Complexity and Universality of Iterated Finite Automata

Iterated Finite Automaton (IFA) is invented by Wolfram for studying the conventional Finite State Automata(FSA) by means of A New Kind of Science (NKS) methodology. An IFA is a composition of a finite state automaton and a tape with limited cells. The complexity of behaviors generated by various FSA operating on different tapes can be visualized by two dimensional patterns. Through enumerating all possible 2-state and 3-color IFA, this paper shows that there are a variety of complex behaviors in these simple computational systems. These patterns can be divided into 8 classes roughly such as regular patterns, noisy structures, complex behaviors, and so forth. Also they show the similarity between iterated finite automata and elementary cellular automata. Furthermore, any cellular automaton can be emulated by an IFA and vice versa. That means IFA supports universal computation.