1 import pylab as P

     2 

     3 def split_line(pt1, pt2):

     4     """Given two complex numbers p1 and p2 return a list of the

     5     necessary points pairwise.

     6     """

     7     # The points we generate are p1, p2, p3, p4 and p5

     8     p1, p5 =  pt1, pt2

     9     diff = pt2 - pt1

    10     segment = diff/3.0

    11     p2 = p1 + segment

    12     p4 = p5 - segment

    13     # Now rotate a line given by 60degrees.

    14     # Recall that complex multiplication does this easily.

    15     # Complex numbers are defined by complex(a, b) also.

    16     p3 = p2 + segment*complex(P.cos(P.pi/3), P.sin(P.pi/3))

    17     return [(p1, p2), (p2, p3), (p3, p4), (p4, p5)]

    18 

    19 def koch(n):

    20     start = complex(0, 0)

    21     end = complex(1, 0)

    22     points = [(start, end)]

    23     for level in range(n):

    24         new_points = []

    25         for (p1, p2) in points:

    26             new_points.extend(split_line(p1, p2))

    27         points = new_points

    28     points.insert(0, (start, points[0][0]) )

    29     points.append((points[-1][1], end))

    30     return points

    31 

    32 def plot_koch(n):

    33     points = koch(n)

    34     x = [t[0].real for t in points]

    35     y = [t[0].imag for t in points]

    36 

    37     P.plot(x, y, 'r-')

    38     P.ylim(0, 1)

    39     P.xlim(0, 1)

    40