Arc-length characterization of finite, radial growth patterns

TL;DR

This paper introduces a novel method to characterize the distribution of length scales in finite, radially symmetric disordered patterns, enabling analysis where traditional methods fail, and applies it to various pattern types.

Contribution

The paper presents a new approach for quantifying length-scale distributions in finite, disordered patterns with radial symmetry, including a technique to locate the pattern's center without full connectivity.

Findings

Successfully distinguishes different pattern types

Effectively identifies characteristic length scales

Applicable to various physical and biological patterns

Abstract

We present a method to characterize the distribution of length-scales of finite, disordered patterns with, on average, radial symmetry. This method makes it possible to quantify the distribution of characteristic length scales in cases where the conventional "linear" chord method does not work. We show that the method can clearly distinguish regular patterns, patterns that are formed by diffusion-limited aggregation, and patterns that form during the slow drying of confined, colloid-laden droplets, explained by Beechey-Newman et al.1 We also introduce a method to find the centre-point of these finite patterns, without assuming a full connectivity in the pattern. The method should be widely applicable to other, finite quasi-two-dimensional patterns like dendritic structures, viscous fingering, liquid crystal patterns and bacterial growth.