Use the information dimension , not the Hausdorff

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.