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

TL;DR

This paper compares various partitioning schemes for the box-counting algorithm in multifractal analysis, demonstrating that using non-integer box sizes and averaging over box origins improves accuracy in analyzing the Anderson localization model.

Contribution

It introduces a novel partitioning scheme with non-integer box sizes and averaging, reducing error bounds compared to standard integer-ratio methods.

Findings

Non-integer box sizes reduce error bounds.

Averaging over box origins improves reliability.

Enhanced analysis of Anderson localization in 2D and 3D.

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, 77-82 (2009)) to yield the most reliable results.