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arXiv · 1912.00692

Gardens of Eden in the Game of Life

Ville Salo·Ilkka Törmä
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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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Ville Salo, Ilkka Törmä. 2019-12-02. Gardens of Eden in the Game of Life. https://arxiv.org/abs/1912.00692

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