Partitioning Schemes and Non-Integer Box Sizes for the Box-Counting Algorithm in Multifractal Analysis

Details Partitioning Schemes and Non-Integer Box Sizes for the Box-Counting Algorithm in Multifractal Analysis Partitioning Schemes and Non-Integer Box Sizes for the Box-Counting Algorithm in Multifractal Analysis

2012-04-17

arxiv.org/abs/1204.3755v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages, 9 figures

Scientific paper

We compare different partitioning schemes for the box-counting algorithm in the multifractal analysis by computing the singularity spectrum and the distribution of the box probabilities. As model system we use the Anderson model of localization in two and three dimensions. We show that a partitioning scheme which includes unrestricted values of the box size and an average over all box origins is better suited than the standard method using only integer ratios of the linear system size and the box size which was concluded to yield the best results by Rodriguez et al. (Eur. Phys. J. B 67, 77-82 (2009)).

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