## How do you keep track of INT rules?

For discussion of other cellular automata.
confocaloid
Posts: 1561
Joined: February 8th, 2022, 3:15 pm

### How do you keep track of INT rules?

What can be said usefully about every range-1 Moore neighbourhood isotropic non-totalistic rule, or at least about sufficiently many of them? I'm looking for some kind of information that can be stated concisely (e.g. as a single number) and is cheap to compute, and yet is somehow useful for quickly knowing something specific about the rule, even before seeing its behaviour/exploring it/reading more about the rule.
I'm asking this question after seeing that people often talk about some properties of rules (strobing, explosive, apgsearchable, nonrelativistic, can escape bounding box/bounding diamond, ...) and wondering whether this pile of properties can be made into some kind of a useful/interesting/curious classification. Is there a method behind the madness of INT rules, or it is mad to look for one method to rule them all?
I'll give several examples that I can imagine.

For every rule one can say how many isotropic birth/survival conditions have to be toggled to reach Life; it is a cheap-to-compute nonnegative integer. Even though toggling one condition may significantly change the behaviour of the rule, it seems useful to count "toggles away from Life" to distinguish those rules that were (probably) obtained by modifying Life from those rules that were (probably) obtained by random choice or in some other way.

For every rule one can find the least number of toggles that are needed to reach some outer-totalistic rule (not necessarily Life); the reasoning is the same as above. It is also possible to choose a "base outer-totalistic rule" which is as few isotropic conditions away as possible, but this is not always unique.

For every rule, it is possible to enumerate all non-unreasonably-growing patterns with small bounding boxes and write down the longest time to stability as a function of the bounding box area. The result is an integer sequence and first few terms are relatively cheap to compute for many rules. Even if this may not be too useful to distinguish between similar rules, it might be a helpful way to express how some rules behave in a significantly different way than other rules.

It is possible to choose a few objects from Life (e.g. a few spaceships and oscillators). Then for every rule one can write down which of the chosen objects evolve in exactly the same way, which evolve in "essentially the same" way (e.g. pentadecathlon in B3/S238, copperhead/goldenhead in B37/S23, Gabriel's p138 in B3/S234c), and which evolve in a completely different way. If n objects from Life are chosen, there are up to 3^n possibilities. This is also cheap to compute, it can be written down concisely as a ternary string (after choosing three symbols and an ordering of the n objects), and it might be useful for someone who decides to use this as a classification scheme to quickly know which rules support which objects.
127:1 B3/S234c User:Confocal/R (incomplete table of INT rules)
Unlikely events happen.
My silence does not imply agreement, nor indifference. If I disagreed with something in the past, then please do not construe my silence as something that could change that.