Eur. Phys. J. B (2013) 86: 48
https://doi.org/10.1140/epjb/e2012-30410-x

Regular Article

Partitioning schemes and non-integer box sizes for the box-counting algorithm in multifractal analysis

Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany

^a e-mail: stefanie.thiem@physik.tu-chemnitz.de

Received: 22 May 2012
Received in final form: 2 October 2012
Published online: 11 February 2013

Abstract

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 leads to smaller error bounds than the standard method using only integer ratios of the linear system size and the box size which was found by Rodriguez et al. [Eur. Phys. J. B 67, 77 (2009)] to yield the most reliable results.