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Numbers of cellular automata

All cellular automata I have considered this far have used the standard Moore neighbourhood, a 3×3 square with the current cell in the middle and eight neighbours. Yesterday I extended my program to support larger neighbourhoods. Now it supports neighbourhoods of arbitrary range. If the range is r, the neighbourhood consists of all cells you can reach in no more than r steps from the current cell, each step being horizontal, vertical, or diagonal. Hence, the range-r Moore neighbourhood is a square consisting of (2r + 1)2 cells, with the current cell in the middle. r = 1 yields the standard eight-cell Moore neighbourhood.

The number of possible extended-range cellular automata is nearly ungraspable. Let us do some simple math.


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