day2/koch.py
author Madhusudan.C.S <madhusudancs@gmail.com>
Tue, 29 Dec 2009 19:25:11 +0530
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permissions -rwxr-xr-x
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import pylab as P
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def split_line(pt1, pt2):
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    """Given two complex numbers p1 and p2 return a list of the
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    necessary points pairwise.
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    """
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    # The points we generate are p1, p2, p3, p4 and p5
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    p1, p5 =  pt1, pt2
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    diff = pt2 - pt1
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    segment = diff/3.0
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    p2 = p1 + segment
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    p4 = p5 - segment
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    # Now rotate a line given by 60degrees.
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    # Recall that complex multiplication does this easily.
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    # Complex numbers are defined by complex(a, b) also.
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    p3 = p2 + segment*complex(P.cos(P.pi/3), P.sin(P.pi/3))
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    return [(p1, p2), (p2, p3), (p3, p4), (p4, p5)]
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def koch(n):
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    start = complex(0, 0)
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    end = complex(1, 0)
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    points = [(start, end)]
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    for level in range(n):
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        new_points = []
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        for (p1, p2) in points:
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            new_points.extend(split_line(p1, p2))
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        points = new_points
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    points.insert(0, (start, points[0][0]) )
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    points.append((points[-1][1], end))
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    return points
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def plot_koch(n):
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    points = koch(n)
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    x = [t[0].real for t in points]
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    y = [t[0].imag for t in points]
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    P.plot(x, y, 'r-')
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    P.ylim(0, 1)
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    P.xlim(0, 1)
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