Life theorems
- Tom Mazanec
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Life theorems
What would you say are the top ten theorems of Life?
- Majestas32
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Re: Life theorems
Probably #1 is that no spaceship can go above speed (M,N)/2(M+N) for M and N pos. integers.
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Re: Life theorems
2. That life can do universal computations
3. That orphans exist
3. That orphans exist
Re: Life theorems
I would go with: there exist a spaceship of any valid speed and direction i.e. any speed slower than (M,N)/2(M+N).
- praosylen
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Re: Life theorems
Has that actually been proven? Plus, aren't speeds equal to (M,N)/2(M+N) an open question in any case?simsim314 wrote:I would go with: there exist a spaceship of any valid speed and direction i.e. any speed slower than (M,N)/2(M+N).
former username: A for Awesome
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The only decision I made was made
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praosylen#5847 (Discord)
The only decision I made was made
of flowers, to jump universes to one of springtime in
a land of former winter, where no invisible walls stood,
or could stand for more than a few hours at most...
Re: Life theorems
I think your wording is ambiguous there. Certainly there exists a ship for any speed strictly slower than (M,N)/2(M+N) (and that is an amazing theorem!), but apart from c/2 and (1,1)c/4 we don't know whether any ships with exactly that speed exist.simsim314 wrote:I would go with: there exist a spaceship of any valid speed and direction i.e. any speed slower than (M,N)/2(M+N).
Re: Life theorems
Good point. Interesting enough - no natural nor constructable ship with this property exists, or has been proven to exist.Macbi wrote:but apart from c/2 and (1,1)c/4 we don't know whether any ships with exactly that speed exist.
Proven yes, by a theoretical construction (actually I've found several ways to construct a universal ship). But no actual construction was made yet...A for awesome wrote:Has that actually been proven?
Re: Life theorems
#4. There are no period-3 phoenixes.
#5. The Block is the only (finite) still life where all cells have three neighbors.
#5. The Block is the only (finite) still life where all cells have three neighbors.
Still drifting.
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Re: Life theorems
I thought it was proven that there were no p3 phoenices.Bullet51 wrote:#4. There are no period-3 phoenixes.
I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules. I also wrote EPE, a tool for searching in the INT rulespace.
Things to work on:
- Find (7,1)c/8 and 9c/10 ships in non-B0 INT.
- EPE improvements.
Things to work on:
- Find (7,1)c/8 and 9c/10 ships in non-B0 INT.
- EPE improvements.
- Majestas32
- Posts: 549
- Joined: November 20th, 2017, 12:22 pm
- Location: 'Merica
Re: Life theorems
Exactly, this is why this is in the Theorems thread and not Unsolved Conjectures.AforAmpere wrote:I thought it was proven that there were no p3 phoenices.Bullet51 wrote:#4. There are no period-3 phoenixes.
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