Marriage

[Pooping_Alien]

Marriage is a group of 3 rules: 2/2, 2/2/3 and 2/2/4 (longer histories tend to be less interesting).
In 3- and 4-state versions of the rule, a domino becomes a growing diamond with two c p1 corners and two c/2 p2 corners and firm boundaries. In same versions, if rears of all 3 parts of an "ant" (as in "ants" of GoL) are changed into G2, the ant becomes a C P1 spaceship.
What did you discover in Marriage and its history-enabled counterparts? Have you heard of this rule family before?
Marriage - rulestring 2/2
Marriage: Living with Parents (2/2/3)
Marriage: Living with Grandparents (2/2/4)
Of the three, LWP is my favorite, but LWG has lower density of patterns, especially within a "diamond".

[Hektor]

(2/2/3)
From this basic spaceship (just like in Brian's Brain),

Code: Select all

x = 6, y = 4, rule = 2/2/3
4.AB$2.AB$AB2.AB$AB!

I found some rakes:

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x = 11, y = 31, rule = 2/2/3
$4.AB$2.AB2.A$AB2.AB.A$AB4.AB10$6.AB$4.AB$2.AB.2A$AB2.AB$AB3.AB9$4.AB
.2A.A$2.AB2.BA.A$AB2.AB2.B$AB!

Also this double spaceship:

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x = 4, y = 8, rule = 2/2/3
.AB$2A$AB3$AB$2A$.AB!

--------------
(2/2/4)
From this reaction:

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x = 3, y = 8, rule = 2/2/4
.A$A2B$A2B3$A2B$A2B$.A!

I found two stable patterns:

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x = 6, y = 30, rule = 2/2/4
.A$A2B$A2B3$2.ABC$ABC$ABC$2.ABC3$A2B$A2B$.A7$.A$A2B$A2B2$3.ABC$3.ABC
2$A2B$A2B$.A!

and another rake:

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x = 4, y = 10, rule = 2/2/4
.A$A2B$A2B$2.2A3$2.2A$A2B$A2B$.A!

I do prefer LPG, because of its stability, but also LPW has some nice features!

[Tropylium]

LWP has a nifty p9:

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x = 5, y = 5, rule = 2/2/3
.A.A$2A.2A2$2A.2A$.A.A!

eta: another small p4 twinship from LWG:

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x = 7, y = 8, rule = 2/2/4
3.CA$4.2BA$C3.C2A3$C3.C2A$4.2BA$3.CA!

also this fairly general method of constructing rakes/puffers/sparky ships in X/2/3 or X/2/4 still works:

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x = 34, y = 18, rule = 2/2/4
6.2A11.2A$6.2B11.2B10.2A$5.A2CA9.A2CA9.2B$5.B2.B9.B2.B8.A2CA$4.AC2.C
8.AC2.C8.B2.B$4.B12.B11.AC2.C$3.ACA10.ACA10.B$3.B.B10.B.B9.ACA$2.ACAC
9.ACACA8.B.B$2.B12.B3.B7.ACACA$.ACACA8.ACACACA6.B3.B$.B.BAB8.B.BAB.B
5.ACACACA$A12.ACA.A.ACA4.B.BAB.B$B12.B7.B3.ACA.A.ACA$C11.ACA5.AC3.B7.
B$12.B.B5.B4.CA5.AC$12.C.C5.C5.B5.B$13.B12.C5.C!

[Hektor]

Four spaceships and two rakes generated by spacing two basic pieces: (on the left side there's the number of spaces)

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x = 12, y = 97, rule = 2/2/4
11.A$3C7.A$C.C7.A$C.C7.A$C.C7.A$3C8.A4$11.A$10.A$.C8.A$2C$.C8.A$.C8.A
$3C8.A4$11.A$10.A$10.A$.C$C.C$2.C7.A$.C8.A$3C8.A4$11.A$10.A$10.A2$2C$
2.C$.C8.A$2.C7.A$2C9.A4$11.A$10.A$10.A3$C$C$2C8.A$3C7.A$.C9.A4$11.A$
10.A$10.A4$3C$C$3C7.A$2.C7.A$2C9.A4$11.A$10.A$10.A5$3C$C$3C7.A$C.C7.A
$3C8.A4$11.A$10.A$10.A6$3C$2.C$.2C7.A$2.C7.A$2.C8.A!

