Garden Of Eden Pattern

In the study of cellular automata, Garden of Eden patterns are configurations that cannot be reached from any other starting configuration. They are named after the biblical Garden of Eden because they have no predecessor configurations—they must be created as such. These configurations were named by John Tukey in the 1950s, long before John Conway invented his Game of Life.

General consequences

Let some configuration at timestep t be denoted by Ct, and the function (the automaton) f to map the configuration Ct to Ct+1. A Garden of Eden pattern Gt means that there does not exist any configuration Gt-1 such that f(Gt-1)=Gt. This means that the automaton is not surjective. Garden of Eden patterns are not unique.

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