Christopher Essex, M. A. H. Nerenberg
Abstract
It is shown that for often encountered nonpathological sets the limit capacity and the Hausdorff dimension differ. This raises the question in the context of physics as to which of these should be called the ‘‘fractal’’ dimension.
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It is shown that for often encountered nonpathological sets the limit capacity and the Hausdorff dimension differ. This raises the question in the context of physics as to which of these should be called the ‘‘fractal’’ dimension.
Key concepts: Hausdorff dimension, Packing dimension, Minkowski–Bouligand dimension, Dimension function, Effective dimension, Fractal dimension, Physics, Limit (mathematics)