On the equality of Hausdorff and box counting dimensions
arXiv:chao-dyn/9303007 · doi:10.1063/1.165970
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.
CYCLER Paper 93mar001 Latex file with 3 PostScript figures (needs psfig.sty)