azulavoir wrote: ↑February 17th, 2024, 9:11 am
confocaloid wrote: ↑February 16th, 2024, 3:54 pm
Removing the death transition (cellstate 1 -> cellstate 0, with the other three transitions still allowed)
Really? You're
so against the idea that someone might disagree with you about the definition of a word, that when they use it in a way people generally understand, you completely misinterpret them to avoid answering their question in the way they're clearly after?
I think you are misinterpreting my intent in the answer. I simply wanted to point out what I consider an interesting and natural interpretation of the question. (And instead of providing what you would consider a better answer to the question, you are attacking an existing answer.)
Actually, it is not clear to me at this point whether or not I answered the intended question. That can only become clear if/when the asker clarifies their question enough, to either accept or exclude my answer as valid.
Please note that the question did not limit the rulespace in any way --
Is there a nonexplosive rule, where adding, or removing any single transition will make it explosive?
In particular, you could consider multistate rules. There is nothing in the question that requires the rule to be two-state.
Now, in a three-state rule, there would be up to nine possible transitions (instead of just four): 0->0, 0->1, 0->2, 1->0, 1->1, 1->2, 2->0, 2->1, 2->2.
In a four-state rule, there would be up to 16 possible transitions.
To be able to have a rule with 102 different transitions, you would need at least 11 cellstates including the background (which would allow up to 121 transition).
A reason why this is interesting, is that disabling certain transitions leads to interesting rulespaces.
For example, for three-state rules, forbidding the three transitions "0->2", "1->1", "2->1" leads to the rulespace of old/new cells, which is basically "two-state rules except each alive cell remembers whether or not it was alive in the previous generation". There are only six possible transitions in that rulespace.
