139 lines
3.4 KiB
Python
139 lines
3.4 KiB
Python
#!/usr/bin/python
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""" 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 tkinter.turtle import *
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from time import sleep, 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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