Title

Weak Gardens Of Eden For 1-Dimensional Tessellation Automata

Keywords

Cellular automata; Gardens of Eden; parallel maps; tessellation automata

Abstract

If T is the parallel map associated with a 1-dimensional tessellation automaton, then we say a configuration f is a weak Garden of Eden for T if f has no preimage 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 = Smf where Sm is the shift defined by (Smf)(j) = f(j+m). Subject to a mild restriction on m, the equation Tf = Smf 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. © 1985, Hindawi Publishing Corporation. All rights reserved.

Publication Date

1-1-1985

Publication Title

International Journal of Mathematics and Mathematical Sciences

Volume

8

Issue

3

Number of Pages

579-587

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1155/S0161171285000631

Socpus ID

84956443827 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84956443827

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