Growth Mode Selection of Radially Growing Turing Patterns

TL;DR

This study investigates how Turing patterns form in two-dimensional systems undergoing radial growth, revealing how different growth speeds influence pattern orientation and morphology.

Contribution

It introduces a comprehensive simulation framework for analyzing Turing pattern growth modes under various radial growth conditions using COMSOL.

Findings

Fast growth causes patterns parallel to the boundary

Intermediate growth results in perpendicular pattern formation

Slow growth leads to interior pattern development

Abstract

We study Turing pattern formation in a system undergoing radial growth in two dimensions. The Lengyel-Epstein two variable model is implemented in COMSOL Multiphysics and solved on domains growing at different speeds while sweeping other parameters to examine a wide range of Turing pattern morphologies. By altering the configuration of the finite element mesh, we examine patterning in several simulation growth modes. The observed pattern morphologies match previously observed trends for Turing pattern growth modes. Fast growth leads to pattern formation parallel to the growing boundary, intermediate growth leads to pattern formation perpendicular to the growing boundary, and slow growth leads to pattern growth from the interior. Exponential growth leads to the expected fast-growth mode of pattern formation parallel to the moving boundary. Simulations to replicate interior growth using logistic illumination do not show simple pattern trends due to the effects of partial pattern suppression from the illumination.