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