Emergent Patterns from Probabilistic Generalisations of Lateral Activation and Inhibition
Journal of the Royal Society Interface
The Royal Society Publishing
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Willis, L., & Kabla, A. (2016). Emergent Patterns from Probabilistic Generalisations of Lateral Activation and Inhibition. Journal of the Royal Society Interface, 13 https://doi.org/10.1098/rsif.2015.1077
The combination of laterally activating and inhibiting feedbacks is well known to spontaneously generate spatial organisation. 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 generalisations 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.
lateral inhibition, pattern formation, nonlinear stochastic model
This work began while L.W. was supported by an EPSRC fellowship.
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External DOI: https://doi.org/10.1098/rsif.2015.1077
This record's URL: https://www.repository.cam.ac.uk/handle/1810/255130