Here's the writeup I mentioned yesterday, that could be a starting point for a LifeWiki page. Existing uses of "transition" could link to this explanation.
Now is not necessarily the right time to add a page like this to the LifeWiki -- I'm happy to continue the discussion as long as there seem to be new things to discuss.
The idea here is that,
if the existing uses of "transition" are retained in the two dozen or so LifeWiki pages where they're currently found,
then it seems as if any potential confused readers might benefit from having a quick obvious link on the first use of "transition" in each of those pages, to explain the intended meaning.
This is my first shot at an explanation along those lines. No doubt it could be made clearer and more succinct in all sorts of ways -- succinctness is admittedly not my strong suit. Feedback is welcome!
One idea that might be helpful is to have the name of the LifeWiki page be something like
transition (CA rule), rather than just plain
transition. Again, the goal is to have some easy location to link to, when the term "transition" is being used in this way.
EDITed slightly (bold red text) to address
confocaloid's point about "transition rule". I think the common meaning of "transition" does indeed derive from the longer phrase "transition rule" -- it's just that it has now become rather awkward and confusing to use "transition rule", because just the one word "transition" is now the more common usage.
EDIT2: Reworded the paragraph that now says "Note that..." in red, to simplify the point about standard English vs. the technical definition.
EDIT3: slightly simplified some wording in the example sections, e.g., removing an unnecessary "respectively".
EDIT4: changed order of "transition rule" and "transition" in definition; added some suggested wording from confocaloid (in
purple).
EDIT5: confocaloid has objected to my calling this "suggested wording from confocaloid" -- here's the
text I was working from, with some further explanation.
EDIT7: Added note about variables in Golly rule tables (after the purple text). I'm thinking it might be confusing to dive too deep into this subject, and possibly it will be simpler not to mention rule tables at all. Additional subtleties include the fact that the symmetry setting in a rule table will change the number of transitions that can be defined line-by-line in a rule table -- "permute" symmetry corresponds with the set of 18 outer-totalistic transitions, whereas "rotate4reflect" symmetry corresponds to the set of 102 isotropic transitions.
EDIT8: Added a couple of section headings for organizational purposes.
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A '''transition rule''' (or, in common usage, often simply '''transition''') is the elementary unit of a cellular-automaton [[rule]] definition. Every non-trivial CA rule is made up of one or more transitions. Each transition is a combination of a '''condition''' plus an action that should be taken if the condition is met.<ref="post172264" />
==Example for outer-totalistic rules==
The standard [[rulestring]] for Conway's Life is "B3/S23". This is a slightly abbreviated encoding of the three [[outer-totalistic]] transitions that make up the Life rule -- "B3" (birth when there are three neighbors), "S2" (survival when there are two neighbors), and "S3" (survival when there are three neighbors).
For the "B3" transition, the "3" specifies the three-neighbors condition, and the "B" describes the action (birth of a new ON cell, or equivalently the change of a cell state from 0 to 1) that will happen when that condition is met.
Note that the action is not always a "transition" in the standard English-language definition of the word. For example, births involve cells that actually change from state 0 to state 1, but surviving cells simply remain unchanged in state 1.
A rule such as "B3/S23" is assumed to provide instructions for all possible situations that can arise -- including all transitions complementary to the stated transitions:
* if there's no matching condition that says a cell will be born, the cell will not be born: it will start in state 0 and end in state 0, a transition sometimes known as "stagnation" or "abstain" (abbreviation 'A').
* If there's no matching condition that says a cell will survive, the cell will die (abbreviation "D".)
Thus Conway's Life rules could theoretically be written as "A01245678/D0145678", but not surprisingly the simpler "B3/S23" is almost universally used instead.
==Example for isotropic rules==
Rulespaces other than outer-totalistic "Life-like" rules have different sets of elementary transitions. For [[isotropic]] rules, for example, there are 102 elementary transitions that subdivide the 18 outer-totalistic ones. The size of a CA rulespace depends on the number of elementary transitions making up that rulespace; thus there are 2<sup>18</sup> outer-totalistic Life-like rules, but 2<sup>102</sup> possible isotropic rules.
* "S2" can be subdivided into S2c, S2e, S2k, S2a, S2i, and S2n [[Hensel notation|isotropic transitions]]
* "B3" can be subdivided into B3c, B3e, B3k, B3a, B3i, B3n, B3y, B3q, B3j, and B3r
* "S3" can be subdivided into S3c, S3e, S3k, S3a, S3i, S3n, S3y, S3q, S3j, and S3r
So the standard Conway's Life rule could non-canonically be written as "B3cekainyqj/S2cekain3cekainyqj", explicitly listing all of the isotropic transitions that make up the rule.
==Transition definitions in lines of Golly rule tables==
The main part of a Golly ruletable can be read line-by-line, with each line defining a transition, especially if no variables are used. Variables are often defined in an earlier section of the rule table, which can allow multiple elementary transitions to be defined in a single line. See the [[RuleLoader]] article for more information and further references.
== Similar terms==
In common usage, a reference to an isotropic transition such as "B3j" may equally well use the word "condition" instead, often with a modifier -- "birth condition" or "survival condition". It's correct to use either 'condition' or 'transition' to refer to the elementary units of a rulestring.<ref="post172264" />
==See also==
[[Transition (disambiguation)]]
<references>
<ref name="post72264">{{LinkForumThread
|format = ref
|title = Re: Next steps on getting back to normal editing for OCA:tlife
|p = 72264
|author = Adam P. Goucher
|date = November 30, 2023
}}</ref>
</references>
