Cellular Automata in a non-ridged universe?

Question

Cellular automata usually exist in a 'universe' consisting of a 1 or 2 dimensional grid, or sometimes in other ridged tessellations. Has there been any research into CA's existing in a more malleable universe, where the local time-space geometry is affected by the activity of the CA. For example, could the 'universe' itself react to local concentrations of populated cells by altering the rate of the local clock, or by distorting the spacial geometry, adding or removing cells.

Similarly, are is there research into CA's where the rules are defined on a per-cell basis and where the rules for a 'live' cell are inherited from the adjacent cells and where each generation has a probability of mutation of the rules?

Answer 1

It's been a long time since I studied them as an academic discipline. In practice, the grid is often 3, 4, or more dimensions. Software and hardware aren't limited by correspondence to physical reality.

If such a construct is dynamically reconfigurable, I don't know if anyone would still call it a CA. It's hard to map real world problems into a structure like this, and the complexity exacts a cost.

You can probably find what you're looking for, but it might not be defined or discussed in the same terms you used.