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