Finite-size effects on the characterization of fractal sets:f(α) construction via box counting on a finite two-scaled Cantor set

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Abstract
We study box counting on finite fractal sets and investigate how to obtain the generalized dimensions and the spectrum of scaling indices with highest possible accuracy. As a model we use a simple one-dimensional Cantor set for which the f(α) spectrum may be found analytically—the exact result is compared with the box-counting solution on the finite levels. There is a connection between the q value and the size of the boxes giving the most accurate result for the f(α) spectrum on any finite level.