title: Computer simulations of three-dimensional Turing patterns in the Lengyel-Epstein model.
abstract: We investigate numerically Turing patterns in the Lengyel-Epstein model in three dimensions. In a bulk homogeneous system under periodic boundary conditions, we obtain not only lamellar, cylindrical, and spherical structures but also several interconnected periodic structures including the Schwartz P-surface structure. In order to examine Turing patterns in the conditions accessible experimentally, we consider inhomogeneous systems where a parameter in the reaction-diffusion equations depends on the space coordinate with either Dirichlet or Neumann boundary conditions. In this situation, we find that a perforated-lamellar structure and an Fddd structure, both of which have a uniaxial symmetry, appear depending on the boundary conditions.
authors: Department of Physics, Graduate School of Medical Science, Kyoto Prefectural University of Medicine, Taishogun, Kita-ku, Kyoto 603-8334, Japan.
authors: Hiroto
authors: H
authors: Shoji
authors: Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan.|Toyota Physical and Chemical Research Institute, Nagakute, Aichi 480-1192, Japan.
authors: Takao
authors: T
authors: Ohta