A Study of Fuzzy and Many-Valued Logics in Cellular Automata

We consider the effect of the underlying logical structure on the asymptotic behavior of space-time diagrams of elementary Boolean cellular automata by focussing on the important case of Rule 110 and its counterparts under various many-valued logics. In particular we show that for a (continuous) probabilistic logic the corresponding rule, dubbed PCA 110, appears to have space-time diagrams with limiting behavior at infinity, a somewhat counter-intuitive result. New methods will be required to handle the general cases in contrast to the classical fuzzy case consider by other authors.