Increasing to more than seven cells the space between them, you need another spaceship to stabilize the reaction:

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x = 20, y = 56, rule = 2/2/4
14.A$13.A$13.A4$15.ABC$15.ABC2$4.3C$4.C.C$4.3C6.A$4.C.C6.A$4.3C7.A5$
14.A$13.A$13.A2$17.ABC$17.ABC2$16.ABC$16.ABC2$17.ABC$.C2.3C10.ABC$2C
2.C.C$.C2.C.C6.A$.C2.C.C6.A$3C.3C7.A5$14.A$13.A$13.A4$15.ABC$15.ABC3$
15.ABC$15.ABC2$.C3.C$2C2.C.C$.C4.C6.A$.C3.C7.A$3C.3C7.A!

Also no sign of diagonal or non-p2 spaceships...

[knightlife]

Non-symmetrical case yields rakes:

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x = 135, y = 23, rule = 2/2/4
55.CBA$55.CBA$122.CBA$122.CBA4$.CB.A58.CB.A56.2A$3.2BA59.2BA55.2B$2.C
2BA58.C2BA54.A2CA5.BA$.C2A59.C2A56.B2.B5.2C2A$122.C2.C.A4.B2A$126.2A
2.CA.A$123.ABACACB2A$C2A59.C2A57.CAC$.C2BA58.C2BA53.CABA.AC4A$2.2BA
59.2BA53.B4.AB2.CA.A$CB.A58.CB.A53.A.C2.C.A4.B2A$119.A2B2.B5.2C2A$
119.C2B2C6.BA$57.CBA56.CBA.C2A$57.CBA58.CB2.CBA$122.CBA!

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x = 7, y = 12, rule = 2/2/4
2.CB.A$4.2BA$3.C2BA$2.C2A5$C2A$.C2BA$2.2BA$CB.A!

edit:

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x = 63, y = 12, rule = 2/2/4
CB.A30.CB.A20.CB.A$2.2BA31.2BA21.2BA$.C2BA30.C2BA20.C2BA$C2A31.C2A21.
C2A2$2.2A$2.B2A$2.2CBA52.2A$5.C2A25.C2A22.2BA$5.2BA26.C2BA21.2CBA$4.C
A29.2BA21.2C2A$33.CB.A21.C.BA!

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x = 84, y = 39, rule = 2/2/4
CB.A72.CB.A$2.2BA73.2BA$.C2BA72.C2BA$C2A73.C2A2$2.2A74.2A$2.B2A73.B2A
$2.2CBA72.2CBA$5.C2A73.C2A$5.2BA73.2BA$4.CA74.CA$57.CBA$57.CBA$55.CBA
15$4.CA74.CA$5.2BA73.2BA$5.C2A73.C2A$2.2CBA72.2CBA$2.B2A73.B2A$2.2A
74.2A2$C2A73.C2A$.C2BA72.C2BA$2.2BA73.2BA$CB.A72.CB.A!

[Hektor]

Infinite basic spaceship can be stacked upon all the reactions found before! (sometimes with minimal changes)

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x = 44, y = 47, rule = 2/2/4
7.A$6.2BA$5.C2BA$4.C2A2$.CBA$2.CBA$CBA.CB.A$6.2BA$5.C2BA33.A$4.C2A34.
2BA$40.C2BA$39.C2A$4.C2A15.A$5.C2BA12.2BA12.CBA$6.2BA11.C2BA13.CBA$7.
A11.C2A13.CBA.CB.A$41.2BA$16.CBA21.C2BA$17.CBA19.C2A$15.CBA.CB.A$21.
2BA12.CBA$20.C2BA13.CBA$19.C2A13.CBA.CB.A$41.2BA$16.CBA21.C2BA$17.CBA
19.C2A$15.CBA.CB.A$21.2BA12.CBA$20.C2BA13.CBA$19.C2A13.CBA.CB.A$41.2B
A$40.C2BA$19.C2A17.C2A$20.C2BA$21.2BA12.CBA$22.A14.CBA$35.CBA.CB.A$
41.2BA$40.C2BA$39.C2A3$39.C2A$40.C2BA$41.2BA$42.A!

Some other examples:

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x = 56, y = 41, rule = 2/2/4
54.A$53.2BA$52.C2BA$51.C2A2$48.CBA$49.CBA$47.CBA.CB.A$53.2BA$52.C2BA$
51.C2A$7.A23.A$6.2BA21.2BA15.CBA$5.C2BA20.C2BA16.CBA$4.C2A21.C2A16.CB
A.CB.A$53.2BA$.CBA21.CBA24.C2BA$2.CBA21.CBA22.C2A$CBA.CB.A16.CBA.CB.A
$6.2BA21.2BA$5.C2BA20.C2BA$4.C2A21.C2A2$51.C2A$52.C2BA$.CBA24.C2A22.
2BA$.CBA25.C2BA14.CBA.CB.A$30.2BA16.CBA$24.CBA.CB.A16.CBA$26.CBA$4.C
2A18.CBA23.C2A$5.C2BA43.C2BA$6.2BA19.C2A22.2BA$7.A21.C2BA14.CBA.CB.A$
30.2BA16.CBA$31.A16.CBA2$51.C2A$52.C2BA$53.2BA$54.A!

