Abstract
We extend Kenkel’s model for determining the minimal allowable box size s* to be used in computing the box counting dimension of a self-similar geometric fractal. This minimal size s* is defined in terms of a specified parameter ε which is the deviation of a computed slope from the box counting dimension. We derive an exact implicit equation for s* for any ε. We solve the equation using binary search, compare our results to Kenkel’s, and illustrate how s* varies with ε. A listing of the Python code for the binary search is provided. We also derive a closed form estimate for s* having the same functional form as Kenkel’s empirically obtained expression.
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References
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Rosenberg, E. Minimal box size for fractal dimension estimation. COMMUNITY ECOLOGY 17, 24–27 (2016). https://doi.org/10.1556/168.2016.17.1.4
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DOI: https://doi.org/10.1556/168.2016.17.1.4