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On the equality of Hausdorff and box counting dimensions
1Center for Nonlinear Studies, MS B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545.
Chaos (Woodbury, N.Y.)
|April 1, 1993
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.