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Turing patterns in three dimensions
Hiroto Shoji1, Kohtaro Yamada, Daishin Ueyama
1Department of Physics, Kyoto University, Kyoto, Japan. hshoji@math.meiji.ac.jp
Abstract:
We investigate three-dimensional Turing patterns in two-component reaction diffusion systems. The FitzHugh-Nagumo equation, the Brusselator, and the Gray-Scott model are solved numerically in three dimensions. Several interconnected structures of domains as well as lamellar, hexagonal, and spherical domains are obtained as stable motionless equilibrium patterns. The relative stability of these structures is studied analytically based on the reduction approximation. The relation with the microphase-separated structures in block copolymers is also discussed.
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