Minimal box size for fractal dimension estimation

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