This is a cool subcommunity! Had no idea there were still open problems that people were working on. Surprised to see human intuition is still around – would have expected a solution through pure brute force.
The state space is much too large for generic brute-forcing. The number of possible patterns in a 16 x 16 grid is already roughly the number of atoms in the universe, or 10^31 years in Planck time units.
In that respect, it reminds me a bit of the busy beaver problem.
I wonder: consider the decision problem of determining whether or not a given still life is glider-constructible. Is this problem known to be undecidable?
It's straightforward to show that an "inverse" of this problem -- given an arbitrary glider construction sequence, does it result in a still life? -- is undecidable, because gliders can construct patterns that behave like arbitrary Turing machines.
If there haven't been any proposals for a friendly name for the 23 bit holdout it looks like a pair of glasses to me. So perhaps "spectacles" would be a nice one, similar to the spectre of recent aperiodic monotile fame.
Ever since programming GOL in assembly on Z80 i dreamt of this.
Game for two persons.
The game runs, you can go back in time and modify by introducing gliders.
Only problem is, how to turn it into a real game, what is the object.
Maybe split the world in two and try building a stable configuration. The opponenent can launch the glider towards your turf, or something like that.
I just found out that there's a 1D cellular automaton called Rule 54 that is conjectured to be Turing complete, but for which there isn't yet a proof.
I think Gemini (an LLM) and me are in agreement that the proof will likely be found by a neuro-symbolic AI. As evidence for this, see AlphaEvolve and the agents which received IMO Gold.
linolevan|1 month ago
layer8|1 month ago
teraflop|1 month ago
I wonder: consider the decision problem of determining whether or not a given still life is glider-constructible. Is this problem known to be undecidable?
It's straightforward to show that an "inverse" of this problem -- given an arbitrary glider construction sequence, does it result in a still life? -- is undecidable, because gliders can construct patterns that behave like arbitrary Turing machines.
OisinMoran|1 month ago
amelius|1 month ago
Someone should invent a GoL (that is still interesting) with that property.
AlotOfReading|1 month ago
https://en.wikipedia.org/wiki/Critters_(cellular_automaton)
GaryHak|1 month ago
Game for two persons. The game runs, you can go back in time and modify by introducing gliders. Only problem is, how to turn it into a real game, what is the object. Maybe split the world in two and try building a stable configuration. The opponenent can launch the glider towards your turf, or something like that.
avadodin|1 month ago
no, thank you. I already have hobbies to consume my life.
ogogmad|1 month ago
I think Gemini (an LLM) and me are in agreement that the proof will likely be found by a neuro-symbolic AI. As evidence for this, see AlphaEvolve and the agents which received IMO Gold.