The Limiting Behavior of Non-cylindrical Elementar y Cellular Automata
Carole Twining · Complex Systems · 1992
A classification of cellular automata (CAs) complementary to th at of Wolfram was recently proposed by Binder. This classifica tion is motivat ed by t he limiting behavior seen in automat a wit h fixed boundaries. In what follows, we show t hat for a number of elemen tary CA rules it is possible to obtain complete solut ions for t he periods and numbers of all limit cycles, plus, in some cases, informat ion on t he st ructure of t he cycles t hemselves. In part icular , we are able t o confirm t he existence of globally at t ractive limit cycles of fixed period for several CA rules.