1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
|
import pylab as P
def split_line(pt1, pt2):
"""Given two complex numbers p1 and p2 return a list of the
necessary points pairwise.
"""
# The points we generate are p1, p2, p3, p4 and p5
p1, p5 = pt1, pt2
diff = pt2 - pt1
segment = diff/3.0
p2 = p1 + segment
p4 = p5 - segment
# Now rotate a line given by 60degrees.
# Recall that complex multiplication does this easily.
# Complex numbers are defined by complex(a, b) also.
p3 = p2 + segment*complex(P.cos(P.pi/3), P.sin(P.pi/3))
return [(p1, p2), (p2, p3), (p3, p4), (p4, p5)]
def koch(n):
start = complex(0, 0)
end = complex(1, 0)
points = [(start, end)]
for level in range(n):
new_points = []
for (p1, p2) in points:
new_points.extend(split_line(p1, p2))
points = new_points
points.insert(0, (start, points[0][0]) )
points.append((points[-1][1], end))
return points
def plot_koch(n):
points = koch(n)
x = [t[0].real for t in points]
y = [t[0].imag for t in points]
P.plot(x, y, 'r-')
P.ylim(0, 1)
P.xlim(0, 1)
|
