thumb|right|Gun and antigun demonstrating the symmetry of Day & Night.
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.
Dynamics and symmetry
Because of its black/white reversal symmetry, every finite pattern on an otherwise empty background has a corresponding antipattern obtained by inverting live and dead cells on an otherwise fully live background. The antipattern evolves under the rule exactly as the original pattern does, but with live and dead cells interchanged at every time step. In particular, every localized object has a corresponding antiobject that behaves identically against the inverted background.
The global qualitative evolution differs from Conway's Game of Life, but Day and Night also supports long-lived localized structures. Typical evolutions contain a mixture of stable regions, oscillatory regions, and moving patterns such as spaceships and debris.
Known patterns
Day and Night supports a large variety of small still lifes, oscillators, spaceships, puffers, rakes, and guns. Many examples arise spontaneously from low-density starting patterns and have been catalogued in pattern collections.