ConwayLife.com

Could I be trusted, please?

conjecture: every pattern has at least one parent which is a GoE That's an interesting one -- assuming that you add the caveat "every pattern that has any parents at all ". Otherwise it's definitely just not true. "Every pattern" includes the empty pattern, so it will have to be possible to find a ...

Could it be possible to make unsynthesizable spaceships? In principle, yes, with the same approach. We'd just search for self-forcing agars that evolve into translated versions of themselves after n steps, and then search for finite patches of them that force themselves in their nth predecessor but...

I don't know how this was found, but can the same method used to find this agar be generalized to agars of different periods, creating unsynthesizable oscillators of different periods? In principle the method works for any period, but you need a "stroke of luck" to get results. The agars and patche...

I was more thinking in terms of sample results of your script. Sorry for the delay. The repository now contains a folder of search results for some small-ish parameters: self-forcing still life agars of spatial period up to 6x6 (possibly incomplete for 6x6), and self-forcing period-2 agars of spati...

Exciting! Could we have a sneak preview of some results? Our results, and their proofs apart from the SAT solver computations, are in the preprint (you can download a pdf from the top right). It hasn't gone through peer review yet, so take the details with a grain of salt. We are confident about th...

I and Ville Salo have published Python scripts for enumerating self-forcing agars of given periods (in both space and time). By "self-forcing" we mean that the agar has exactly one chain of predecessors. In other words, if the agar oscillates at period p and goes through configurations a(1), a(2), ....

I'm not sure if anyone has done this already, but I confirmed the result with JLS (took a few hours, I think). It's great to have an independent confirmation! Also, this showcases the power of modern SAT solvers: with our encoding, Glucose 4.1 verifies the result in less than 2 minutes on my old-is...

New results (by me and Ville Salo). There exists a finite pattern that forces itself to occur entirely in each of its preimages. It's this one (surrounded by gray cells): x = 30, y = 24, rule = LifeHistory 5.22F$2.4FA4.2A4.2A4.2A.2F$.2FA2.A.2A2.A.2A2.A.2A2.A.A2F$2F2A.A2.2A.A 2.2A.A2.2A.A2.2AF$F4.2A4...

there's a unique predecessor for each step backwards, ending with the original agar with just one bit flipped. JLS doesn't even have to run an actual search to decide this; that result shows up just from the preliminary instantaneous analysis of which cells are forced by a surrounding ring of that ...

I forgot to include bounds for the sizes of the patches. According to my computations, a padding of 12 cells in every direction is enough to force any 6x3 patch of the agar into its predecessors. This means that to get a level-n orphan, it's enough to take any (28n+13)x(28n+7) patch of the agar, fli...

I got together with Ville Salo this week to think about this self-forcing agar. We ended up solving the generalized version of the grandfather problem ( https://www.conwaylife.com/wiki/Grandfather_problem ): for all n there exists a pattern that has an nth predecessor but not an (n+1)st predecessor....

How computationally intensive is the analysis being done here? I suppose I'm asking about both the initial search (to find the "most forcing" stable agar in an MxN box) and the frame-shift analysis. But I guess once the stability-compatible MxN agars are enumerated, all the frames will already be i...

For example, the above 34x31 pattern contains a 30x28 patch of agar. I think that means that if this pattern shows up in an old universe, the center 6x3 patch is guaranteed to have existed unchanged for at least a few ticks -- and if we want to guarantee no changes at the center farther back in tim...

Infinite still life patterns could not be handled with this approach, and maybe some of them have only themselves as a predecessor. For the periodic case, these can be viewed as finite patterns on a toroidal grid. I ran a search for such a periodic pattern and found one of size 6x3: #C [[ THUMBNAIL...

This lead to Ville Salo and Ilkka Törmä learning about the problem, and they've managed to solve it! I'm one of the authors (and writing on behalf of Ville Salo as well). In our preprint we give two different algorithms for deciding if a finite-population configuration is GoE: check that the boundi...