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by symmetricsaurus 1318 days ago
I don't understand the update rules as described in the readme.

In an 3x3 neighborhood there are 2^9, not 2^5 states. So we should get 2^512 possible update rules, not 2^32.

I think something similar is described in https://conwaylife.com/wiki/Rule_integer.

I'm not sure that all of those rules are valid. We must have translational invariance. One way to do that is to only update the state of the central cell in each considered neighborhood. In that case 2^9 rules are enough. Are there other ways to define consistent rules for a CA?

1 comments

> One can conceive of other update rules. If one considers the five relevant cells...

I think they're looking at alternative update rules. The one you question ignores diagonals.

Conway's Game of Life does consider diagonals. Since they start and finish by talking about GoL I think they've made a mistake.
I can't believe I missed this. I always wondered why getting the types of patterns mentioned in literature were hard. Will definitely need to make an update. Thank you