All 23-Bit Still Lifes Are Glider Constructible
mvr.github.io
All 23-Bit Still Lifes Are Glider Constructible
1–10 of 17 posts
Re: All 23-Bit Still Lifes Are Glider Constructible
#2This 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.
Re: All 23-Bit Still Lifes Are Glider Constructible
#3This 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.
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.
Re: All 23-Bit Still Lifes Are Glider Constructible
#4This 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.
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 patt…
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...
Re: All 23-Bit Still Lifes Are Glider Constructible
#5This 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.
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 patt…
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.
Re: All 23-Bit Still Lifes Are Glider Constructible
#6Earlier quoted context omitted.
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 patt…
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.
Aah, but construction in GoL is not limited to gliders...still.
Re: All 23-Bit Still Lifes Are Glider Constructible
#7Earlier quoted context omitted.
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 patt…
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 tha…
> 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?
I always enjoy the absolutely incomprehensible GoL jargon
Re: All 23-Bit Still Lifes Are Glider Constructible
#8This 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.
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 patt…
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.
Re: All 23-Bit Still Lifes Are Glider Constructible
#9It's annoying here that you can't run CGoL in reverse, like you can with the laws of physics.
Someone should invent a GoL (that is still interesting) with that property.
Re: All 23-Bit Still Lifes Are Glider Constructible
#10It's annoying here that you can't run CGoL in reverse, like you can with the laws of physics. Someone should invent a GoL (that is still interesting) with that property.
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.