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Computer simulations of three-dimensional Turing patterns in the Lengyel-Epstein model
Hiroto Shoji1, Takao Ohta2,3
1Department of Physics, Graduate School of Medical Science, Kyoto Prefectural University of Medicine, Taishogun, Kita-ku, Kyoto 603-8334, Japan.
Summary
This study numerically explores Turing patterns in the Lengyel-Epstein model, revealing diverse structures like lamellar and spherical forms in homogeneous systems and unique perforated and Fddd structures in inhomogeneous systems.
Area of Science:
- Chemical kinetics
- Pattern formation
- Computational modeling
Background:
- Turing patterns are crucial for understanding pattern formation in reaction-diffusion systems.
- The Lengyel-Epstein model provides a framework for studying these patterns.
Purpose of the Study:
- To numerically investigate Turing patterns in the three-dimensional Lengyel-Epstein model.
- To explore pattern formation in both homogeneous and inhomogeneous systems with varying boundary conditions.
Main Methods:
- Numerical simulations of the Lengyel-Epstein reaction-diffusion model in 3D.
- Analysis of pattern formation under periodic, Dirichlet, and Neumann boundary conditions.
Main Results:
- In homogeneous systems, lamellar, cylindrical, spherical, and interconnected structures (including Schwartz P-surface) were observed.
- In inhomogeneous systems, perforated-lamellar and Fddd structures with uniaxial symmetry emerged, dependent on boundary conditions.
Conclusions:
- The Lengyel-Epstein model supports a rich variety of Turing patterns in 3D.
- System inhomogeneity and boundary conditions significantly influence the resulting pattern morphology, offering insights into experimentally accessible scenarios.