Even with one of the asymmetricals:

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x = 10, y = 19, rule = 2/2/4
5.CB.A$7.2BA$6.C2BA$5.C2A5$4.C2A$5.C2BA$6.2BA$CBA.CB.A$2.CBA$.CBA2$4.
C2A$5.C2BA$6.2BA$4.CB.A!

[knightlife]

Glider collision produces natural backrake in 2/2/3:

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x = 58, y = 21, rule = 2/2/3
48.2B$48.2A12$56.AB$56.AB2$10.AB$4.AB2.BA.B$2.AB.2A2.A.BA6.BA6.BA$AB
2.AB2.A.B.A3.BA.BA3.BA.BA$AB4.AB.AB6.BA6.BA!

[knightlife]

BTW the basic three cell pattern in 2/2/4 explodes but contains a binary count sequence

Code: Select all

x = 2, y = 3, rule = 2/2/4
.A$A$A!

Along the SW side of the explosion is a stable full row of puffers producing chaos, but along the NW side the row of puffers occasionally has gaps. If you wait long enough the gaps propagate along the edge, taking twice as long to move another step. Each gap could represent a "1" if counting up, or could represent a "0" if counting down. The counting continues on to infinity since more positions are created at the top of the explosion. The carry is kind of slow, so the LSB toggles before the ripple carry is done, but the count continues no problem.

[Tropylium]

Glider collision produces (…)

I believe the term for width-2 lightships is "photons".

[Hektor]

I believe the term for width-2 lightships is "photons".

Yeah, though I don't know if exists an official nomenclature for the Generations rulespace...

In 2/2/4, starting from this "tagalong" attached to the basic photons,

Code: Select all

x = 7, y = 4, rule = 2/2/4
4.CBA$CBA.CBA$A.CBA$CBA!

I found three rakes (one of them is continuous):

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x = 13, y = 38, rule = 2/2/4
10.CBA$2.CBA5.CBA$CBA.CBA.CBA$4.A.CBA$4.CBA$2.CBA10$10.CBA$6.CBA.CBA$
6.A.CBA$2.CBA.CBA$2.A.CBA$2.CBA$CBA10$2.CBA$4.CBA3.CBA$2.CBA.CBA.CBA$
6.A.CBA$6.CBA$4.CBA$2.CBA!

And an eating spaceship for each one (the continuous' one is really strange):

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x = 50, y = 66, rule = 2/2/4
2.CBA$2.CBA42.CBA$CBA36.CBA5.CBA$37.CBA.CBA.CBA$41.A.CBA$41.CBA$39.CB
A14$2.CBA42.CBA$2.CBA38.CBA.CBA$CBA40.A.CBA$39.CBA.CBA$39.A.CBA$39.CB
A$37.CBA14$38.CBA$40.CBA3.CBA$38.CBA.CBA.CBA$42.A.CBA$42.CBA$40.CBA$
38.CBA17$14.CBA$16.CBA$16.CBA!

Also I built a reaction that "cleans" a rake signal:

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x = 67, y = 32, rule = 2/2/4
55.CBA$57.CBA3.CBA$55.CBA.CBA.CBA$59.A.CBA$59.CBA$57.CBA$55.CBA7$64.C
BA$60.CBA.CBA$60.A.CBA$56.CBA.CBA$56.A.CBA$CBA53.CBA$CBA51.CBA6$5.CBA
56.CBA$.CBA.CBA52.CBA.CBA$.A.CBA54.A.CBA$.CBA52.CBA.CBA$56.A.CBA$56.C
BA$54.CBA!

[Wojowu]

Three cell chaotic growth pattern looks a bit like failed replicator

[Hektor]

Three cell chaotic growth pattern looks a bit like failed replicator

Yes, the chaos in 2/2/4 is (nearly) always based on this "replicating" spaceship:

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x = 5, y = 4, rule = 2/2/4
2.ABC$2AC$A2B$2.AC!

Found also a Sierpinski pattern

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x = 2, y = 577, rule = 2/2/4
2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$
2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$
2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$
2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$
2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$
2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$
2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$
2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$
2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A4$2A!

EDIT:
Another beautiful Sierpinski pattern, with filled triangles (too bad it's chaotic in the end...)

