Spaceships in Generations Rules

[lemon41625]

Back in 2020, I started a database for ships within 3-state Generations rules (including B0 rules). Now, I've finally gotten back to maintaining it again. Initially, I was going to create this thread after I release cfind, but I have no clue when that will be. Regardless, since I've begun running systematic searches for ships in these rules, I think now would be a good time to create the thread.

The database itself can be found at https://raw.githubusercontent.com/jedli ... ers.db.txt and can be accessed via https://gliderdb-reader.vercel.app/ or Caterer on the Discord server.

Other than just showing which rules have ships and which don't, it would be interesting to try and look at what speeds of ships are allowed in each rule. When I was searching for ships, it does seem like in many rules, there are just some speeds which are impossible (i.e. the search terminates almost immediately even at large widths). For example, it seems like in Frogs, orthongonal speeds faster than c/5 are impossible.

I've managed to prove that in rules with no survival conditions, speeds of the form c/p are only possible if p = 1 or p > C where C is the number of states. It would be interesting to see more such proofs.

Another goal would be to try and prove the existence / non-existence of ships in all rules with B2. We are actually already quite close to this goal, thanks to the following rather versatile ships.

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#C (0, 1)c/1
#C Min Rule: /2/3
#C Max Rule: 02345678/2345678/3
x = 1, y = 1, rule = 0/2/3
2B$2A!

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#C (0, 2)c/3
#C Discovered by: Lemon41625, 2020
#C Min Rule: 1/2/3
#C Max Rule: 145678/245678/3
x = 2, y = 1, rule = 1/2/3
BAB$.A!

So there aren't that many more rules to be looked at. I've been conducting some systematic searches for 2c/3s in 13/2/3 - 1345678/245678/3 and recently, LaundryPizza03 managed to find some p4 photons in 12/2/3 - 12678/2678/3.

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#C (4, 0)c/4
#C Discovered by: LaundryPizza03, 2024
#C Min Rule: 12/26/3
#C Max Rule: 12678/2678/3
x = 24, y = 20, rule = 12/26/3
3.B3.B6.B9.$2.A5.A15.$2A3.A2.B9.B5.$2A2.3A3.2A7.A4.$.A3.B.7A2.B2.B4.$.2A
2B.2A4.2A10.$2.B2.2A.B5.2A8.$A2B.2A8.2BA2.A4.$A2B.A8.3B2.A.A2.B$.A.2A6.
A2B2.2B2.A3.$.A.2A6.A2B2.2B2.A3.$A2B.A8.3B2.A.A2.B$A2B.2A8.2BA2.A4.$2.
B2.2A.B5.2A8.$.2A2B.2A4.2A10.$.A3.B.7A2.B2.B4.$2A2.3A3.2A7.A4.$2A3.A2.
B9.B5.$2.A5.A15.$3.B3.B6.B!

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#C (4, 0)c/4
#C Discovered by: LaundryPizza03, 2024
#C Min Rule: 12/2/3
#C Max Rule: 1278/278/3
x = 37, y = 20, rule = 12/2/3
2.A.B25.A.B.A2.$2.4B2.B21.5B2.$A2B2.5B18.A2B3.2BA$A2B.A.B2.2BA12.B3.A.B
3.2B.$.A.A3.A.2B12.A7.B2.2B.$8.3B.B.A6.2A7.A2B.2B.$9.6B6.2A2.A3.A2.A.2B
.$7.A2.B3.2B.A4.2A.2B2.2A3.2B.$7.BA.A2.2B.3A3.A.2B2.3A3.2BA$5.A2B.A.2B
.2A2.2A2.A2B9.B2.$5.A2B.A.2B.2A2.2A2.A2B9.B2.$7.BA.A2.2B.3A3.A.2B2.3A3.
2BA$7.A2.B3.2B.A4.2A.2B2.2A3.2B.$9.6B6.2A2.A3.A2.A.2B.$8.3B.B.A6.2A7.A
2B.2B.$.A.A3.A.2B12.A7.B2.2B.$A2B.A.B2.2BA12.B3.A.B3.2B.$A2B2.5B18.A2B
3.2BA$2.4B2.B21.5B2.$2.A.B25.A.B.A!

[eRroR_6o6]

(maybe) p12 photon frontend for 13/2/3 (i ran some patterns)

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x = 9, y = 11, rule = 13/2/3
$7.BA$3.2A.3A$.A2.A.B$.3AB$A.B2.A$.3AB$.A2.A.B$3.2A.3A$7.BA!

[ababa11e]

I was messing around with generations versions of B3/S234, and at 24 i found this (2,1)c/6 knightship. Probably not discovered by me.

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x = 23, y = 17, rule = 234/3/24
5$13.BA$11.HDAC2A$9.NJEIG3A$7.TPKOMFG2EA$6.VQUSLM2KDC$5.W2.RS2QJI$8.2W
PO$8.VU!

[hibiscus]

My first spaceship: a c/4o in 0134/3/3 found using genfind

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x = 15, y = 12, rule = 0134/3/3
6.B.B$6.ABA$2.BA3.A3.AB$2.2A.B3.B.2A$2.3A.A.A.3A$4.A.BAB.A$4.A5.A$2.A
2.5A2.A$.2A.B2.A2.B.2A$.2BAB2A.2ABA2B$.A3.A.A.A3.A$A.A4.A4.A.A!

Database entry:

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:hibiscus, 2024:0134/3/3:013478/38/3:4:0:-1:15:12:6.B.B6.$6.ABA6.$2.BA3.A3.AB2.$2.2A.B3.B.2A2.$2.3A.A.A.3A2.$4.A.BAB.A4.$4.A5.A4.$2.A2.5A2.A2.$.2A.B2.A2.B.2A.$.2BAB2A.2ABA2B.$.A3.A.A.A3.A.$A.A4.A4.A.A!

It's also extendable:

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x = 16, y = 12, rule = 0134/3/3
6.B2.B$6.A2BA$2.BA3.2A3.AB$2.2A.B4.B.2A$2.3A.A2.A.3A$4.A.B2AB.A$4.A6.
A$2.A2.6A2.A$.2A.B2.2A2.B.2A$.2BAB2A2.2ABA2B$.A3.A.2A.A3.A$A.A4.2A4.A
.A!

Maybe it's time to build a version of Glider_DatabaseOT.py call it, Glider_DatabaseGENS.py, and make it display known ships?
Edit: c/5o

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x = 8, y = 8, rule = 0134/3/3
3.2B$2.A2.A$.BA2BAB$B2A2.2AB$3A2.3A$3A2.3A$.B4.B$3.2A!

Edit 2: I'm on a roll, here's a c/6o:

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x = 9, y = 13, rule = 0134/3/3
.2B3.2B$.2A.A.2A$B7.B$.BA3.AB$2.A3.A$3.A.A$A7.A$2A5.2A$3A3.3A2$2.A3.A
$.BAB.BAB$.3A.3A!