To be able to compare two different cellular automata for "similarity", one would need a clear definition of similarity.
For example, if you evolve many soups in B3/S23 (Conway's Life) and keep track / count how often every isotropic 3-by-3 condition occurs during the evolution, then the condition "S4c" unambiguously would be the least frequent condition, for many reasonable choices of parameters:
Code: Select all
1 0 1
0 1 0
1 0 1
Likewise, one could repeat measurements (evolving many soups and measuring frequencies of 3-by-3 conditions) for B3/S234c, and again observe that "S4c" is the least frequent condition for many reasonable choices of parameters.
The above reasoning suggests that B3/S234c can be said to be "the most similar ruleset to" B3/S23, within the space of all two-state isotropic CA with range-1 Moore neighbourhood.
However, B3/S234c is actually very different from B3/S23 in another sense:
- Switch engine based technology no longer works in B3/S234c. (Contrast with B3/S236e, where switch engine based technology does exist.)
- The sparky alien p62 oscillator doesn't exist in Conway's Life, and can be used for a p62n stationary technology; this can be compared to p30n and p46n technologies in Conway's Life.
- "Checkerboard still lives" exist in B3/S234c, but not in Conway's Life. (3-by-n and 4-by-n checkerboard still lives are glider constructible for all n >= 2. I don't know much about constructibility of wider checkerboards.)
WhiteHawk wrote: November 7th, 2024, 7:49 pm Guess this is a change of topic from the previous discussion, but kind of a silly question which I have been brewing over: which Outer-totalistic/Isotropic non-totalistic rulespace is the most similar to life (In terms of the commonness of patterns, spaceships, evolutions of common sequences, etc.)? I have a suspicion that it's Conway++, but won't discount Pedestrian Life or some other variant.
Edit: Also, what would it take to take advantage of Pedestrian Life's numerous infinite growth patterns to construct some sort of alien universal constructor - or at least make universal constructor(s) in other rules?
b-engine wrote: November 7th, 2024, 9:13 pmUniversal constructors exist in OCA, but you'll need more components to make one:WhiteHawk wrote: November 7th, 2024, 7:49 pm Edit: Also, what would it take to take advantage of Pedestrian Life's numerous infinite growth patterns to construct some sort of alien universal constructor - or at least make universal constructor(s) in other rules?
- Reflectors.
- Common spaceship reactions (to actually construct things).
Or optionally (for universal computer):
- Recipe (of spaceship reactions).
- Logic gates.
- Diagram (of the computer).