/a | fd(fl) |
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| 31 | n/a | rt(36) |
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| 32 | n/a | fd(fl) |
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| 33 | n/a | rt(108) |
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| 34 | n/a | fd(l) |
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| 35 | n/a | rt(144) |
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| 36 | n/a | |
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| 37 | n/a | def dart(l): |
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| 38 | n/a | fl = f * l |
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| 39 | n/a | lt(36) |
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| 40 | n/a | fd(l) |
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| 41 | n/a | rt(144) |
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| 42 | n/a | fd(fl) |
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| 43 | n/a | lt(36) |
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| 44 | n/a | fd(fl) |
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| 45 | n/a | rt(144) |
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| 46 | n/a | fd(l) |
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| 47 | n/a | rt(144) |
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| 48 | n/a | |
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| 49 | n/a | def inflatekite(l, n): |
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| 50 | n/a | if n == 0: |
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| 51 | n/a | px, py = pos() |
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| 52 | n/a | h, x, y = int(heading()), round(px,3), round(py,3) |
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| 53 | n/a | tiledict[(h,x,y)] = True |
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| 54 | n/a | return |
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| 55 | n/a | fl = f * l |
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| 56 | n/a | lt(36) |
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| 57 | n/a | inflatedart(fl, n-1) |
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| 58 | n/a | fd(l) |
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| 59 | n/a | rt(144) |
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| 60 | n/a | inflatekite(fl, n-1) |
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| 61 | n/a | lt(18) |
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| 62 | n/a | fd(l*d) |
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| 63 | n/a | rt(162) |
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| 64 | n/a | inflatekite(fl, n-1) |
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| 65 | n/a | lt(36) |
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| 66 | n/a | fd(l) |
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| 67 | n/a | rt(180) |
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| 68 | n/a | inflatedart(fl, n-1) |
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| 69 | n/a | lt(36) |
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| 70 | n/a | |
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| 71 | n/a | def inflatedart(l, n): |
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| 72 | n/a | if n == 0: |
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| 73 | n/a | px, py = pos() |
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| 74 | n/a | h, x, y = int(heading()), round(px,3), round(py,3) |
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| 75 | n/a | tiledict[(h,x,y)] = False |
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| 76 | n/a | return |
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| 77 | n/a | fl = f * l |
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| 78 | n/a | inflatekite(fl, n-1) |
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| 79 | n/a | lt(36) |
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| 80 | n/a | fd(l) |
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| 81 | n/a | rt(180) |
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| 82 | n/a | inflatedart(fl, n-1) |
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| 83 | n/a | lt(54) |
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| 84 | n/a | fd(l*d) |
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| 85 | n/a | rt(126) |
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| 86 | n/a | inflatedart(fl, n-1) |
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| 87 | n/a | fd(l) |
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| 88 | n/a | rt(144) |
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| 89 | n/a | |
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| 90 | n/a | def draw(l, n, th=2): |
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| 91 | n/a | clear() |
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| 92 | n/a | l = l * f**n |
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| 93 | n/a | shapesize(l/100.0, l/100.0, th) |
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| 94 | n/a | for k in tiledict: |
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| 95 | n/a | h, x, y = k |
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| 96 | n/a | setpos(x, y) |
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| 97 | n/a | setheading(h) |
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| 98 | n/a | if tiledict[k]: |
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| 99 | n/a | shape("kite") |
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| 100 | n/a | color("black", (0, 0.75, 0)) |
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| 101 | n/a | else: |
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| 102 | n/a | shape("dart") |
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| 103 | n/a | color("black", (0.75, 0, 0)) |
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| 104 | n/a | stamp() |
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| 105 | n/a | |
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| 106 | n/a | def sun(l, n): |
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| 107 | n/a | for i in range(5): |
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| 108 | n/a | inflatekite(l, n) |
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| 109 | n/a | lt(72) |
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| 110 | n/a | |
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| 111 | n/a | def star(l,n): |
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| 112 | n/a | for i in range(5): |
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| 113 | n/a | inflatedart(l, n) |
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| 114 | n/a | lt(72) |
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| 115 | n/a | |
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| 116 | n/a | def makeshapes(): |
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| 117 | n/a | tracer(0) |
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| 118 | n/a | begin_poly() |
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| 119 | n/a | kite(100) |
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| 120 | n/a | end_poly() |
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| 121 | n/a | register_shape("kite", get_poly()) |
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| 122 | n/a | begin_poly() |
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| 123 | n/a | dart(100) |
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| 124 | n/a | end_poly() |
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| 125 | n/a | register_shape("dart", get_poly()) |
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| 126 | n/a | tracer(1) |
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| 127 | n/a | |
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| 128 | n/a | def start(): |
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| 129 | n/a | reset() |
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| 130 | n/a | ht() |
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| 131 | n/a | pu() |
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| 132 | n/a | makeshapes() |
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| 133 | n/a | resizemode("user") |
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| 134 | n/a | |
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| 135 | n/a | def test(l=200, n=4, fun=sun, startpos=(0,0), th=2): |
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| 136 | n/a | global tiledict |
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| 137 | n/a | goto(startpos) |
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| 138 | n/a | setheading(0) |
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| 139 | n/a | tiledict = {} |
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| 140 | n/a | a = clock() |
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| 141 | n/a | tracer(0) |
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| 142 | n/a | fun(l, n) |
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| 143 | n/a | b = clock() |
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| 144 | n/a | draw(l, n, th) |
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| 145 | n/a | tracer(1) |
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| 146 | n/a | c = clock() |
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| 147 | n/a | print("Calculation: %7.4f s" % (b - a)) |
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| 148 | n/a | print("Drawing: %7.4f s" % (c - b)) |
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| 149 | n/a | print("Together: %7.4f s" % (c - a)) |
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| 150 | n/a | nk = len([x for x in tiledict if tiledict[x]]) |
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| 151 | n/a | nd = len([x for x in tiledict if not tiledict[x]]) |
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| 152 | n/a | print("%d kites and %d darts = %d pieces." % (nk, nd, nk+nd)) |
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| 153 | n/a | |
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| 154 | n/a | def demo(fun=sun): |
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| 155 | n/a | start() |
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| 156 | n/a | for i in range(8): |
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| 157 | n/a | a = clock() |
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| 158 | n/a | test(300, i, fun) |
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| 159 | n/a | b = clock() |
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| 160 | n/a | t = b - a |
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| 161 | n/a | if t < 2: |
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| 162 | n/a | sleep(2 - t) |
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| 163 | n/a | |
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| 164 | n/a | def main(): |
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| 165 | n/a | #title("Penrose-tiling with kites and darts.") |
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| 166 | n/a | mode("logo") |
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| 167 | n/a | bgcolor(0.3, 0.3, 0) |
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| 168 | n/a | demo(sun) |
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| 169 | n/a | sleep(2) |
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| 170 | n/a | demo(star) |
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| 171 | n/a | pencolor("black") |
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| 172 | n/a | goto(0,-200) |
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| 173 | n/a | pencolor(0.7,0.7,1) |
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| 174 | n/a | write("Please wait...", |
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| 175 | n/a | align="center", font=('Arial Black', 36, 'bold')) |
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| 176 | n/a | test(600, 8, startpos=(70, 117)) |
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| 177 | n/a | return "Done" |
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| 178 | n/a | |
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| 179 | n/a | if __name__ == "__main__": |
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| 180 | n/a | msg = main() |
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| 181 | n/a | mainloop() |
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