Still Life problem

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AforAmpere
Posts: 1049
Joined: July 1st, 2016, 3:58 pm

Still Life problem

This is a strange challenge, and it probably can be solved by a computer program, but here it is:
For a n-cell polyplet in Life, what is the specific n-cell polyplet that takes the most cells to stabilize? This is excluding Coolout Conjecture examples. For n = 1, 2, 3, and 4, the solutions are 4, 4, 7, and 13 respectively, with the polyplet with maximal stabilization in white:

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``````x = 6, y = 25, rule = LifeHistory
CA\$2A5\$2A\$2C4\$2.2A\$3.A\$3C\$A5\$4.2A\$2A3.A\$A2.C\$2.3C\$5.A\$4.2A!
``````
Does anyone understand what I mean? I think this might be an interesting problem, but I really don't know. Feel free to ask questions.
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

Rhombic
Posts: 1056
Joined: June 1st, 2013, 5:41 pm

Re: Still Life problem

Is it one of these? (probably not)
https://oeis.org/search?q=4%2C4%2C7%2C1 ... &go=Search

By the way, polyplet or polyomino?
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

AforAmpere
Posts: 1049
Joined: July 1st, 2016, 3:58 pm

Re: Still Life problem

No, that sequence is not it, it is a different thing. Use polyplets, essentially connected patterns, and only use polyplets that have no cells with 4 or more live neighbors (essentially use polyplets that can be stabilized). So exclude polyplets like this phase of the glider, where the middle cell in this phase has 4 cells around it:

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``````x = 3, y = 3, rule = LifeHistory
.A\$.2A\$A.A!
``````
However, other patterns, like the other phase of the glider, have no cells with 4 or more neighbors, and can be stabilized:

Code: Select all

``````x = 6, y = 4, rule = LifeHistory
.2C.2A\$C.C.2A\$A.C\$.2A!
``````
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)