Updating Turing's model of pattern formation

turingpattern-formationself-organizationbiologymathematics

Abstraction: New proof that Turing pattern instabilities arise even with equal diffusion rates

Key points:

Turing's 1952 model proposed that biological patterns (animal spots/stripes, vegetation clusters) arise from symmetry-breaking instabilities between two diffusing chemical species
A key weakness of the original model: it assumed chemicals diffuse at different rates, which is unrealistic in many biological systems
Asllani et al. (University of Limerick, EPJ B 2020) proved mathematically that in sufficiently large rings of cells with diffusion asymmetry, instabilities always arise even when both species diffuse at the same rate
Resulting patterns either remain stationary or propagate as waves around the ring
Published in European Physical Journal B, DOI: 10.1140/epjb/e2020-10206-3

Connections: Alan Turing · Turing Instability · Pattern Formation · Self Organization