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[FearfulJesuit]

Using the rules of Conway's Game of life:

1. Are there any stable patterns (stable being defined as a pattern consisting only of still lifes, oscillators and gliders/spaceships) which cannot be produced using only gliders? We disregard anything outside the pattern we wanted- if we wanted a beehive, and we get a beehive plus a block somewhere else, we can disregard the block.

2. Can all patterns, stable and unstable, be constructed using only gliders?

My conjecture is that both are false, but I'm not sure...

[Urist Imiknorris]

There is a math help thread, you know.

[Eagleon]

Very difficult problem. You're working with three-dimensional permutations, since the gliders and everything they create shifts with each frame. If you have proof of being able to produce a number of common patterns, and you can infer the ability to construct the remaining patterns using those, you have proof of 1. Good luck with that, though. For the second, you only have to find one pattern you can't make with gliders, but depending on what you mean by "only" gliders, you could also use patterns created by the gliders to create the unstable/stable pattern. Basically a NP problem, since you can always think up a larger pattern that might be impossible to create, and you can't evaluate whether some time down the line, your pattern won't be created.

[Strife26]

Yeah, the board can stretch to infinity, so I don't think that there is anyway to prove either.

[Vector]

Yeah, the board can stretch to infinity, so I don't think that there is anyway to prove either.

Double-induction would do it, if he were able to reduce every pattern down to certain components of its starting position.

[Strife26]

Yeah, the board can stretch to infinity, so I don't think that there is anyway to prove either.

Double-induction would do it, if he were able to reduce every pattern down to certain components of its starting position.

We're past my barely remembered AP Calc skills then.