title: Emergent patterns from probabilistic generalizations of lateral activation and inhibition.
abstract: The combination of laterally activating and inhibiting feedbacks is well known to spontaneously generate spatial organization. It was introduced by Gierer and Meinhardt as an extension of Turing's great insight that two reacting and diffusing chemicals can spontaneously drive spatial morphogenesis per se In this study, we develop an accessible nonlinear and discrete probabilistic model to study simple generalizations of lateral activation and inhibition. By doing so, we identify a range of modes of morphogenesis beyond the familiar Turing-type modes; notably, beyond stripes, hexagonal nets, pores and labyrinths, we identify labyrinthine highways, Kagome lattices, gyrating labyrinths and multi-colour travelling waves and spirals. The results are discussed within the context of Turing's original motivating interest: the mechanisms which underpin the morphogenesis of living organisms.
authors.affiliation: The Sainsbury Laboratory, University of Cambridge, Cambridge CB2 1LR, UK lisa.willis@slcu.cam.ac.uk.
authors.forename: Lisa
authors.identifier: 0000-0003-0568-1442
authors.initials: L
authors.lastname: Willis
authors.affiliation: Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK.
authors.forename: Alexandre
authors.initials: A
authors.lastname: Kabla
mesh_terms: D008962:Models, Theoretical
keywords: lateral inhibition; nonlinear stochastic model; pattern formation