Matlab Database > GUIs, Graphics & Visualization > Fractals > 1D, 2D and 3D Box-counting (fractal dimension)

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Title: 1D, 2D and 3D Box-counting (fractal dimension)
Author: Frederic Moisy
Institution: Laboratoire FAST, Universite Paris Sud, France
Description: [N, R] = BOXCOUNT(C), where C is a D-dimensional array (with D=1,2,3), counts the number N of D-dimensional 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 320-by-200 image is padded to 512-by-512). The output vectors N and R are of size P+1. For a RGB color image (m-by-n-by-3 array), a summation over the 3 RGB planes is done first.

The Box-counting 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 Minkowski-Bouligand dimension, or Kolmogorov capacity, or Kolmogorov dimension, or simply box-counting dimension.
Keywords: fractal, fractal dimension, box-count, box-counting
File Name:
File Size: 1593 KB
File Version: 1.0
Matlab Version: 7.0 (R14)
Date: 2006-11-23
Downloads: 7555
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