With that in mind, here's a proposal for some fairly simple (in concept) but rigorous classes which cellular automata can be filtered into:
- Unbounded Omnikinetic (Class 1): Spaceships exist for all rational velocities ≤ c. No 'Life-like' rule that is not "B0 without S8" is able to qualify for this title as all B1 rules explode and B2 rules have an upper limit of c/2 diagonal for any expansion. I don't know if any CA exist in this class. Technically not unbounded as lightspeed is the boundary.
- Class 2: Not sure what to call this one. Like Class 1, except spaceships do not exist for all rational velocities with at least 1 of the orthogonal components equal to c.
- Bounded Omnikinetic or Omnikinetic (Class 3): Infinitely many velocities exist, and if each velocity (h,k)c/p (with at least one of h,k co-prime with p) is plotted at the coordinate (h/p, k/p), then spaceships exist at all rational velocities on or within the convex hull of all extant velocities.
- Limit Omnikinetic (Class 4): Like Class 3, but not all rational velocities on the convex hull are possible. CGoL is probably Class 4 (unless by some miraculous feat it turns out it is Class 3).
- Class 5: Not all velocities within the velocity limit are possible, but infinitely many do still exist.
- Finite (Class 6): Only a finite number of velocities are possible.
For example, it's possible that there is some CA rule that is class 3 but has no parametric solutions for finding velocities at all... Such a rule would extremely likely be impossible to prove as being class 3...
TL;DR: This post discusses possible spaceship-based analogues of omniperiodicity and ways to describe rules based on allowed velocities.