All 23-Bit Still Lifes Are Glider Constructible(mvr.github.io)
60 pointsby HeliumHydride7 hours ago1 comment
  • linolevan3 hours ago
    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.
    • teraflop2 hours ago
      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.

      • vintermann5 minutes ago
        Is it that easy though? Because the Turing machine constructions we have in the game of life are clearly not still lifes, and I don't know if you can construct a Turing machine which freezes into a still life upon halting.
      • LegionMammal9782 hours ago
        My understanding is that the only still-lifes known not to have a glider synthesis are those containing the components listed at [0], which are 'self-forcing' and have no possible predecessors other than themselves. Intuitively, one would think there must be other cases of unsynthesizable still-lifes (given that a still-life can have arbitrary internal complexity, whereas gliders can only access the surface), but that's the only strategy we have to find them so far.

        [0] https://conwaylife.com/forums/viewtopic.php?f=2&t=6830&p=201...

        • isoprophlex30 minutes ago
          > Maybe it's time to try pushing the envelope on this: what's the biggest blobbiest most spacedustful period-4 c/2 orthogonal spaceship that current technology can come up with? Might there be some kind of extensible greyship-like thing that escorts a patch of active agar instead of a stable central region, that might allow an easier proof of non-glider-constructibility?
      • CraftingLinksan hour ago
        Since GoL is Turing Complete,is such an inconstructable pattern an example of godels incompleteness theorem? I feel like I must be confusing some things here.
        • CraftingLinksan hour ago
          Aah, but construction in GoL is not limited to gliders...still.