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Turing patterns beyond hexagons and stripes
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2006The best known Turing patterns are composed of stripes or simple hexagonal arrangements of spots. Until recently, Turing patterns with other geometries have been observed only rarely. Here we present experimental studies and mathematical modeling of the formation and stability of hexagonal and square Turing superlattice patterns in a photosensitive ...
Lingfa, Yang +3 more
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Turing pattern formation in heterogenous media
Physica D: Nonlinear Phenomena, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Voroney, J.-P. +2 more
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Particle dynamics simulations of Turing patterns
The Journal of Chemical Physics, 2012The direct simulation Monte Carlo method is used to reproduce Turing patterns at the microscopic level in reaction-diffusion systems. In order to satisfy the basic condition for the development of such a spatial structure, we propose a model involving a solvent, which allows for disparate diffusivities of individual reactive species.
P, Dziekan, A, Lemarchand, B, Nowakowski
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Science, 2011
Turing patterns—self-organized structures created by systems that undergo reaction and diffusion—are a possible mechanism underlying pattern formation in living organisms. Although there are many experimental studies of two-dimensional (2D) pattern formation—three-dimensional (3D) structures, the most relevant to biology, have been difficult to observe
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Turing patterns—self-organized structures created by systems that undergo reaction and diffusion—are a possible mechanism underlying pattern formation in living organisms. Although there are many experimental studies of two-dimensional (2D) pattern formation—three-dimensional (3D) structures, the most relevant to biology, have been difficult to observe
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Turing conditions for pattern forming systems on evolving manifolds
Journal of Mathematical Biology, 2019The study of pattern-forming instabilities in reaction–diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental chemistry ...
R. V. Van Gorder +2 more
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Conventional and unconventional Turing patterns
The Journal of Chemical Physics, 1992The formation of two-dimensional Turing patterns in nonequilibrium chemical systems is studied by numerical simulations with an activator-substrate depletion model. The relative stabilities of the different hexagonal patterns and the striped patterns are discussed, in particular in the vicinity of the transition, and compared with the present state ...
V. Dufiet, J. Boissonade
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A localized extrinsic collocation method for Turing pattern formations on surfaces
Applied Mathematics Letters, 2021Zhuochao Tang +3 more
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