Dimensionality effects in Turing pattern formation

TL;DR

This paper investigates how the dimensionality of space influences Turing pattern formation, analyzing linear stability, pattern selection, and transitions between 2D and 3D structures, with implications for experimental observations.

Contribution

It provides a detailed analysis of dimensionality effects on Turing patterns, including stability, pattern selection, and the transition from quasi-2D to 3D structures, which is a novel exploration.

Findings

Differences in pattern robustness between 2D and 3D.

Preliminary results on transitions between quasi-2D and 3D structures.

Relation of theoretical results to experimental data.

Abstract

The problem of morphogenesis and Turing instability are revisited from the point of view of dimensionality effects. First the linear analysis of a generic Turing model is elaborated to the case of multiple stationary states, which may lead the system to bistability. The difference between two- and three-dimensional pattern formation with respect to pattern selection and robustness is discussed. Preliminary results concerning the transition between quasi-two-dimensional and three-dimensional structures are presented and their relation to experimental results are addressed.