ConwayLife.com

Class V: Turing Complete with finite patterns.

A proper Turing machine requires some equivalent of limited memory, so if you require it to be finite then logically you need some form of infinite growth. You have that listed as the top spot on a hierarchy though and it doesn't always have to be ...

I tried this out with 5% soup density, and unfortunately it seems pretty similar. Most of the visible differences are found in the bottom part of the graph, which is now slightly more asymmetrical.
Thank you for trying this. I don't think it's necessarily a bad result to find your values are ...

This is a really neat exercise. In absence of defined clusters, it might be interesting to see if other known properties relate to regions of the graph. Like you say, Wolfram's classification is not easy to apply, though certainly anything with B1 or B2 will be explosive. David Eppstein (2010 ...

B368/S245 gets called Morley for the investigations Stephen Morley did on it. Is there any surviving record of what he actually discovered beyond the few patterns in Golly? The page safalra.com is referenced in a couple places but gives a 410 Gone error, and is excluded from the archive.org wayback ...

There are a couple rules from a long time ago where patterns had been given names, but they have never been used much in part since a lot of them conflict with names in B3/S23. I had some thoughts on how to adapt these to be easier to use while still hopefully respecting the originals, which I ...

Some more inane thoughts on names:
The small p2 could also be compared to a clock, in which case it is clearly a ticktock since the cell count goes 6-7-6-7.
Hunter's p37 is good for so many things that it can fairly be considered Flockenstein's doctor.

I ran into this infinitely extending domino track. The population growth isn't actually a sawtooth, just bounces between two linear functions in a similar way, but I thought it was kind of neat. It's hard to tell if it's ever been posted before.

x=10, y=16, rule=B2/S2
5bo$7bo$2bo4bo$bo3bo2$7o$7bo ...

Also a lot of still lifes in this rule seem to be shared with Flock, so maybe the thread for that has some common names for the still lifes in B35/S126.

For the record all the still lifes here will work in Flock. Any exception would have to have some cells with 6 neighbours. But assuming there ...

Since you're inviting suggestions...the second p1 makes sense as a partial beehive, or a beefive if you want something short. Then second last you have a beehive split in two, specifically into bananas, so you could call it a banana split. (There is another 5-cell p1 in B3/S12 that is also a beehive ...

What to name the glider. I have came up with 4 names that I think would suit it. Ufo, Vacuum Cleaner, Go Kart, or Skedaddler .

I personally like the trend of naming them agent nouns for how they move – glider, creeper, crawler, etc. So that would go with skedaddler. They usually just stay ...

As said these are xor oscillators, equivalent to W90 so long as the dots don't end up next to each other. But so far you're only getting some of the possible periods because you're only looking at track lengths that break evenly into dominoes (or the little hat things). Compare for example these ...

Oops, thank you for that. Then in case they're of interest here a couple little p2 spaceships that work in this rule. The c/2 one is in gliders.db, the others are from stabilizing some fronts that often show up in explosions.

x=70, y=12, rule=B2/S34
39b2o19b2o$39b2o19b2o$o9bo23b2o3b2o3b2o13bo2bo ...

This is one of a few B2 rules that allow those kind of boxes that are stable no matter what is inside them...I'm not sure if they have an accepted name but I've been calling them soup containers. Out of those B2/S23, B2/S34, B2/S45, B2/Sx56 for x = 1 to 3, and derivatives are kind of neat because ...

The still lifes are from B7/S236 not B27/S36, which doesn't actually have any. It doesn't look much different from B2/S3. That includes the simple p8 mentioned above and a series of domino tracks, which are xor oscillators so can be made for all even periods:

# B2(678)/S3(45678) - closed ends ...

Good catch that S8 isn't needed there. I'd also missed this very simple case:

# Rule 150: B2(78)/S(0)1(2)45(678)
x=10, y=10, rule=B2/S145
o8bo$b8o$b8o$o8bo$4b2o$4b2o$o8bo$b8o$b8o$o8bo!

Edit Feb 26 : On the discord we also found this emulator with ends by sylvani and Layz Boi. That should finish ...

Sokwe has helpfully provided a proof that both rule 150 and rule 90 are omniperiodic on segments with always-on or always-off ends. This confirms a lot more life-like cellular automata as omniperiodic. Here are examples I have collected that are not in the list above:

# Rule 90: B2(78)/S(0)23(4678 ...

My apologies. I was writing too many numbers down and I guess got it mixed up with a larger one, in part because Johnston does list 524286 as the period when n=18. And in fact rather requires it with his theorem 2, which must then have missed some detail, and I am guessing likewise gives a multiple ...

Looking at just the linear 4n×2 oscillators, the ones that have a single outer cell frequency all have periods of the form 2^(n+1)-2. Johnston (2010) mentions this is the highest value possible and when it is not reached it means there are rectangles missing from the evolution of the oscillator ...

Ideas like this (for Margolus-emulating rules) and this (for Wolfram's Rule 150-emulating rules) could easily generalize to a large varieties of rules.
Unfortunately both of those use a method for dividing periods that does not always work. Basically if you have an oscillator of period n, then ...

And the other part, getting rid of other prime factors, went very luckily because of the B2c/S2c inspiration.
Say you have a x = 16, y = 2, rule = B3r4ai/S1e2aei3aeir4ir5i o7b7o$16o! , which is p15. Now you want to make it p5. What you will have to do is just copy the cells in the first row, run ...

All right, my list is thankfully back up and as requested now gives dates where I can. I should say I don't know how to verify many of them though. For the B34/S34 patterns in particular I've left off credit since several are mentioned in Lifeline, but Eppstein instead credits the small spaceship to ...

This has been one of my favourite rules. Since it doesn't seem to have been brought up yet, here is a fuse to go with the simple wickstretcher that Sphenocorona had mentioned. There are also shoots that can run up the side but they quickly outrun the front (putting two of the common spaceships side ...

I didn't imagine that they weren't known, just that they belonged here. For instance right near the start the counterfeit glider thread included the well-known p4 from B368/S245. I'm sorry if I misunderstood the intent.

Some simple counterfeit clocks that keep the same time but not the same reflection.

Right, same as Eppstein's glider.db. I made an export that is supposed to be available here but unfortunately the site is down right now. I've attached a static copy here rather than keep you waiting. I hope it's of some use.

Thinking more about oscillators with very few cells I also had an idea ...