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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 (longtransients). These properties of Class 4 CA's has led to the conjecture thatClass 4 rules are Universal Turing machines i.e. they are bases forcomputational universality. We describe an embedding of a ``small'' universalTuring machine due to Minsky, into a cellular automaton rule-table. Thisproduces a collection of $(k=18,r=1)$ cellular automata, all of which arecomputationally universal. However, we observe that these rules are distributedamongst the various Wolfram classes. More precisely, we show that theidentification of the Wolfram class depends crucially on the set of initialconditions used to simulate the given CA. This work, among others, indicatesthat a description of complex systems and information dynamics may need a newframework for non-equilibrium statistical mechanics.Comment: Latex, 10 pages, 5 figures uuencode

Role of initial conditions in the classification of the rule space of cellular automata dynamics