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c8b45a385a
* gh-118673: Remove shebang and executable bits from stdlib modules. * Removed shebangs and exe bits on turtledemo scripts. The setting was inappropriate for '__main__' and inconsistent across the other modules. The scripts can still be executed directly by invoking with the desired interpreter.
138 lines
3.4 KiB
Python
138 lines
3.4 KiB
Python
""" turtle-example-suite:
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tdemo_fractalCurves.py
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This program draws two fractal-curve-designs:
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(1) A hilbert curve (in a box)
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(2) A combination of Koch-curves.
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The CurvesTurtle class and the fractal-curve-
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methods are taken from the PythonCard example
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scripts for turtle-graphics.
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"""
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from turtle import *
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from time import sleep, perf_counter as clock
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class CurvesTurtle(Pen):
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# example derived from
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# Turtle Geometry: The Computer as a Medium for Exploring Mathematics
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# by Harold Abelson and Andrea diSessa
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# p. 96-98
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def hilbert(self, size, level, parity):
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if level == 0:
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return
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# rotate and draw first subcurve with opposite parity to big curve
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self.left(parity * 90)
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self.hilbert(size, level - 1, -parity)
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# interface to and draw second subcurve with same parity as big curve
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self.forward(size)
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self.right(parity * 90)
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self.hilbert(size, level - 1, parity)
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# third subcurve
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self.forward(size)
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self.hilbert(size, level - 1, parity)
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# fourth subcurve
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self.right(parity * 90)
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self.forward(size)
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self.hilbert(size, level - 1, -parity)
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# a final turn is needed to make the turtle
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# end up facing outward from the large square
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self.left(parity * 90)
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# Visual Modeling with Logo: A Structural Approach to Seeing
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# by James Clayson
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# Koch curve, after Helge von Koch who introduced this geometric figure in 1904
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# p. 146
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def fractalgon(self, n, rad, lev, dir):
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import math
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# if dir = 1 turn outward
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# if dir = -1 turn inward
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edge = 2 * rad * math.sin(math.pi / n)
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self.pu()
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self.fd(rad)
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self.pd()
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self.rt(180 - (90 * (n - 2) / n))
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for i in range(n):
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self.fractal(edge, lev, dir)
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self.rt(360 / n)
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self.lt(180 - (90 * (n - 2) / n))
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self.pu()
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self.bk(rad)
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self.pd()
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# p. 146
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def fractal(self, dist, depth, dir):
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if depth < 1:
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self.fd(dist)
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return
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self.fractal(dist / 3, depth - 1, dir)
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self.lt(60 * dir)
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self.fractal(dist / 3, depth - 1, dir)
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self.rt(120 * dir)
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self.fractal(dist / 3, depth - 1, dir)
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self.lt(60 * dir)
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self.fractal(dist / 3, depth - 1, dir)
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def main():
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ft = CurvesTurtle()
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ft.reset()
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ft.speed(0)
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ft.ht()
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ft.getscreen().tracer(1,0)
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ft.pu()
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size = 6
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ft.setpos(-33*size, -32*size)
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ft.pd()
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ta=clock()
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ft.fillcolor("red")
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ft.begin_fill()
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ft.fd(size)
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ft.hilbert(size, 6, 1)
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# frame
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ft.fd(size)
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for i in range(3):
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ft.lt(90)
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ft.fd(size*(64+i%2))
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ft.pu()
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for i in range(2):
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ft.fd(size)
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ft.rt(90)
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ft.pd()
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for i in range(4):
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ft.fd(size*(66+i%2))
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ft.rt(90)
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ft.end_fill()
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tb=clock()
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res = "Hilbert: %.2fsec. " % (tb-ta)
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sleep(3)
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ft.reset()
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ft.speed(0)
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ft.ht()
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ft.getscreen().tracer(1,0)
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ta=clock()
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ft.color("black", "blue")
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ft.begin_fill()
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ft.fractalgon(3, 250, 4, 1)
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ft.end_fill()
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ft.begin_fill()
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ft.color("red")
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ft.fractalgon(3, 200, 4, -1)
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ft.end_fill()
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tb=clock()
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res += "Koch: %.2fsec." % (tb-ta)
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return res
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if __name__ == '__main__':
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msg = main()
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print(msg)
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mainloop()
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