Demo/turtle/tdemo_fractalcurves.py

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