Day and Night (cellular automaton)

Day and Night is a two-dimensional Life-like cellular automaton rule related to Game of Life. It is defined by the rule notation B3678/S34678: a dead cell is born if it has 3, 6, 7, or 8 live neighbors, and a live cell survives if it has 3, 4, 6, 7, or 8 live neighbors, where neighborhoods are taken in the Moore neighborhood. The rule was invented and named in 1997 by Nathan Thompson and was subsequently studied in detail by David I. Bell, who constructed many of the currently known patterns and pattern libraries.

The name "Day & Night" refers to a symmetry between the two cell states: if all live and dead cells in a pattern are inverted, then every future generation of the inverted pattern is the inversion of the corresponding generation of the original pattern. Equivalently, if a cell has exactly 3, 6, 7, or 8 neighbors that are all in the same state (all live or all dead), it takes that state in the next generation; otherwise it does not change. In Wolfram's qualitative classification of cellular automata, Day and Night belongs to class 4, with long-lived, interacting local structures and complex behavior.

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