Accuracy of the box-counting algorithm for noisy fractals

A. Z. Górski (), M. Stróż, P. Oświȩcimka and J. Skrzat
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A. Z. Górski: H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, Kraków, 31-342, Poland
M. Stróż: AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Kraków, Poland
P. Oświȩcimka: H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, Kraków, 31-342, Poland
J. Skrzat: Department of Anatomy, Collegium Medicum, Jagellonian University, Kraków, Poland

International Journal of Modern Physics C (IJMPC), 2016, vol. 27, issue 10, 1-11

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 γ=10−5−10−1. The accuracy of calculated numerical values of the fractal dimensions is analyzed as a function of γ for different sizes of the data sample. In particular, it has been found that even in case of pure fractals (γ=0) as well as for tiny noise (γ≈10−5) one has considerable error for the calculated exponents of order 0.01. For larger noise the error is growing up to 0.1 and more, with natural saturation limited by the embedding dimension. This prohibits the power-like scaling of the error. Moreover, the noise effect cannot be cured by taking larger data samples.

Keywords: Fractals; noise; box-counting; accuracy (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S0129183116501126

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