Fractal Dimension Computation in Python Code

Huaiyu Zhu hzhu at
Sat Sep 30 04:37:35 CEST 2000

On Fri, 29 Sep 2000 20:01:10 -0000, Jake Speed <speed@?.com> wrote:
>And having said that, here's an updated version.  Note
>that in the examples the points aren't limited to the 
>0.0 -> 1.0 range anymore.


I've changed your code to use Numeric module so that it is applicable to any
dimension of the containing space.  This can also be used as a module.

""" - calculate fractal dimensions
Adopted by Huaiyu Zhu from

From: speed@?.com (Jake Speed)
Newsgroups: comp.lang.python
Subject: Re: Fractal Dimension Computation in Python Code
Date: Fri, 29 Sep 2000 20:01:10 -0000

from math import log
from Numeric import *

def N(points, scale):
    """Return (num of coverage, scale) of points by boxes of size 1/scale"""
    unique = {}
    for point in points:
        box = tuple((point * scale).astype(Int))
        unique[box] = 1
    return float(len(unique)), scale

def dim(points):
    """ Calculate dimensions of points at various scale = 2**level"""
    f0 = 1, 1
    for level in xrange(1, 12):
        f1 = N(points, 2.0**level)
        dim = log(f1[0]/f0[0]) / log(f1[1]/f0[1])
        print "%2d:  %.4g" % (level, dim)
        f0 = f1

M = array([[0,-1], [1,0]]) * sqrt(3)/2

def makekoch(x1, x2, level, flist=[]):
    """ Return a list of points on Koch curve, subdivided levels """
    if level == 0: return flist
    xd = (x2 - x1) / 3.
    xa = x1 + xd
    xb = x2 - xd
    xm = (x1 + x2) / 2.0 - matrixmultiply(M, xd)
    makekoch(x1, xa, level-1, flist)
    makekoch(xa, xm, level-1, flist)
    makekoch(xm, xb, level-1, flist)
    makekoch(xb, x2, level-1, flist)
    return flist

if __name__ == "__main__":
    print "line dimension"
    x = (arange(100)/100.)[:,NewAxis]

    print "plane dimension"
    list2d = []
    for x in xrange(100):
        for y in xrange(100):
            list2d.append(array((x, y))/100.0)

    print "space dimension"
    list3d = []
    for x in xrange(30):
        for y in xrange(30):
            for z in xrange(30):
                list3d.append(array((x, y, z))/30.0)

    print "koch dimension"
    listkoch = makekoch(array((0,0)), array((1,0)), 7)

Huaiyu Zhu                       hzhu at
Matrix for Python Project 

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