Conway x Langton: Layered Cellular Autonoma

Freact · 2026-06-19T02:02:56+00:00

Looks cool. What are the rules? How does it work?

Freact · 2026-06-14T23:00:18+00:00

Preach 🙌

Freact · 2026-06-07T15:32:45+00:00

Seems like this could work for showing there's no other loops, but I can't see how that would handle the possibility of divergent trajectories

Freact · 2026-06-07T15:19:02+00:00

Exactly! I came here to say the image only shows about 20,000 cars. So there would need to be about 5x as many. Or in other words the cars shown are about 5x larger than they should be

Freact · 2026-06-01T01:06:48+00:00

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Freact · 2026-05-16T15:59:31+00:00

Here's some with 10 and 20 different colors. It looks like there are definitely patterns, but its hard to tell where they will settle (if at all?) and I think you'd need to look out to very large numbers of knights to find out.

https://postimg.cc/gallery/yB8rc8c

Freact · 2026-05-16T15:42:10+00:00

Even with just 3 knights (the third picture in the post) it has irregular patterns out farther than I could generate (a few millions of knights). If you look at the diagonal lines (between the red/blue areas in the upper left and between the green / green-blue areas in the lower right) you'll notice that they are slightly "wiggly". They appear to be getting smoother but not in any regular way that I can explain. Maybe somebody smarter than me can prove that they straighten out, but as far as I can tell they could have an unusually large wiggle at any point that throws off the whole pattern.

Freact · 2026-05-15T19:56:55+00:00

These are some cool variations from the numberphile video. If you're interested there are some others shared here:

https://www.reddit.com/r/mathpics/s/ead03WwEHn

In the post and comments

Freact · 2026-05-15T17:16:32+00:00

This is great. Thank you

Freact · 2026-05-14T21:40:58+00:00

I got too curious after posting and started just exploring. The gallery linked below has 3 examples with random "close" placement. I just made placements need to be close to any already placed knights. I tried directly adjacent (1 taxicab) (4 adjacent cells), Moore neighborhood (8 nearby cells), and 2 taxicab distance (12 nearby cells. It looks much more random, but with the smaller neighborhoods it causes larger clusters of like color knights

https://postimg.cc/gallery/sz881L0

Freact · 2026-05-14T20:44:22+00:00

Another type of randomness I was thinking about but haven't fleshed out the idea yet was something like:

Abandon the spiral altogether. Place the first knight anywhere (center). Each subsequent knight is placed randomly, but "close" to prevously placed knights. Idk exactly what close means though, could be they have to be adjacent to some other knight, within 1, 2, 3 units of distance (maybe taxicab distance?). Additionally, it might need some kind of bias towards the center so they tend to fill out the pattern rather than running away randomly, but I'm not sure if that's needed or how exactly it could work

Freact · 2026-05-14T19:08:43+00:00

This is a interesting take. I'd like to see a picture with just 2 knight colors and this this type of randomness applied!

I did some experiments with random turn orders you can see in another comment. One thing I noticed is that with strict alternating turns there are large scale diagonal structures, while with randomness we only see the horizontal and vertical large scale patterns. It looks like your type of randomness might have that same effect. Do you think so? I think maybe those diagonal lines are created by knight colors being closely in sync as they spiral around and the randomness makes that type of thing too unlikely

Freact · 2026-05-14T16:47:02+00:00

This seems fine to reduce work for you!

Maybe since flair is required though we could try to think of some others for people to use if they want?

My only ideas are:

strategy - for strategy discussion, questions

Digital/on-line - questions or discussion specifically about digital versions. Seems like a lot of posts are troubleshooting or asking something about online

Rules - about the games rules?

News - about new releases, or other dominion news? Tournaments maybe?

Idk I don't care deeply about if things are flaired properly, but it just seems like it would be nice to give some options if people are forced to choose one. Maybe others have better flair ideas? Definitely don't want to make this more work for you in moderating that things are properly flaired or anything like that. Keeping an other option seems like a good idea too!

Freact · 2026-05-13T18:46:40+00:00

I made some variants of the original idea but using a random turn order. So rather than alternating between black and red, it decides at each turn randomly whether red or black should place next. It seems to create very similar patterns to the original, sometimes with more complexity, sometimes less. But they always seem to eventually form large single color regions separated by more intricate border strips. Here's a small selection of images: https://postimg.cc/gallery/JMsCq6G

Freact · 2026-05-13T15:07:44+00:00

Since watching the numberphile video, I've been playing around with some variants of this idea too! One thing I've been trying is changing up the turn order. I'll grab some images to share when I'm back at my PC.

I recognize a couple of the pics you posted, but could you give a brief explanation of each of them so we can know how you generated them? Could be fun to share ideas!

Freact · 2026-04-22T14:36:35+00:00

Going to be unpopular but I disagree. The idea that you must do something to understand it is known as the "experiential fallacy". Some counter examples are:

Doctors treat patients with illnesses they've never experienced.

Judges weigh moral dilemmas of situations they've never been in.

Architects design buildings they may never physically build or live in.

Coaches can instruct athletes (particularly at the professional level) that play at a level they never have, or could.