Code: Select all

x = 3, y = 769, rule = 2/2/4
3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$
3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$
3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$
3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$
3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$
3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$
3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$
3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$
3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$
3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$
3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$3A4$
3A4$3A4$3A4$3A4$3A4$3A!

[Pooping_Alien]

ound also a Sierpinski pattern

Weird! Instead of plain debris, those are laid out in spaceships?!?
And, there are no "tagalongs". Most (if not all) technology is built from "branching" of the "boundary". And, I call the width-2 ships in LWP/LWGP "bullets" or "photons". And, I knew of various branch-based "period" effects, it's even possible to build a glide-symmetric p2 spaceship using tne p2 "branch" you showed as the starting point.

Also no sign of diagonal or non-p2 spaceships...

Code: Select all

x = 13, y = 12, rule = 2/2/4
CBA$A.CBA$.B2.CBA$C.AB2.CBA$4.CBA.CBA$10.CBA$10.CBA$4.CBA.CBA$C.AB2.C
BA$.B2.CBA$A.CBA$CBA!

Or glide-symmetric:

Code: Select all

x = 15, y = 12, rule = 2/2/4
2.CBA$2.A.CBA$3.B2.CBA$2.C.AB2.CBA$6.CBA.CBA$12.CBA$12.CBA$6.CBA.CBA$
2.ABC.A.CBA$.BC.A.CBA$C.A.CBA$2.CBA!

[Wojowu]

Sierpiński triangles are often arising in many rules. Also, this spaceship

Code: Select all

x = 6, y = 8, rule = 2/2/4
.B2CB$C.2A.C$B.2A.B$AC2.CA$.B2.B$.A2CA$2.2B$2.2A!

can be considered as this spaceship with tagalong

Code: Select all

x = 6, y = 7, rule = 2/2/4
C4.C$B4.B$AC2.CA$.B2.B$.A2CA$2.2B$2.2A!

[Tropylium]

this spaceship

Code: Select all

x = 6, y = 8, rule = 2/2/4
.B2CB$C.2A.C$B.2A.B$AC2.CA$.B2.B$.A2CA$2.2B$2.2A!

can be considered as this spaceship with tagalong

Code: Select all

x = 6, y = 7, rule = 2/2/4
C4.C$B4.B$AC2.CA$.B2.B$.A2CA$2.2B$2.2A!

Or it might be considered the wings of one spaceship perturbing another. The back part is not dependant on the front for propulsion:

Code: Select all

x = 8, y = 11, rule = 2/2/4
.2C2.2C$.2B2.2B2$2.B2CB$.C.2A.C$.B.2A.B$.AC2.CA$2.B2.B$2CA2.A2C$2B4.
2B$2A4.2A!

[Hektor]

Well, I'm not an expert of life lexicon so forgive me for my inaccuracies...

Also no sign of diagonal or non-p2 spaceships...

Sorry! What I meant to say was lightspeed spaceship. I know of the c/4 "butterfly" in Brian's Brain, so maybe there is a similar one (more likely in 2/2/3).

[Wojowu]

Code: Select all

x = 4, y = 4, rule = 2/2/3
2.B$3.A$BAB$.A!

Also works in this rule. I will make search for any other non-lightspeed ships

[Pooping_Alien]

Code: Select all

x = 4, y = 4, rule = 2/2/3
2.B$3.A$BAB$.A!

Also works in this rule. I will make search for any other non-lightspeed ships

Here's a collision of your "gliders" that produces an average "bounded diamond" pattern:

Code: Select all

x = 9, y = 6, rule = 2/2/3
2.B$2.2A$B.B4.A$.A4.B.B$5.2A$6.B!

Seeing how weird the local glider is, I'd imagine Marriage is too weird and too unstable to be of interest.

[Tropylium]

there are no "tagalongs". Most (if not all) technology is built from "branching" of the "boundary".

Well, the parts may be contiguous, but actually there's no interaction going forward from any cell, so in a sense it's rather that EVERY 2 or 3-cell "boundary" part is a tagalong.

[Pooping_Alien]

Every "boundary" piece is not a tagalong but an extension.
Chaos in 2/2/4 is, as someone here stated, based on a weird methuselah that is like a "burst of magma" in Golly's default gradient, so I called it "magmaselah". 2 magmaselahs can be turned into a spaceship:

Code: Select all

x = 5, y = 9, rule = 2/2/4
.CA$2.2BA$2.CBA$.B2A$AC.A$.B2A$2.CBA$2.2BA$.CA!

