\[ \partial_t{u}=-uv^2+F(1-u)+ D_u \nabla^2 u \]

\[ \partial_t{v}=uv^2-(F+k)v + D_v \nabla^2 v \]

based on Complexity Explorable:

" Hopfed Turingles -
This reaction-diffusion system generates a variety of spatio-temporal patterns
"