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Fractal dimension computation from equal mass partitions.

Abstract : Numerical methods which utilize partitions of equal-size, including the box-counting method, remain the most popular choice for computing the generalized dimension of multifractal sets. However, it is known that mass-oriented methods generate relatively good results for computing generalized dimensions for important cases where the box-counting method is known to fail. Here, we revisit two mass-oriented methods and discuss their strengths and limitations. V C 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4885778] Fractal sets are characterized by self-similarity, and power laws can be associated with them. Examples of fractals in nature are ubiquitous. Their discovery led to the extension of the notion of dimension. For monofrac-tals, the scaling pattern is homogeneous and the set can be characterized by a single dimension. In contrast, mul-tifractals are inhomogeneous and require a spectrum of dimensions D q to capture their geometry. In finding the generalized dimensions, the box-counting method has been by far the most popular choice among researchers across various fields. However, it is known that the class of methods which deal with partitions into cells of equal size, including the box-counting method, is ill-suited for computing the generalized dimensions on some domain of q. In this paper, two alternative methods which utilize mass-oriented partitions, rather than partitions of equal-size, are investigated.
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Yui Shiozawa, Bruce N. Miller, Jean-Louis Rouet. Fractal dimension computation from equal mass partitions. . Chaos: An Interdisciplinary Journal of Nonlinear Science, American Institute of Physics, 2014, 24, pp.94902 - 234912. ⟨10.1063/1.4885778⟩. ⟨insu-01087937⟩

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