On the equality of Hausdorff and box counting dimensions

Ronnie Mainieri

doi:10.1063/1.165970

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arXiv · chao-dyn/9303007

On the equality of Hausdorff and box counting dimensions

Ronnie Mainieri

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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.

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Ronnie Mainieri. 1993-03-03. On the equality of Hausdorff and box counting dimensions. https://doi.org/10.1063/1.165970

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