Practically, in LWGP, almost all reactions are based on photon/ant (boundary) and Magmaselah.
Generally, aside from the binary counter (again based on magmaselah), LWGP (2/2/4) should be less interesting than LWP (2/2/3). Generationless Marriage tends to go into over-simplified patterns.
In 2/2/4 (again), I discovered a sideways rake that emits "one-legged ants", and turned it into a spaceship based on side-rake output eater as seen in "eating spaceships" example:

Code: Select all

x = 65, y = 45, rule = 2/2/4
24.2A3.2A3.2A3.2A$23.2ABA.AB5ABA.AB2A$23.B2CABA2CA.A2CABA2CB$24.3C.3C
B.B3C.3C$23.CA2C.2CA.A.A2C.2CAC$24.2B3.B5.B3.2B$24.A2.C.2A.A.2A.C2.A$
26.BCB2.B.B2.BCB$27.A.2ACAC2A.A$30.B3.B$29.C5.C$29.B5.B$30.C3.C8$31.C
.C$32.B$24.ABC11.CBA$24.ABC11.CBA$26.ABC7.CBA8$14.ABC31.CBA$14.ABC31.
CBA$16.ABC27.CBA6$2A61.2A$2B61.2B$2CA.ABC51.CBA.A2C$2.B.ABC51.CBA.B$
2.C3.ABC47.CBA3.C!

[Tropylium]

Every "boundary" piece is not a tagalong but an extension.

I'm not sure what distinction you're trying to make here. Either way it's a question of pieces you can add or leave unadded with no difference to the parts in the front.

[Pooping_Alien]

Every "boundary" piece is not a tagalong but an extension.

I'm not sure what distinction you're trying to make here. Either way it's a question of pieces you can add or leave unadded with no difference to the parts in the front.

Tagalong/pushalong has, in at least one of its stages, a gap between it and the host ship Therefore, boundary pieces (123) are "extensions.
00123
12300
12300
00123
Two of those pieces turned into a single block is a "head" of almost every spaceship in LWGP.
0012
1200
1200
0012
LWP version.
Schick Engine is a tagalong, boundary piece is an extension.

[Tropylium]

Tagalong/pushalong has, in at least one of its stages, a gap between it and the host ship Therefore, boundary pieces (123) are "extensions".

Hm, I see. Personally, I'd retain the term "tagalong" as a term referring to both classes, and place the "extension/not extension" boundary at being disconnected in *all* phases (so while a Schick engine would still not be an "extension", a Coe ship for example would; at least I have generally not seen it considered a tagalong).

So in other words, this breaks down to four classes altogether (a cover term and three subclasses), not two:
• parts that can be added to a spaceship
— parts that are not connected to the mothership in any phase
— parts that are connected to the mothership in all phases
— parts that are connected in some phases, disconnected in others

On another note, I don't think consider the dying states of Generations necessarily count for the purposes of connectedness; they are incapable of "doing" anything else than taking space, so their neighborhood has a radius 0 in a sense. And the "ant" here is effectively the same spaceship as this one from Seeds (or for that matter, plain Marriage):

Code: Select all

x = 3, y = 4, rule = B2/S
o$2bo$2bo$o!

(Granted, the extension procedure doesn't work here, so here they're required "wing" parts, not extensions.)

[Pooping_Alien]

Tagalong/pushalong has, in at least one of its stages, a gap between it and the host ship Therefore, boundary pieces (123) are "extensions".

Hm, I see. Personally, I'd retain the term "tagalong" as a term referring to both classes, and place the "extension/not extension" boundary at being disconnected in *all* phases (so while a Schick engine would still not be an "extension", a Coe ship for example would; at least I have generally not seen it considered a tagalong).

So in other words, this breaks down to four classes altogether (a cover term and three subclasses), not two:
• parts that can be added to a spaceship
— parts that are not connected to the mothership in any phase
— parts that are connected to the mothership in all phases
— parts that are connected in some phases, disconnected in others

On another note, I don't think consider the dying states of Generations necessarily count for the purposes of connectedness; they are incapable of "doing" anything else than taking space, so their neighborhood has a radius 0 in a sense. And the "ant" here is effectively the same spaceship as this one from Seeds (or for that matter, plain Marriage):

Code: Select all

x = 3, y = 4, rule = B2/S
o$2bo$2bo$o!

(Granted, the extension procedure doesn't work here, so here they're required "wing" parts, not extensions.)

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".
ANd, just realized that S2 is really self-destructive, so without Generations it's basically Seeds. It is in Generations that S2 truly comes into action (watch a domino evolve in /2/3, /2/4, 2/2/3 and 2/2/4)

[Tropylium]

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:

Code: Select all

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

Code: Select all

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.