Gardens of Eden in the Game of Life

Published 2 Dec 2019 in math.DS and cs.FL | (1912.00692v2)

Abstract: We prove that in the Game of Life, if the thickness-four zero-padding of a rectangular pattern is not an orphan, then the corresponding finite-support configuration is not a Garden of Eden, and that the preimage of every finite-support configuration has dense semilinear configurations. In particular finite-support Gardens of Eden are in co-NP.

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