Comment by bts

You should look into the "comonad" abstraction from the functional programming world. Dual to monads, they're a natural fit for situations where you might have a value with some sort of (possibly infinite) context (think: neighborhood, or history, etc.) that can be either pre-computed or computed on-demand.

This StackOverflow post[1] is a good starting point for understanding comonads. It points out that they can be used to model cellular automata (like Conway's Game of Life), sequences, streams, etc.

[1] https://stackoverflow.com/questions/8428554/what-is-the-como...