1 research outputs found
Universal Cellular Automata and Class 4
Wolfram has provided a qualitative classification of cellular automata(CA)
rules according to which, there exits a class of CA rules (called Class 4)
which exhibit complex pattern formation and long-lived dynamical activity (long
transients). These properties of Class 4 CA's has led to the conjecture that
Class 4 rules are Universal Turing machines i.e. they are bases for
computational universality. We describe an embedding of a ``small'' universal
Turing machine due to Minsky, into a cellular automaton rule-table. This
produces a collection of cellular automata, all of which are
computationally universal. However, we observe that these rules are distributed
amongst the various Wolfram classes. More precisely, we show that the
identification of the Wolfram class depends crucially on the set of initial
conditions used to simulate the given CA. This work, among others, indicates
that a description of complex systems and information dynamics may need a new
framework for non-equilibrium statistical mechanics.Comment: Latex, 10 pages, 5 figures uuencode