Consider cellular automata in which a cell's next state depends on both its local neighborhood and a few possible distant interactions. Inspired by chess (future post). The distant interactions could be with the first nonempty cell for each of the directions a chess queen can move (or no interaction if there is nothing along a ray).
"Mostly local but with a few distant interactions" tells a story that people can relate to (to be elaborated on in a future post).
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