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Life theorems

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Life theorems

Postby Tom Mazanec » December 18th, 2017, 5:29 pm

What would you say are the top ten theorems of Life?
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Re: Life theorems

Postby Majestas32 » December 18th, 2017, 6:02 pm

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

Postby Macbi » December 18th, 2017, 7:00 pm

2. That life can do universal computations

3. That orphans exist
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Re: Life theorems

Postby simsim314 » December 20th, 2017, 12:32 pm

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).
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Re: Life theorems

Postby A for awesome » December 20th, 2017, 12:39 pm

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).

Has that actually been proven? Plus, aren't speeds equal to (M,N)/2(M+N) an open question in any case?
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

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Re: Life theorems

Postby Macbi » December 20th, 2017, 12:40 pm

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).

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.
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Re: Life theorems

Postby simsim314 » December 24th, 2017, 4:36 pm

Macbi wrote:but apart from c/2 and (1,1)c/4 we don't know whether any ships with exactly that speed exist.


Good point. Interesting enough - no natural nor constructable ship with this property exists, or has been proven to exist.

A for awesome wrote:Has that actually been proven?


Proven yes, by a theoretical construction (actually I've found several ways to construct a universal ship). But no actual construction was made yet...
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Re: Life theorems

Postby Bullet51 » December 25th, 2017, 6:35 am

#4. There are no period-3 phoenixes.
#5. The Block is the only (finite) still life where all cells have three neighbors.
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Re: Life theorems

Postby AforAmpere » December 25th, 2017, 1:23 pm

Bullet51 wrote:#4. There are no period-3 phoenixes.

I thought it was proven that there were no p3 phoenices.
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
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Re: Life theorems

Postby Majestas32 » December 25th, 2017, 10:29 pm

AforAmpere wrote:
Bullet51 wrote:#4. There are no period-3 phoenixes.

I thought it was proven that there were no p3 phoenices.


Exactly, this is why this is in the Theorems thread and not Unsolved Conjectures.
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