Rosenberg, E. (2016) Minimal box size for fractal dimension estimation. Community Ecology, 17 (1). pp. 24-27. ISSN 1585-8553
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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.
| Item Type: | Article |
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| Subjects: | Q Science / természettudomány > QH Natural history / természetrajz > QH540 Ecology / ökológia |
| Depositing User: | Ágnes Sallai |
| Date Deposited: | 27 Jul 2016 07:12 |
| Last Modified: | 30 Jun 2017 23:24 |
| URI: | http://real.mtak.hu/id/eprint/38038 |
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