The purpose of this article is the numerical generation of Turing like patterns on 3D bounded surfaces, based on the analysis of Turing instability in certain types of reaction-diffusion systems in planar regions. We first include a well known 2D-study and analysis of these systems that yield the mathematical conditions under which spatial patterns arise, and which is based on temporal solutions where the classical Laplace diffusion operator is considered. Then, we extend the numerical study to 3D surfaces, employing the Laplace-Beltrami operator to simulate diffusion while keeping the same reaction terms, thus generating similar Turing patterns. The solutions to the involved systems will be calculated numerically using a semi-implicit time discretization in combination with a linear finite element method for spatial discretization using triangular meshes. Details about the numerical implementation are provided for clearness to a broader audience.
Abstract The purpose of this article is the numerical generation of Turing like patterns on 3D bounded surfaces, based on the analysis of Turing instability in certain types of reaction-diffusion [...]
Numerical Turing Patterns Formation on 3D Surfaces with a Linear Finite Element Method 
