Turing patterns on radially growing domains: experiments and simulations

Area of Science:

• Chemical kinetics
• Pattern formation
• Reaction-diffusion systems

Background:

• Turing patterns are complex spatial structures arising from reaction-diffusion processes.
• Radial growth introduces dynamic boundaries that influence pattern development.
• Photosensitive reactions offer a method to control pattern formation.

Purpose of the Study:

• To investigate the influence of radial growth rate on Turing pattern morphology.
• To identify and characterize different growth modes in a photosensitive reaction-diffusion system.
• To understand pattern formation dynamics in a growing two-dimensional system.

Main Methods:

• Utilizing a photosensitive chlorine dioxide-iodine-malonic acid reaction under controlled illumination.
• Experimentally varying the linear radial growth rate of a non-illuminated domain.
• Performing numerical simulations using the Lengyel-Epstein model with modifications for photosensitivity.

Main Results:

• Observed that faster radial growth leads to Turing patterns forming concentric rings parallel to the boundary.
• Found that slower radial growth results in patterns forming perpendicular to the growing boundary.
• Identified three distinct growth modes for Turing patterns, correlated with the radial growth rate.

Conclusions:

• The radial growth rate is a critical factor determining Turing pattern morphology in this system.
• The study provides insights into pattern formation mechanisms in dynamic, growing environments.
• Findings may inform understanding of pattern development in biological systems with growth components.