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Garden of Eden (GOE) states in cellular automata are grid configurationswhich have no precursors, that is, they can only occur as initial conditions.Finding individual configurations that minimize or maximize some criterion ofinterest (e.g., grid size, density, etc.) has been a popular sport inrecreational mathematics, but systematic studies of the set of GOEs for acellular automaton have been rare. This paper presents the current results ofan ongoing computational study of GOE configurations in Conway's Game of Life(GoL) cellular automaton. Specifically, we describe the current status of a mapof the layout of GOEs and nonGOEs in density/size space, characterize how thedensity-dependent structure of the number of precursors varies with increasinggrid size as we approach the point where GOEs begin to occur, provide a catalogof all known GOE configurations up to a grid size of 11x11, and initiate astudy of the structure of the network of constraints that characterize GOE vs.nonGOE configurations.

Cultivating the Garden of Eden