Dear Denis,
some time ago I posted a Demonstration of a Gray-Scott pattern based on cellular automata.
See here:
https://demonstrations.wolfram.com/EvolutionInACellularAutomatonModelOfGrayScottReactionDiffusi/
It's not very fast but it works quite nicely for the chosen parameters. I hope it can be helpful.
There's an awful amount of literature on this subject, though.
Besides, have you checked also the Wolfram Documentation example based on the finite-element method at the following link?
https://www.wolfram.com/language/12/nonlinear-finite-elements/transient-gray-scott-model.html
