During a recent programming adventure, I discovered that finite elementary cellular automata with periodic boundary conditions can be simulated using matrix-vector multiplication with a circulant matrix and a strange kind of algebra, which I call a kernel algebra. [1] I wonder if this same idea could be generalized to higher dimensional automata on other topological surfaces.

[1]: https://github.com/breandan/galoisenne/blob/8f0f1e9e4e02062c...