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.]] 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 ''C''''t'', and the function (the automaton) ''f'' to map the configuration ''C''''t'' to ''C''''t''+1. A Garden of Eden pattern ''G''''t'' means that there does not exist any configuration ''G''''t''-1 such that ''f''(''G''''t''-1)=''G''''t''. This means a cellular automaton which possesses Garden of Eden pattern(s) is not Surjective . One other characteristic of certain cellular automata is that of "reversibility", that is, given a configuration ''C''''t'', there is a unique predecessor configuration ''C''''t''-1 easily determined from ''C''''t''. This condition implies that the automaton function is Bijective . From the definition of bijectivity, cellular automata which possess Garden of Eden patterns are clearly not reversible. In fact, all non- Injective automata possess Garden of Eden patterns. Since the Game of Life is easily seen not to be injective, it was known such patterns existed in it even before any were discovered. Garden of Eden patterns are not necessarily unique. IN FICTION In Greg Egan 's novel '' Permutation City '', the concept of a ''Garden of Eden configuration'' arises in the ''Autoverse'', a projection of Conway's Game Of Life into the future, in which interactions between chemical molecules can be simulated through Cellular Automata . EXTERNAL LINKS |
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