# boxcount

Version 1.0.0.0 (1,6 MB) von
Fractal dimension using the 'box-counting' method for 1D, 2D and 3D sets
Aktualisiert 10. Jul 2008

Lizenz anzeigen

BOXCOUNT Box-Counting of a D-dimensional array (with D=1,2,3).

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 the number N of boxes of size R needed to cover the set scales as R^(-DF). DF is known as the Minkowski-Bouligand dimension, or Kolmogorov capacity, or Kolmogorov dimension, or simply box-counting dimension.

[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.

BOXCOUNT(C,'plot') also shows the log-log plot of N as a function of R
(if no output argument, this option is selected by default).

BOXCOUNT(C,'slope') also shows the semi-log plot of the local slope DF = - dlnN/dlnR as a function of R. If DF is contant in a certain range of R, then DF is the fractal dimension of the set C.

The execution time depends on the sizes of C. It is fastest for powers
of two over each dimension.

Examples:

c = (rand(1,2048)<0.2);
boxcount(c);

c = randcantor(0.8, 512, 2);
boxcount(c);
figure, boxcount(c, 'slope');

### Zitieren als

Frederic Moisy (2024). boxcount (https://www.mathworks.com/matlabcentral/fileexchange/13063-boxcount), MATLAB Central File Exchange. Abgerufen .

##### Kompatibilität der MATLAB-Version
Erstellt mit R2006a
Kompatibel mit allen Versionen
##### Plattform-Kompatibilität
Windows macOS Linux
##### Kategorien
Mehr zu Fractals finden Sie in Help Center und MATLAB Answers

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

#### boxcount/html/

Version Veröffentlicht Versionshinweise
1.0.0.0

help text improved