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AforAmpere

C/936: x = 1, y = 1, rule = MAPhhPAngATIAQAQhUPOQP1BAEEGAaDjzN2CgEBABMfeSgAAwIiEAcESA4AGzZAL/f/UR5HTwP3BCAWAxEPERNBAA o! EDIT, C/1142: x = 1, y = 1, rule = MAPhhPAnAATJAQAQhUPKSO1BAEAGA6Djxd2CgMRAHM/HSgAAQIqEAcESA4AGQJAK/f/UAJHTxL3BCAWAwEPERMBAA o! C/1308: x = 1, y = 1, rule = MAPhhPAnAATJAQAQhUPKSO...

AforAmpere

OogaBooga_ wrote: ↑
April 10th, 2026, 7:27 pm
2-dimensional sqrt growth
Code: Select all
x = 3, y = 3, rule = B3aijr4j5e6n/S2-ci3-aky4ceinrz5jkc6e
3o$obo$2bo!

Interestingly this is actually t^(2/3) in population (or cbrt growth if you just want the growth in width) so this is arguably even more interesting than sqrt.

AforAmpere

./rlife llsss-recentering-wao --rule 'B2-a3-i45678/S0123-a45-i678' --ends [odd,even,none] --filters bcaf 2c8-s2s '@bg' 8 This seems to crash for me on the latest master version. Here is the backtrace: thread 'main' (6269) panicked at src/table/engine.rs:314:9: assertion failed: next_idx <= AD::BIT_...

AforAmpere

Inspired by a question from NimbleRogue on the Discord, a constant population adjustable ship: x = 17, y = 4, rule = B2e3aijky4ait5ajnqy6k/S1c2-kn3-ceny4kwy5ein6an 2o$2o4b2o7b2o$8bo6b2o$6b2o! As always with this type, there are adjustable slope ships, which are also constant population: x = 19, y = ...

AforAmpere

B468S02357 wrote: ↑
April 20th, 2026, 7:06 pm
A rule i found has no ships but an adjustible oscillator family consisting of lines of length (n+1) where n is twice the length of the last osc

The pattern immediately breaks on the next one, so this does not actually work:

Code: Select all

x = 63, y = 1, rule = B2-ac3ai4aei567/S04cqz5eik678
63o!

AforAmpere

A suprisingly rare spaceshp which AFAIK is the first 3c/8 in the entirety of CA Not even remotely true, 3c/8 ships have been known for many years even in just 2 state rules. In all of CA, every speed under the neighborhood's speed limit is easy to construct with enough states. Here's a 3-cell examp...

AforAmpere

R2INT wrote: ↑
March 12th, 2026, 3:11 pm
Interesting explosive rule with 3 different density modes (0%, 50%, 100%):

Wow, I like how you can clearly see the phase transitions when watching the population graph.

AforAmpere

1-cell growth with an unusual pop-plot that sort of looks like a slanted version of the Blancmange curve:

Code: Select all

x = 1, y = 1, rule = B01c2akn3-jr4ajknqyz5cijkn6-k78/S01c2en3-er4-aejy5-iny6ik
o!

AforAmpere

With the oscillators above, they cover all periods p104 and above. With these 1-cell oscillators in the 5s database for B0 INT rules up to p102, this proves that all periods can be constructed in B0 INT rules in 2 cells or less: 1, B018/S, 0, 0, 2, o! 1, B01e4e/S06i, 0, 0, 4, o! 1, B01e2c4ce6e/S02c4...

AforAmpere

I figured this would be the best thread for this, even though this is B0. B0INT now has 2-cell adjustable oscillators. p(48n), n>=2: x = 13, y = 1, rule = B01c2-ce3eiqry4aikrwz5-aey6-kn7/S02ekn3-ar4-aqrtw5-inqy6n o11bo! p(2+48n), n>=2: x = 15, y = 1, rule = B01c2-ce3-aej4-eqtw5ijknq6-n7/S02en3-cjk4-...

AforAmpere

I discovered this over 2 years ago and put it on Discord, but it never found its way here, a 6c/7 in B1e:

Code: Select all

x = 3, y = 18, rule = B1e2c3cin4aiqrty5jn6cen7e/S1c2a3aeir4jqry5cenqr6-in7c
2o$o$2bo$obo$2bo$2bo$2bo$b2o$obo$obo$b2o$2bo$2bo$2bo$obo$2bo$o$2o!

AforAmpere

Not for INT, but for B0INT, a smaller 13c/14 at 6 cells:

Code: Select all

x = 3, y = 4, rule = B02-n3-cik4-jnwz5ajqy6ak7e/S01c2ckn3-eiky4aiknq5cejnr6aci
b2o$o$o$b2o!

AforAmpere

From a discussion with rabbit and Docsy on Discord, a C/5 that exists with only B2c3a for birth conditions, found with LLS: x = 8, y = 9, rule = B2c3a/S1c2a3-cj4aejnryz5-aiq6-c78 4bo2$4bo$ob4obo2$ob4obo$4bo2$4bo! I've tried finding faster ships, but all results have come up negative, including any C...

