Some thoughts about formalism (or lack thereof)
I like to distinguish between cells and their states. I think the distinction is helpful. I believe making the distinction between cells and their states visible improves clarity. (For example in CGoL, a cell may be dead or alive, or the cell's current state may be unspecified/unknown.)
As a consequence, I like to distinguish between (1)
the neighbourhood of a cell and (2)
a specific 3x3 configuration (a specific assignment of current states to the neighbours).
In CGoL, the neighbourhood of every cell is always the
Moore neighbourhood, no exceptions; and it always includes precisely eight other cells.
Although there are many possibilities for the assignment of states to those cells. There are 512 possible 3x3 configurations. How many "essentially different" possibilities of course depends on how exactly one decides to count them and what "essentially different" means. This leads to the concept of an
equivalence relation, as in "these two 3x3 configurations are equivalent
up to rotations and reflections".
- For Life-like cellular automata, this naturally leads to the 18 equivalence classes of 3x3 configurations (two possibilities for the middle cell times 9 possibilities for the number of alive neighbours).
- For isotropic not-necessarily-outer-totalistic two-state CA with Moore neighbourhood, this leads to 102 equivalence classes of 3x3 configurations (two possibilities for the middle cell times 51 possibilities for its "current environment").
- For arbitrary two-state CA with Moore neighbourhood, this leads to 512 equivalence classes, each of which contains only one 3x3 configuration.
At different time in CA-related discussions (including these forums and "external" discussions), people were referring to (what amounts to) such equivalence classes of 3x3 configurations as 'conditions'. I like this choice of wording, and I unambiguously prefer this wording, because it matches the intuition. Indeed, in a phrase such as "the condition of a cell", the word 'condition' reads as "the circumstances or factors affecting the cell". This reading correctly matches the underlying idea. Saying that
a cell is currently dead and has precisely three alive neighbours does in fact tell "the circumstances or factors affecting the cell".
Of course it is also shorter to write "the condition of a cell" instead of "the equivalence class of 3x3 configurations to which the cell's 'current environment' belongs", but that isn't the primary advantage. (I would accept long verbose wording, if it was clearer and more intuitive compared to one or two words.)