Accuracy analysis of the box-counting algorithm

Accuracy of the box-counting algorithm for numerical computation of the fractal exponents is investigated. To this end several sample mathematical fractal sets are analyzed. It is shown that the standard deviation obtained for the fit of the fractal scaling in the log-log plot strongly underestimate...

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Bibliographic Details
Published inarXiv.org
Main Authors Gorski, A Z, Drozdz, S, Mokrzycka, A, Pawlik, J
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 24.11.2011
Subjects
Accuracy
Algorithms
Data points
Errors
Exponents
Fractal analysis
Numerical analysis
Physics - Adaptation and Self-Organizing Systems
Physics - Computational Physics
Physics - Data Analysis, Statistics and Probability
Scaling
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Summary:Accuracy of the box-counting algorithm for numerical computation of the fractal exponents is investigated. To this end several sample mathematical fractal sets are analyzed. It is shown that the standard deviation obtained for the fit of the fractal scaling in the log-log plot strongly underestimates the actual error. The real computational error was found to have power scaling with respect to the number of data points in the sample (\(n_{tot}\)). For fractals embedded in two-dimensional space the error is larger than for those embedded in one-dimensional space. For fractal functions the error is even larger. Obtained formula can give more realistic estimates for the computed generalized fractal exponents' accuracy.
ISSN:2331-8422
DOI:10.48550/arxiv.1111.5749