ConwayLife.com

Oh sure, I can reword the nomination:
Proof that phoenix spaceships without B012a are slower than c/2o and c/3d (and related oblique speeds).

It's worth noting that Eppstein had proved many years ago that it was the case for rules without B012ac. Not sure if that should be noted as a caveat.

In the CHANGES.md file, the LLM notes that it now rejects inputting a width over 14 due to "crashing". It also is rejecting -q below 4 for the same reason.

I doubt it's still open, given it started and stopped once, but if it is, I'd like to nominate my proof that phoenix spaceships without B012a can't reach the speed limit.

Proof that phoenix spaceships without B012a cannot reach the speed limit of rules without B012a - Docsy
https://conwaylife.com ...

Dont know if I mentioned the sidecar tech from discord but basically sidecars can be combined together:

x = 47, y = 100, rule = B358/S126
o2bo$bo$obo$bo$4bo$4bobo$4bobo$5bo$8b2o$7b4o$8b3o$9bo$11bo2bo$12bo$11b
obo$12bo$15bo$15bobo$15bobo$16bo$19b2o$18b4o$19b3o$20bo$22bo2bo$23bo$
22bobo$23bo$26bo ...

That is a neat idea for finding some rules, but it seems pretty limited in application for the particular purpose.

I think a cool idea for a script would be a script that helps you find rules where some basic pattern occurs the most often in random soups. Like you input a base pattern, a min and max rule, a soup size, and a number of generations to check, and it'll run soups for rules across the space to find ...

These are incredible splitter!

also, as a note, I said earlier that 89-loopability was the record for RROs, but that's not true. Ampere found a 104-loopable RRO here:
https://conwaylife.com/forums/viewtopic ... 05#p135905

Might be a useful seed for SMORROs as well.

Adapting Ampere's guide here: https://conwaylife.com/forums/viewtopic ... 829#p72829

Here's an oblique ship, (2,-6)c/54:

I'd like to note, the mechanism behind the adjustable ships is the exact mechanism that powers adjustable slope ships, so there are infinitely many speeds and slopes in this rule. Diagonal/oblique gun when?

Agree. Loopable flipping oscillators exist;
x = 88, y = 169, rule = B2i3-jkny4qz5cy6cn/S2aek3-aky4eiyz5knq6-kn
20bob2o$21b4o$25bo$22b3obo$21bo3bo$21bob2o2$19b2o$19b2o$17bobo$17b3o$
18bo4$18bo$17b3o$17bobo$19b2o$19b2o2$21bob2o$21bo3bo$22bo2bo2$21b2obo
$20bobo2b2o$21b6o$24bo$23b2o$20b3o3b2o ...

Yes. In principle, loopability for oscillators is just the property that you can layer non-overlapping, non-interacting copies of itself to produce oscillators of a lower period. Rotation makes this a lot easier to achieve, often you just have a "failed" spaceship that produces a rotated copy of ...

- verify that the oscillator's kinetic symmetry is one of the following: n.c, n.e, n.k, nrc, nrk

As a note, while every loopable pattern I've seen has some rotational symmetry, in principle loopability doesn't require any symmetry, so fully requiring this would break the script for some ...

RRO definition: You can't do reflector loops, that's cheating!
Spaceships: Fine, we'll do it ourselves.

Reflectorless relays are fun.

Hunter showed off a pushalong for the c/3 spaceship in the Discord a while back:
x = 6, y = 8, rule = B35/S126
4b2o$3b3o$3b2o$4b2o$bo$obo$obo$o!

I noticed that the pushalong can be attached to itself, leading to an extensible spaceship like this:
x = 47, y = 100, rule = B35/S126
o2bo$bo$obo$bo ...

https://i.postimg.cc/y8ryfg1B/Better-RRO.gif

I realized even the design I showed earlier is not really the simplest way to do an adjustable RRO. You actually only need one kind of spaceship and a specific reaction when two of them collide just right. Here's a visual of the design. It's possible ...

Could i please perhaps see the L89 rro?


It can be found here: https://conwaylife.com/forums/viewtopic.php?p=79716#p79716


There is a similar design of adjustable RRO that is basically the original design, turned sideways. It uses orthogonal and diagonal spaceships that are the same speed.
Are ...

In terms of trying to find records, I'd agree that maximizing non-adjustable loopability is still of interest, 89 is the largest there. But I would say it is still a rule that contains RROs of arbitrary loopability, making an adjustable RRO that can be looped indefinitely was a nontrivial problem ...

No worries if this is too central to the wiki to casually propose changes for, but I think the Portal list on the front page could be in a slightly tidier ordering. I think Still Lifes, Oscillators, and Spaceships should be all towards the left or the top, to be the first ones seen by the average ...

May I be given trusted status on the wiki?

This is my account: https://conwaylife.com/wiki/User:Docsy

Recently in the Discord, I had been looking at this old design for an adjustable RRO that should be arbitrarily loopable, and I realized that it could be dramatically simplified (with one caveat) and still function. The design I came up with uses an orthogonal spaceship (red), a diagonal spaceship ...

pifricted wrote: June 12th, 2026, 9:14 am A spacefiller I found quite long ago:

Code: Select all

 x = 4, y = 4, rule = B37/S2345678
bo$3o$b3o$2bo!

Is this actually a linear growth?

It is, yeah. While the wiki still refers to spacefillers as quadratic growths, they don't actually have to be, it's just an easy form for them to take.

x = 43, y = 9, rule = B2ek3ei4at/S23
4bo2bo2bo2bo2bo2bo2bo3bo2bo2bo2bo2bo$4b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2o2$o2bo23bo14bo$o2b2o21b2o14bo$o2bo23bo14bo2$4b2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2o$4bo2bo2bo2bo2bo2bo2bo3bo2bo2bo2bo2bo!
x = 45, y = 9, rule = B2ek3ei4at/S23 ...

I suggest that the article for spacefillers note that growing at a quadratic rate is often true but not required to be a spacefiller, because it is possible to have linear growth patterns that fill all of space with an agar. Spiral growth patterns are an example of this.

Edit [10/3/2026]: Better written proof: https://docs.google.com/document/d/1VoFwEwYk-eQKZXAkggi5gIceFbsvt-26uP5aAYlEjx8/edit?usp=sharing
Edit [10/4/2026]: Proof that spaceships in INT rules without B01/S012acekn3acijnq4anw5a (survival conditions are subsets of S5a) can only move as fast as |dx|+|dy ...

I've recently been considering the idea of a cell's family tree. The idea is that a living cell can be considered to have given rise to a cell in the next generation if there's a living cell in the same position in the next generation, or if a cell neighboring it was born. These cells are its ...