Consider a variation of Conway's game of Life in which cells further than 1 chess-king-move away are counted as neighbors. However, distant cells have less weight in the sum to decide wither a cell lives or dies. How should the weight decrease with distance? In the extreme version, cells no matter how far away can contribute to the total: the weight function might be a discretized Gaussian with infinite basis.
We can also continue to enforce the speed of light. It is not the current state of a distant cell that affects the total but the state in the past allowing for time for the information to propagate.
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