Pseudofractals and box counting algorithm
Gorski, Andrzej Z
Original · EN
We show that for sets with the Hausdorff--Besicovitch dimension equal zero the box counting algorithm commonly used to calculate Renyi exponents (dq) can exhibit perfect scaling suggesting non zero dq's. Properties of these pathological sets (pseudofractals) are investigated. Numerical, as well as analytical estimates for dq'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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