Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/56426
Type: | Report |
Title: | Use the information dimension, not the Hausdorff |
Author: | Roberts, Anthony John |
Publisher: | arXiv.org |
Issue Date: | 2005 |
School/Discipline: | School of Mathematical Sciences |
Statement of Responsibility: | A. J. Roberts |
Abstract: | Multi-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. |
Rights: | Submitted to Cornell University’s online archive www.arXiv.org in 2005 by Tony Roberts. Post-print sourced from www.arxiv.org |
Published version: | http://arxiv.org/abs/nlin.PS/0512014 |
Appears in Collections: | Mathematical Sciences publications |
Files in This Item:
File | Size | Format | |
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hdl_56426.pdf | 116.46 kB | Publisher's post-print | View/Open |
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