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This isn't a new terminology per se, but I'll give my own viewpoint on the definition of a gliderless gun.

A gliderless gun is a gun where there is no component firing gliders, that the rest of the pattern could be removed so that the pattern becomes a pure glider gun. This is to exclude things that just happen to fire a stray glider and are just eaten. Obviously, this probably weaker than some would like (herschel loops even with obvious gliders get included, and an H-to-MWSS would even be allowed), but it nicely excludes the sort of "stray gliders for 3 generations" thing, and maybe a nice jumping-off point to make the gliderlessness more strong.

I just realized, right now we could just have a herschel track shooting gliders and going into a syringe-f119 contraption and then synthesise the spaceship using GLIDERS. Not the most optimal definition, I have to say..............

A 2-state cellular automaton has exactly two types of colour invariance: none (as in Life) and self-complement (as in Day and Night).

3-state CA admit four types of colour invariance, corresponding to the subgroups of the group of permutations on 3 elements up to conjugacy (so that 1<->2 and 1<->3 are the same):

• no symmetry at all (A, B, C all act on their own; 3-state hexagonal INT has 3^276 rules)

• charge-symmetry (swapping A for B is an invariant of the rule, C acts on its own; 3-state HINT has 3^132 rules)

• isocyclicity (swapping colours along the cycle A->B->C->A is an invariant of the rule; 3-state HINT has 3^92 rules)

• isostaticism (swapping A, B, C for any permutation of A, B, C is an invariant of the rule; 3-state HINT has 3^40 rules)

The number of invariances in four states is 11, in five is 19, etc.

Possible Additions to the wiki:

Complex:

• 50000+ Population

• 400+ Generation Lifespan

Dead Patterns:

• Patterns that will result with nothing

True Dead Patterns:

• Same as Dead Patterns

• Cells have to been joined or affecting each other

SeaKrait wrote: August 13th, 2026, 5:45 am

Complex

Why these numbers? You can pick any numbers for the job.

Dead Pattern
True Dead Pattern

Diehards

Modifying B468S02357's term "omnispeedic".
I think "omnivelocious" sounds nicer.
A rule is omnivelocious if every velocity for every slope in the rule can be proven to either exist or not exist.
A slope in a rule is omnivelocious if every velocity for that slope in the rule can be proven to either exist or not exist.

A simple gun is a gun that just uses multiple copies of oscillators and other stable patterns to create the necessary reactions. (example: Maximum volatility gun)

A complex gun, on the other hand, uses more niche technology, like conduits and over-unity reactions, to influence the reactions in the right way to make the spaceship stream (example: New gun 2, Simkin glider gun, maybe even the Gosper Glider Gun).

Strictness: the proportion of cells in a period n oscillator that oscillate with period n to cells which change state at some point during its period.

Omniorthogonal: a rule that is omniorthogonal can be proven to have every orthogonal speed that exists or doesn’t exist.
Omnidiagonal: literally the same but with diagonals.
Omnicomplementary: if a rule is SOMEHOW complementary on vacuum,antivacumm,checkerboard,stripes,periodic agars and more.
Bulkscillator: an oscillator that couldn’t really have much uses.
Bulkship: a spaceship that couldn’t really have much uses.
Relativistic tachyon: a tachyon that’s speed lies in between either c and 2c,2c and 3c,and so on.

Primitive: An object in an INT rule with only one number and letter combo(A rule like b2cs) for example.
Compound: An object in an INT rule with two of the number and letter combo. Like b2ces or b2cs3e

The opacity of an object is the frequency (absolute, not class) of an object, divided by the number of rotations/reflections it has (and divided again by the period if it's an oscillator). (If you take the inverse, it's easier to comprehend, so we'll do that).

For life, which has a well-defined set of frequencies, I'll calculate opacity directly:
For instance, the block is one out of every ~2 objects, and has one form, so it has an opacity of 2.
The beehive is 1/3.8, but has two forms; it has an opacity of 3.8*2 -> 7.6.
The loaf is 1/12.9, has eight forms, so has an opacity of 103.2.

This is easier to see in a different rule. For instance, in TTs, the loaf is the most common still life (it occurs 12 billion times), but it has 8 transformations. The pond, which occurs 4.5 billion times, only has one. I'm trying to figure out how to calculate this clearly but my head is fuzzy right now, so I'm going to calculate the relative opacity:
Loaf is 2.7 times more common than pond
Loaf has 8 times more forms than pond
Therefore, loaf has an opaqueness around 3 times higher than pond.

The higher an object's opaqueness is, the less likely it is to be involved in a transparent reaction.

someone plz help formalize

A rule is pseudo-omniperiodic if it has an oscillator for every period that is not ruled out by the following simple constraints:

• An oscillator's period must be a multiple of the background period (this rules out odd-period oscillators in B0 rules)
  An oscillator's period must be a period in which it is possible for any cell to change according to transitions in the rule and return to its original state (this would apply to Generations rules)

erictom333 wrote: October 18th, 2026, 8:58 am A rule is pseudo-omniperiodic if it has an oscillator for every period that is not ruled out by the following simple constraints:

• An oscillator's period must be a multiple of the background period (this rules out odd-period oscillators in B0 rules)
  An oscillator's period must be a period in which it is possible for any cell to change according to transitions in the rule and return to its original state (this would apply to Generations rules)

I had a similar concept to this lying around in my head for a while, but didn't feel the need to post it. Mine goes as follows:
A rule is quasi-omniperiodic if for any period, there exists an oscillator that contains at least one cell of that period.