Randomness and Apparent Fractality

Details Randomness and Apparent Fractality Randomness and Apparent Fractality

1997-01-28

arxiv.org/abs/cond-mat/9701201v1

Fractals and Chaos in Chemical Engineering", World Scientific, Singapore (1996)

Physics

Condensed Matter

13 pages, 9 figures included. More info available at http://www.fh.huji.ac.il/~dani/

Scientific paper

We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically relevant cutoffs. This range, spanning between one and two decades for densities of 0.1 and lower, is in good agreement with the typical range observed in experiments. The dimensions are not universal and depend on density. Our observations are applicable to spatial, temporal and spectral random structures, all with non-zero measure. Fat fractal analysis does not seem to add information over routine fractal analysis procedures. Most significantly, we find that this apparent fractal behavior is robust even to the presence of moderate correlations. We thus propose that apparent fractal behavior observed experimentally over a limited range in some systems, may often have its origin in underlying randomness.

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