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Fractal dimension computation from equal mass partitions

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Sep 2014Embargo end date: 01 Jan 2015 France English Publisher:AIP PublishingJournal:Chaos: An Interdisciplinary Journal of Nonlinear Science, volume 24, page 33,106 (issn: 1054-1500, eissn: 1089-7682, Copyright policy )
Authors: Shiozawa, Yui; Miller, Bruce N.; Rouet, Jean-Louis;

doi: 10.1063/1.4885778 , 10.48550/arxiv.1501.05273

pmid: 25273186

arXiv: 1501.05273

Fractal dimension computation from equal mass partitions

Abstract

While the numerical methods which utilizes partitions of equal-size, including the box-counting method, remain the most popular choice for computing the generalized dimension of multifractal sets, two mass- oriented methods are investigated by applying them to the one-dimensional generalized Cantor set. We show that both mass-oriented methods generate relatively good results for generalized dimensions for important cases where the box-counting method is known to fail. Both the strengths and limitations of the methods are also discussed.

11 pages, 11 figures

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France
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Keywords

FOS: Physical sciences, Mathematical Physics (math-ph), 004, Fractals, Hausdorff and packing measures, Physics - Data Analysis, Statistics and Probability, [SDU.OTHER] Sciences of the Universe [physics]/Other, [SDU.OTHER]Sciences of the Universe [physics]/Other, Mathematical Physics, Data Analysis, Statistics and Probability (physics.data-an)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Average
Average
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