Effect of randomness and anisotropy on Turing patterns in reaction-diffusion systems

We study the effect of randomness and anisotropy on Turing patterns in reaction-diffusion systems. For this purpose, the Gierer-Meinhardt model of pattern formation is considered. The cases we study are: (i)randomness in the underlying lattice structure, (ii)the case in which there is a probablity p that at a lattice site both reaction and diffusion occur, otherwise there is only diffusion and lastly, the effect of (iii) anisotropic and (iv) random diffusion coefficients on the formation of Turing patterns. The general conclusion is that the Turing mechanism of pattern formation is fairly robust in the presence of randomness and anisotropy.