Garden of Eden pattern
From Biocrawler, the free encyclopedia.
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 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 Ct, there is a unique predecessor configuration Ct-1 easily determined from Ct. 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 unique.
External links
- Garden of Eden (Eric Wesstein's Treasure Trove of The Game of Life) (http://www.ericweisstein.com/encyclopedias/life/GardenofEden.html)fr:Jardin d'Éden (automate cellulaire)
