Complex Systems

The Limiting Behavior of Non-cylindrical Elementary Cellular Automata Download PDF

C. J. Twining
Theoretical Physics, University of Oxford, Keble Road,
Oxford OX1 3NP, UK


A classification of cellular automata (CAs) complementary to that of Wolfram was recently proposed by Binder. This classification is motivated by the limiting behavior seen in automata with fixed boundaries. In what follows, we show that for a number of elementary CA rules it is possible to obtain complete solutions for the periods and numbers of all limit cycles, plus, in some cases, information on the structure of the cycles themselves. In particular, we are able to confirm the existence of globally attractive limit cycles of fixed period for several CA rules.