Garden of Eden (cellular automaton)

In a cellular automaton, a Garden of Eden is a configuration that has no predecessor. It can be the initial configuration of the automaton but cannot arise in any other way.John Tukey named these configurations after the Garden of Eden in Abrahamic religions, which was created out of nowhere. The Garden of Eden theorem of Moore and Myhill asserts that a cellular automaton on the square grid, or on a tiling of any higher dimensional Euclidean space, has a Garden of Eden if and only if it has twins, two finite patterns that have the same successors whenever one is substituted for the other.

Garden of Eden (cellular automaton)

In a cellular automaton, a Garden of Eden is a configuration that has no predecessor. It can be the initial configuration of the automaton but cannot arise in any other way.John Tukey named these configurations after the Garden of Eden in Abrahamic religions, which was created out of nowhere. The Garden of Eden theorem of Moore and Myhill asserts that a cellular automaton on the square grid, or on a tiling of any higher dimensional Euclidean space, has a Garden of Eden if and only if it has twins, two finite patterns that have the same successors whenever one is substituted for the other.