Use the information dimension, not the Hausdorff

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dc.creatorRoberts, A. J.
dc.date2005-12-07
dc.date.accessioned2026-07-07T06:55:55Z
dc.date.available2026-07-07T06:55:55Z
dc.descriptionMulti-fractal patterns occur widely in nature. In developing new algorithms to determine multi-fractal spectra of experimental data I am lead to the conclusion that generalised dimensions $D_q$ of order $q\leq0$, including the Hausdorff dimension, are effectively \emph{irrelevant}. The reason is that these dimensions are extraordinarily sensitive to regions of low density in the multi-fractal data. Instead, one should concentrate attention on generalised dimensions $D_q$ for $q\geq 1$, and of these the information dimension $D_1$ seems the most robustly estimated from a finite amount of data.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/nlin/0512014
dc.identifierhttp://arxiv.org/abs/nlin/0512014
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106447
dc.subjectPattern Formation and Solitons
dc.titleUse the information dimension, not the Hausdorff
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