Idea What if a neighborhood varied over time and space?

This is an unfinished idea or question, so it is probably even less fleshed out than normal notes.

Rather than using a consistent neighborhood network for each cell, what if it varied cell-by-cell. And what if the network changed over time. In Feedback Crystal Studio, both of these variations are possible, but they could be pushed further. For example, what if the neighborhood changed every frame.

I remember a model of computation where each cell connects to one other cell for each clock cycle. Then on the next clock cycle, the connection rotates to the next cell.¹

What if a cell could temporarily cast its influence further afield?