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arXiv · 1412.6664

Accuracy of the box-counting algorithm for noisy fractals

A. Z. Gorski·M. Stroz·P. Oswiecimka·J. Skrzat
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Abstract

The box-counting (BC) algorithm is applied to calculate fractal dimensions of four fractal sets. The sets are contaminated with an additive noise with amplitude $\gamma = 10^{-5} \div 10^{-1}$. The accuracy of calculated numerical values of the fractal dimensions is analyzed as a function of $\gamma$ for different sizes of the data sample ($n_{tot}$). In particular, it has been found that a tiny ($10^{-5}$) addition of noise generates much larger (three orders of magnitude) error of the calculated fractal exponents. Natural saturation of the error for larger noise values prohibits the power-like scaling. Moreover, the noise effect cannot be cured by taking larger data samples.

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A. Z. Gorski, M. Stroz, P. Oswiecimka, J. Skrzat. 2014-12-20. Accuracy of the box-counting algorithm for noisy fractals. https://arxiv.org/abs/1412.6664

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