For simplicity, we discuss binary (S = 2) automata.
The rule of a cellular automaton determines how the current collection of live and dead cells in the state space evolves into the next collection of live and dead cells.
That is, for each of the SN neighborhood configurations, the rule specifies whether the configuration gives rise to a live cell or a dead cell.
We consider only CA with rules applied synchronously, that is, no cell is updated until all the next states of all the cells have been computed.
For example, to apply the rule
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we look at the nbhd of each cell (shaded in blue in gen 1), and if the pattern matches the rule, make the middle cell in the next gen (also shaded blue) alive.
Otherwise, the middle cell is dead.
For example, here we compute the second generation if the first has a single live cell.
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| Click the picture for the nbhd of the next cell. |
Continuing this for a few more generations produces the expected pattern.
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| Click the animation to stop. |
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