Multifractal Distribution of Dendrite on One-dimensional Support

TL;DR

This paper uses multifractal analysis to characterize the complex sidebranch structures of dendritic patterns on a one-dimensional support, revealing multifractality in area, perimeter, and growth rate distributions.

Contribution

It introduces a novel application of multifractal analysis to dendritic sidebranch structures, providing new insights into their multifractal nature and growth dynamics.

Findings

Distributions exhibit multifractality in the growth regime

Area and perimeter distributions can be explained by a simple partitioning process

Analysis offers a phenomenological understanding of sidebranch structure complexity

Abstract

We apply multifractal analysis to an experimentally obtained quasi-two-dimensional crystal with fourfold symmetry, in order to characterize the sidebranch structure of a dendritic pattern. In our analysis, the stem of the dendritic pattern is regarded as a one-dimensional support on which a measure is defined and the measure is identified with the area, perimeter length, and growth rate distributions. It is found that these distributions have multifractality and the results for the area and perimeter length distributions, in the competitive growth regime of sidebranches, are phenomenologically understood as a simple partitioning process.