Title: 
1D, 2D and 3D Boxcounting (fractal dimension)

Author: 
Frederic Moisy 
EMail: 
moisyATfast.upsud.fr

Institution: 
Laboratoire FAST, Universite Paris Sud, France

Description: 
[N, R] = BOXCOUNT(C), where C is a Ddimensional array (with D=1,2,3), counts the number N of Ddimensional boxes of size R needed to cover the nonzero elements of C. The box sizes are powers of two, i.e., R = 1, 2, 4 ... 2^P, where P is the smallest integer such that MAX(SIZE(C)) <= 2^P. If the sizes of C over each dimension are smaller than 2^P, C is padded with zeros to size 2^P over each dimension (e.g., a 320by200 image is padded to 512by512). The output vectors N and R are of size P+1. For a RGB color image (mbynby3 array), a summation over the 3 RGB planes is done first.
The Boxcounting method is useful to determine fractal properties of a
1D segment, a 2D image or a 3D array. If C is a fractal set, with fractal dimension DF < D, then N scales as R^(DF). DF is known as the MinkowskiBouligand dimension, or Kolmogorov capacity, or Kolmogorov dimension, or simply boxcounting dimension.

Keywords: 
fractal, fractal dimension, boxcount, boxcounting

File Name:  boxcount.zip 
File Size: 
1593 KB

File Version:  1.0 
Matlab Version:  7.0 (R14) 
Date:  20061123 
Downloads:  6149 
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