AforAmpere

Are adjustable spaceships possible in hexagonal rules, or is the range-1 2-state space simply not big enough? That's a good question. I'm trying to explore the space by script at the moment for various things, and it is incredibly constrained. Part of the difficulty at the moment is finding common ...

AforAmpere

Are there any other loopable RROs in a hexagonal rule other than this one and AlephAlpha's, or indeed any at all in a triangular rule? Now there are, a 1/2/3-able p342: x = 60, y = 13, rule = B2o3-o4m6/S2-o34p5H 47bo$48bo$48bo$47b2o$5bo2bo39bo$5b4o4$55b2o$56bo$4o43b4o6bo$o2bo43bo2b o7b2o! 1/2-able ...

AforAmpere

Resu wrote: ↑
August 27th, 2025, 3:41 pm
How do you find how "good" a partial is?

It's a qualitative thing, but in this case all of the forward movement was confined to one half of the period, which is usually a bad sign for being supportable.

AforAmpere

LLSSS seems to show that p2, p4 and p6 C/2 ships can't exist. I ran out of RAM trying to do the same for 4c/8, but the partials looked pretty awful.

AforAmpere

1/2/4/8-able RRG: x = 53, y = 53, rule = B3aijr4ejk7c8/S2aek3-acek4ceinty5aj6ack 5b3o$4bo2bo$4bo3bo$3b2o2b2o12b2o26bo$4b2o16b2o6bo17b4o$9b3o14bo3b2o16b o3bo$11bo13bob2o2b2o19bo$9bobo17bobo17bob2o$9b2o15bo2b2o18b2o$27b2o15b 2obo$44bo2bo$45b3o9$6bo$5b3o41bo$4b2o2bo39b2o$7b2o39bo$6bo2bo$6bo2bo 36bo$5bo...

AforAmpere

Crazy 2D rep that has wave-like behavior at large scales:

Code: Select all

x = 3, y = 4, rule = B2i3aijkr4ej5ck7/S2aek3-acey4ciny5acnr6aek7c
3o$2bo$obo$2o!

AforAmpere

This rule had no lightspeed ships (in my copy of the DB at least): x = 42, y = 16, rule = B257/S15 12b2o14b2o$11bo2bo12bo2bo$10bob2obo10bob2obo$9bob4o12b4obo$8bob2obo2bo 8bo2bob2obo$9b2o2b2o5b2o5b2o2b2o$4b2o3b2o7b6o7b2o3b2o$3bo2bo2b2obo2b 12o2bob2o2bo2bo$2bob2obob2o5bo2bo2bo2bo5b2obob2obo$bob4ob2o22...

AforAmpere

Here are more (2,1)c/5 ships: B3568/S2467 ship Shorter one, found with LLSSS: x = 32, y = 75, rule = B3568/S2467 3bo$2b4o$b2obo$b2o2bo$o2b2obo$2b3o$b7o$3bo$5b2o$4b2obo$5bob2o$6b3obo$ 5bo2b2o$6b2o$5b4obo$8b2o$8b4o$8b2ob2o$6b2ob2o$6bo2b2o$7b3obo$10bob2o$ 10bob2o$11b2o$10b4o$10b3obo$12bobo$15b2o$13b3o...

AforAmpere

Speaking of knightships, here are two p5’s: B368/S034678 ship Here is a smaller one: x = 16, y = 27, rule = B368/S034678 b4o$obo2bo$2o2b2o$2o2b3o$bob2ob2o$2b4ob3o$2bo6bo$7bo$9bo$7bo2bo$10b2o$ 7bob2obo$8b2obob2o$9b2ob2o$9b2obobo$9b2o2bo$10b2obo$10bobo$9b2obo2bo$ 9b4o$12bo2bo$10b4o$10bobobo$11bob2o$1...

AforAmpere

Also happens on v2.3 with the corresponding command, and width 4 or 5: qfind v2.3 by Matthias Merzenich, 19 March 2023 Input: ./qfind -r B2ek3cij4ci/S2ce -p 5 -y 2 -s o -w 5 Rule: B2ek3cij4ci/S2ce Period: 5 Offset: 2 Width: 5 Symmetry: odd Queue size: 2^20 Hash table size: 2^20 Minimum deepening inc...

AforAmpere

154x138 SMOSMOSMOS gun, area 21252: x = 154, y = 138, rule = B2e3ceijq4aenqz5kn6a/S1e2ac3nr4ein5aejry6a78 47bo76bo$46bo78bo$15bo$16bo40bo56bo$44bo12bo56bo12bo$44bo82bo2$73b2o3b 2o12b2o3b2o2$48bo28bobo12bobo28bo$47bo12bo50bo12bo$47b2o10bo15bo20bo 15bo10b2o$29bo17bo12bo4bo8bo7bobo2bobo7bo8bo4bo12bo17b...

AforAmpere

Very low period SMOS and SMOSMOS, at C/6d and 4c/17o respectively: x = 41, y = 6, rule = B2a3eqry4anrwz5ciknr6-ek7e/S2-cn3aijn4aijkrtw5cjn6cek8 2o14bo12b3o6b3o$16bobo11bobo4bobo$bo27bob2o4b2obo$13b2o15bobo4bobo2$ 14bo! EDIT, and not a minute after posting this (for context these searches have been g...

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