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This question spins off of Gil Kalai's recent question on Conway's game of life for a random initial configuration. There are numerous configurations in the game of life that are known to be stable-...

If the initial state of Conway's game of life is a line of $n \in [0,100]$ alive cells, then it vanishes completely after some steps iff $n \in \{0,1,2,6,14,15,18,19,23,24 \}$. See below for $n=24$. ...

A $n$-polyplet is a collection of $n$ cells on a grid which are orthogonally or diagonally connected. The number of $n$-polyplets is given by the OEIS sequence A030222: $1, 2, 5, 22, 94, 524, 3031, \...