Still Life problem

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

Still Life problem

Post by AforAmpere »

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:

Code: Select all

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.
The torch of 5S has been passed on again, and is now managed by speedydelete. It can be found here. Also check out my program EPE, a tool for searching for patterns in various rulespaces.
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Rhombic
Posts: 1100
Joined: June 1st, 2013, 5:41 pm

Re: Still Life problem

Post by Rhombic »

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
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AforAmpere
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Posts: 1433
Joined: July 1st, 2016, 3:58 pm

Re: Still Life problem

Post by AforAmpere »

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!
The torch of 5S has been passed on again, and is now managed by speedydelete. It can be found here. Also check out my program EPE, a tool for searching for patterns in various rulespaces.
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