- 期刊
WEAK GARDENS OF EDEN FOR 1-DIMENSIONAL TESSELLATION AUTOMATA
並列摘要
If T is the parallel map associated with a l-dimensional tessellation automaton, then we say a configuration f is a weak Garden of Eden for T if f has no pre-image under T other than a shift of itself. Let WG(T) = the set of weak Gardens of Eden for T and G(T) = the set of Gardens of Eden (i.e., the set of configurations not in the range of T). Typically members of WG(T) - G(T) satisfy an equation of the form Tf = S^mf where S^m is the shift defined by (S^mf)(j) = f(j+m). Subject to a mild restriction on m, the equation Tf = S^mf always has a solution f, and all such solutions are periodic. We present a few other properties of weak Gardens of Eden and a characterization of WG(T) for a class of parallel maps we call (0, 1)-characteristic transformations in the case where there are at least three cell states.
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