On the equality of Hausdorff and box counting dimensions

Preprint

3 March 1993

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.chao-dyn/9303007

Abstract

By viewing the covers of a fractal as a statistical mechanical system, the exact capacity of a multifractal is computed. The procedure can be extended to any multifractal described by a scaling function to show why the capacity and Hausdorff dimension are expected to be equal.

Keywords

MULTIFRACTAL DESCRIBED
COUNTING DIMENSIONS
HAUSDORFF DIMENSION
BOX COUNTING
STATISTICAL
EQUALITY
FRACTAL

All Related Versions

Version 1, 1993-03-03, ArXiv
Published version: Chaos: An Interdisciplinary Journal of Nonlinear Science, 3 (2), 119.

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