Marriage

[Pooping_Alien]

But in plain Marriage only TWO dots follow the couple to form a stable pattern. In its G-variants, it is the spacetakers (dying cells) that provide the boundary stabilization! Just watch a domino evolve in plain and G-variants to see the difference. The boundary piece with all its dying generations IS an "extension".

Sure, it certainly is an extension ("attachable part") only in Generations rules, this was about defining connectedness.

Consider these two patterns:

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x = 29, y = 4, rule = /2/3
AB21.AB$AB21.AB$2.AB21.AB$4.AB21.AB!

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x = 49, y = 4, rule = /2/23
ABCDEFGHIJKLMNOPQRSTUV.ABCDEFGHIJKLMNOPQRSTUV$ABCDEFGHIJKLMNOPQRSTUV.
ABCDEFGHIJKLMNOPQRSTUV$2.ABCDEFGHIJKLMNOPQRSTUV.ABCDEFGHIJKLMNOPQRSTU
V$4.ABCDEFGHIJKLMNOPQRSTUV.ABCDEFGHIJKLMNOPQRSTUV!

Of course, if you count all non-vacuum cells, the 2nd is connected and the 1st is not. The question is, should we count them? They're essentially the same pattern (two independant spaceships).

Then again, since a pattern can influence another even without being connected to it (eg. MWSSs spaced with their noses 5 cell apart will suppress each other's belly sparks), and a pattern can also be connected to another without influencing it (two jams can be placed so that their sparks end up connected diagonally, but this is just as mortal as the dots by themselves; also eg. shiptie), I don't really see connectedness as a particularly useful concept in CA anyway. So maybe I'll stop trying to define a "useful" version of "connected" and leave it at the bare facts about these "ants": non-vacuum cells are connected; live (state 1) cells are not connected.

ANd, just realized that S2 is really self-destructive, so without Generations it's basically Seeds.

Yeah, Generations makes a huge difference in the "structuredness" of most B2 rules. It forces dominos to have "tails", and therefore every pattern based on it must leave more space behind, and therefore there are fewer chaotic puffers and more spaceships, as well as more room for objects to remain distinct rather than coalescing into chaos. And yes, the stable slope-2 "wings" also contribute similarly.

In 23-state, it is NOT connected in the sense I meant, both parts survive on their own.

[Tropylium]

In 23-state, it is NOT connected in the sense I meant, both parts survive on their own.

So you seem to mean something like a "connected as a component" here. But once you start tracking interaction rather than the bare locations of cells (which would be the usual definition of "connected"), non-symmetric interaction becomes an issue, and you can't treat "connected" as a transitiv relation anymore. An "extension" is in this sense connected to its front part, but yet the front part is not connected to the extension.

This is of course exactly what MAKES it an extension rather than a wing, so what do you actually gain by this new sense of "connected"?

[chineseman]

my smallest spaceship:

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x = 11, y = 6, rule = 2/2/4
8.2A$2.2A4.2B$.A2B3.A2C$2.2BA2.B$.B.C.A.C$.C2.B!