Accuracy Analysis of the Box-Counting Algorithm

• Authors: A. Górski , S. Drożdż , A. Mokrzycka , J. Pawlik
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

05.45.Df; 02.60.Gf; 47.52.+j

Discipline

• 05.45.Df: Fractals(see also 47.53.+n Fractals in fluid dynamics; 61.43.Hv Fractals; macroscopic aggregates in structure of solids)
• 47.52.+j: Chaos in fluid dynamics(see also 05.45.-a Nonlinear dynamics and chaos in Statistical physics, thermodynamics, and nonlinear dynamical systems)
• 02.60.Gf: Algorithms for functional approximation

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2012
• Volume: 121
• Issue: 2B
• Pages: B-28-B-30

Dates

published

2012-02

Contributors

author

A. Górski

• H. Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, Kraków, 31-342, Poland

author

S. Drożdż

• H. Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, Kraków, 31-342, Poland
• Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology, 31-155 Kraków, Poland

author

A. Mokrzycka

• H. Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, Kraków, 31-342, Poland
• AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Kraków, Poland

author

J. Pawlik

• H. Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, Kraków, 31-342, Poland
• AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Kraków, Poland

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Identifiers

DOI

10.12693/APhysPolA.121.B-28