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We study two-player \emph{take-away} games whose outcomes emulate two-stateone-dimensional cellular automata, such as Wolfram's rules 60 and 110. Given aninitial string consisting of a central data pattern and periodic left and rightpatterns, the rule 110 cellular automaton was recently proved Turing-completeby Matthew Cook. Hence, many questions regarding its behavior arealgorithmically undecidable. We show that similar questions are undecidable forour \emph{rule 110} game.

Impartial games emulating one-dimensional cellular automata and undecidability