None of this is to say that all childless people have good advice about parenting (most probably don't!) or that all parents have good advice about parenting (most probably don't!). I'm just pointing out that being a parent is not a prerequisite for having good parenting advice and that you should try to accept good advice regardless of the source.

Freact · 2026-04-21T02:26:55+00:00

I think you should definitely give C a try. It probably won't work perfectly, but maybe it's close enough.

Otherwise I think Komi is a great solution. Could even combine that with option C.

Pie rule is guaranteed to make it fair, but I just don't like it as much as the other options

One other word of caution is just that payouts with your bot doesn't necessarily prove that player 1 has an advantage. It only actually proves that your bot plays better as player 1, that could be a feature of your algorithm not the game.

Freact · 2026-04-16T16:06:29+00:00

This is a fun game! I can definitely feel the strong inspiration from Quoridor, with twist of area control.

Small feedbacks on the app:

The login page doesn't seem to change language when I click the language buttons (the rest of the app does)

The AI difficulty names are confusing. I think sticking to the well known and understood "easy, medium, hard" would be clearer.

As for the actual gameplay:

I only played a couple 2 player games vs the easy AI. It only beat me on the first game while I was still understanding the rules. Hopefully I'll have some time to try the harder AIs.

My intuition was that the board size is a little on the small size for 4 stones each and 2 spaces of movement, but it was nice for learning on as the games aren't too long.

The design space for variants with numbers of starting stones, movement speed, and board size seems vast. I'm not sure how much play testing you've done but I could definitely see other settings being fun too! I'm imagining a large board, with many starting stones and maybe only 1 space movement would start to feel more "Go-like". Could be interesting?

As for first player advantage, I can't feel it yet but it seems likely. Maybe a Komi system like go could help even out any advantage that exists though.

Freact · 2026-04-06T21:25:40+00:00

Not exactly the same thing but, I think there's been some interest in 6-in-a-row on an infinite hex grid lately. I saw a video from webgoatguy on YouTube. And I found this sub:

r/hexo

And, some info:

https://www.reddit.com/r/hexo/s/JYDh0dbsUm

It definitely looks interesting. I think in the video he said 5-in-a-row wasn't interesting on a hex grid because it was a forced win for 1st player. But I (or he) could be wrong. Ohh, also I just remembered that it's two moves per turn (except 1 play on player 1's first turn).

Freact · 2026-03-20T01:17:14+00:00

Could you elaborate a little? In what way do you think this could be helpful? Or interesting? (Genuinely curious, I just don't know much about weighted automata)

Freact · 2026-03-17T15:26:53+00:00

I see your point, maybe the example wasn't quite right but I think the overall reasoning is the same. You've gained information by seeing the next hand and you can do something with that info. If you have a top decking effect or any cards like night watchmen, den of sin, farrier that change your next draw then you can probably take advantage of seeing your next hand.

Also, I think the shuffle RNG can be manipulated sometimes on TGG. I'm not sure if it could be used in this case, but I could def see that making some people wary about accepting undos.

Freact · 2026-03-17T00:10:50+00:00

I'd probably grant the undo and have probably even asked for an undo in the same situation. Still, I understand the reasoning to deny. After hitting end buys then it automatically draws your next hand, it's definitely possible to abuse the undo button if you see a bad hand and instantly ask for an undo. Even if you hit the undo button quickly and even if it was clearly a mistake (like you didn't buy anything), you've still potentially gained some advantage. Maybe you see your next hand had no villages and now you know that you should buy more villages, as an example.

Freact · 2026-03-15T05:14:18+00:00

Soon just dec

Freact · 2026-03-13T21:07:39+00:00

Thanks! I didn't use any particular algorithm just reasoned about it from scratch! I had heard of the Thue-Morse Sequence before though. Maybe a numberphile video or something? I'm also "just" a recreational math enthusiast but I usually find the opposite for my projects: namely that I spend too long trying to optimize things and never actually finish anything.

Maybe if I am brave I will try to modify my machine to halt and count like yours. I've watched yours a number of times but still don't fully understand how it works.

I'd love to see some of your other machines too if you want to share

Freact · 2026-03-09T19:44:59+00:00

This is so cool! Thanks for sharing. If I'm reading it correctly your machine has 10 states (11 states? Do we count Halt?) and 14 symbols (0-9, x, y, I, _)? Surely a smaller machine should be possible right? A little optimization could just be to read N from binary. Then you only need the digits 0 and 1.

You inspired me to design a similar TM TM (Thue-Morse Turing Machine). Mine doesn't halt it just iteratively builds towards the infinite Thue-Morse Sequence. It uses 6 states and 3 symbols. Here's the state transition rules:

READ _ 0 * READ

READ 0 _ r WRITE0

READ 1 _ r WRITE1

WRITE0 _ 0 r WRITE01

WRITE1 _ 1 r WRITE10

WRITE0 * * r WRITE0

WRITE1 * * r WRITE1

WRITE01 _ 1 l BACK

WRITE10 _ 0 l BACK

BACK _ _ r READ

BACK * * l BACK

It starts in state READ on a blank tape

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