The Barycentric Fixed Mass Method for Multifractal Analysis

TL;DR

This paper introduces a new multifractal analysis method that enhances accuracy and efficiency by reducing edge effects, validated on synthetic data and applied to Diffusion Limited Aggregation to reveal weak multifractality.

Contribution

The paper presents a novel barycentric fixed mass method for multifractal analysis that outperforms existing techniques in accuracy and computation time.

Findings

The method shows superior performance on synthetic benchmarks.

It reveals weak multifractality in DLA clusters.

Results support previous findings of multifractality in DLA.

Abstract

We present a novel method to estimate the multifractal spectrum of point distributions. The method incorporates two motivated criteria (barycentric pivot point selection and non-overlapping coverage) in order to reduce edge effects, improve precision and reduce computation time. Implementation of the method on synthetic benchmarks demonstrates the superior performance of the proposed method compared with existing alternatives routinely used in the literature. Finally, we use the method to estimate the multifractal properties of the widely studied growth process of Diffusion Limited Aggregation and compare our results with recent and earlier studies. Our tests support the conclusion of a genuine but weak multifractality of the central core of DLA clusters, with Dq decreasing from 1.75+/-0.01 for q=-10 to 1.65+/-0.01 for q=+10.