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Pseudofractals and box counting algorithm

Andrzej Z Gorski
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Abstract

We show that for sets with the Hausdorff--Besicovitch dimension equal zero the box counting algorithm commonly used to calculate Renyi exponents ($d_q$) can exhibit perfect scaling suggesting non zero $d_q$'s. Properties of these pathological sets ({\it pseudofractals}) are investigated. Numerical, as well as analytical estimates for $d_q$'s are obtained. A simple indicator is given to distinguish pseudofractals and fractals in practical applications of the box counting method. Histograms made of pseudofractal sets are shown to have Pareto tails.

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Andrzej Z Gorski. 2001-07-11. Pseudofractals and box counting algorithm. https://doi.org/10.1088/0305-4470%2F34%2F39%2F302

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