Self-similar Turing Patterns: An Anomalous diffusion consequence

TL;DR

This paper demonstrates that specific anomalous diffusion conditions can lead to the formation of self-similar Turing patterns, including novel spiral and rotational symmetry patterns, driven by medium heterogeneity.

Contribution

It introduces a new understanding of how anomalous diffusion, modeled via space-dependent coefficients, results in unique self-similar and complex Turing patterns.

Findings

Self-similar concentration patterns can form under anomalous diffusion.

Novel spiral and mixed rotational symmetry patterns are observed.

Pattern formation is driven by medium heterogeneity and anomalous diffusion conditions.

Abstract

In this work we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through a diffusion-driven instability. We also find spiral patterns and patterns with mixtures of rotational symmetries not reported before. The type of anomalous diffusion discussed in this work, either subdiffusion or superdiffusion, is a consequence of the medium heterogeneity, and is modelled through a space-dependent diffusion coefficient with a power-law functional form.