Aperiodicity in one-dimensional cellular automata
Cellular automata are a class of mathematical systems characterized by discreteness (in space, time, and state values), determinism, and local interaction. A certain class of one-dimensional, binary site-valued, nearest-neighbor automata is shown to generate infinitely many aperiodic temporal sequences from arbitrary finite initial conditions on an infinite lattice. The class of automaton rules that generate aperiodic temporal sequences are characterized by a particular form of injectivity in their interaction rules. Included are the nontrivial linear'' automaton rules (that is, rules for which the superposition principle holds); certain nonlinear automata that retain injectivity properties similar to those of linear automata; and a wider subset of nonlinear automata whose interaction rules satisfy a weaker form of injectivity together with certain symmetry conditions. A technique is outlined here that maps this last set of automata onto a linear automaton, and thereby establishes the aperiodicity of their temporal sequences. 12 refs., 3 figs.
- Research Organization:
- Los Alamos National Lab., NM (USA)
- Sponsoring Organization:
- DOE/MA
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 7230855
- Report Number(s):
- LA-UR-90-761; CONF-8908218--1; ON: DE90008947
- Country of Publication:
- United States
- Language:
- English
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