| 1 | n/a | #!/usr/bin/env python3 |
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| 2 | n/a | """ turtle-example-suite: |
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| 3 | n/a | |
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| 4 | n/a | tdemo_fractalCurves.py |
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| 5 | n/a | |
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| 6 | n/a | This program draws two fractal-curve-designs: |
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| 7 | n/a | (1) A hilbert curve (in a box) |
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| 8 | n/a | (2) A combination of Koch-curves. |
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| 9 | n/a | |
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| 10 | n/a | The CurvesTurtle class and the fractal-curve- |
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| 11 | n/a | methods are taken from the PythonCard example |
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| 12 | n/a | scripts for turtle-graphics. |
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| 13 | n/a | """ |
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| 14 | n/a | from turtle import * |
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| 15 | n/a | from time import sleep, clock |
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| 16 | n/a | |
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| 17 | n/a | class CurvesTurtle(Pen): |
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| 18 | n/a | # example derived from |
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| 19 | n/a | # Turtle Geometry: The Computer as a Medium for Exploring Mathematics |
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| 20 | n/a | # by Harold Abelson and Andrea diSessa |
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| 21 | n/a | # p. 96-98 |
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| 22 | n/a | def hilbert(self, size, level, parity): |
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| 23 | n/a | if level == 0: |
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| 24 | n/a | return |
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| 25 | n/a | # rotate and draw first subcurve with opposite parity to big curve |
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| 26 | n/a | self.left(parity * 90) |
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| 27 | n/a | self.hilbert(size, level - 1, -parity) |
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| 28 | n/a | # interface to and draw second subcurve with same parity as big curve |
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| 29 | n/a | self.forward(size) |
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| 30 | n/a | self.right(parity * 90) |
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| 31 | n/a | self.hilbert(size, level - 1, parity) |
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| 32 | n/a | # third subcurve |
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| 33 | n/a | self.forward(size) |
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| 34 | n/a | self.hilbert(size, level - 1, parity) |
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| 35 | n/a | # fourth subcurve |
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| 36 | n/a | self.right(parity * 90) |
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| 37 | n/a | self.forward(size) |
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| 38 | n/a | self.hilbert(size, level - 1, -parity) |
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| 39 | n/a | # a final turn is needed to make the turtle |
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| 40 | n/a | # end up facing outward from the large square |
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| 41 | n/a | self.left(parity * 90) |
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| 42 | n/a | |
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| 43 | n/a | # Visual Modeling with Logo: A Structural Approach to Seeing |
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| 44 | n/a | # by James Clayson |
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| 45 | n/a | # Koch curve, after Helge von Koch who introduced this geometric figure in 1904 |
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| 46 | n/a | # p. 146 |
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| 47 | n/a | def fractalgon(self, n, rad, lev, dir): |
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| 48 | n/a | import math |
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| 49 | n/a | |
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| 50 | n/a | # if dir = 1 turn outward |
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| 51 | n/a | # if dir = -1 turn inward |
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| 52 | n/a | edge = 2 * rad * math.sin(math.pi / n) |
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| 53 | n/a | self.pu() |
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| 54 | n/a | self.fd(rad) |
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| 55 | n/a | self.pd() |
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| 56 | n/a | self.rt(180 - (90 * (n - 2) / n)) |
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| 57 | n/a | for i in range(n): |
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| 58 | n/a | self.fractal(edge, lev, dir) |
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| 59 | n/a | self.rt(360 / n) |
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| 60 | n/a | self.lt(180 - (90 * (n - 2) / n)) |
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| 61 | n/a | self.pu() |
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| 62 | n/a | self.bk(rad) |
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| 63 | n/a | self.pd() |
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| 64 | n/a | |
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| 65 | n/a | # p. 146 |
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| 66 | n/a | def fractal(self, dist, depth, dir): |
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| 67 | n/a | if depth < 1: |
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| 68 | n/a | self.fd(dist) |
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| 69 | n/a | return |
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| 70 | n/a | self.fractal(dist / 3, depth - 1, dir) |
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| 71 | n/a | self.lt(60 * dir) |
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| 72 | n/a | self.fractal(dist / 3, depth - 1, dir) |
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| 73 | n/a | self.rt(120 * dir) |
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| 74 | n/a | self.fractal(dist / 3, depth - 1, dir) |
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| 75 | n/a | self.lt(60 * dir) |
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| 76 | n/a | self.fractal(dist / 3, depth - 1, dir) |
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| 77 | n/a | |
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| 78 | n/a | def main(): |
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| 79 | n/a | ft = CurvesTurtle() |
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| 80 | n/a | |
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| 81 | n/a | ft.reset() |
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| 82 | n/a | ft.speed(0) |
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| 83 | n/a | ft.ht() |
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| 84 | n/a | ft.getscreen().tracer(1,0) |
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| 85 | n/a | ft.pu() |
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| 86 | n/a | |
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| 87 | n/a | size = 6 |
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| 88 | n/a | ft.setpos(-33*size, -32*size) |
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| 89 | n/a | ft.pd() |
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| 90 | n/a | |
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| 91 | n/a | ta=clock() |
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| 92 | n/a | ft.fillcolor("red") |
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| 93 | n/a | ft.begin_fill() |
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| 94 | n/a | ft.fd(size) |
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| 95 | n/a | |
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| 96 | n/a | ft.hilbert(size, 6, 1) |
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| 97 | n/a | |
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| 98 | n/a | # frame |
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| 99 | n/a | ft.fd(size) |
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| 100 | n/a | for i in range(3): |
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| 101 | n/a | ft.lt(90) |
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| 102 | n/a | ft.fd(size*(64+i%2)) |
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| 103 | n/a | ft.pu() |
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| 104 | n/a | for i in range(2): |
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| 105 | n/a | ft.fd(size) |
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| 106 | n/a | ft.rt(90) |
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| 107 | n/a | ft.pd() |
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| 108 | n/a | for i in range(4): |
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| 109 | n/a | ft.fd(size*(66+i%2)) |
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| 110 | n/a | ft.rt(90) |
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| 111 | n/a | ft.end_fill() |
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| 112 | n/a | tb=clock() |
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| 113 | n/a | res = "Hilbert: %.2fsec. " % (tb-ta) |
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| 114 | n/a | |
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| 115 | n/a | sleep(3) |
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| 116 | n/a | |
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| 117 | n/a | ft.reset() |
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| 118 | n/a | ft.speed(0) |
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| 119 | n/a | ft.ht() |
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| 120 | n/a | ft.getscreen().tracer(1,0) |
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| 121 | n/a | |
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| 122 | n/a | ta=clock() |
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| 123 | n/a | ft.color("black", "blue") |
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| 124 | n/a | ft.begin_fill() |
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| 125 | n/a | ft.fractalgon(3, 250, 4, 1) |
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| 126 | n/a | ft.end_fill() |
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| 127 | n/a | ft.begin_fill() |
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| 128 | n/a | ft.color("red") |
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| 129 | n/a | ft.fractalgon(3, 200, 4, -1) |
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| 130 | n/a | ft.end_fill() |
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| 131 | n/a | tb=clock() |
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| 132 | n/a | res += "Koch: %.2fsec." % (tb-ta) |
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| 133 | n/a | return res |
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| 134 | n/a | |
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| 135 | n/a | if __name__ == '__main__': |
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| 136 | n/a | msg = main() |
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| 137 | n/a | print(msg) |
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| 138 | n/a | mainloop() |
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