2005/12/07 by A. J. Roberts, Roberts, A. J.
Physics and Astronomy · #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS) #nlin.PS
paper · pdf · doi:10.48550/arxiv.nlin/0512014
11 pages
arxiv created 2005/12/07 · arxiv updated 2009/12/01
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 Dq of order q≤0, including the Hausdorff dimension, are effectively 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 Dq for q≥ 1, and of these the information dimension D1 seems the most robustly estimated from a finite amount of data.