Mathematical Sciences: Attracting Sets in Cellular Automata

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Michael Hurley will carry out research in dynamical systems. In particular he will study cellular automata. These are related to the magnetic storage of data. Hurley's objective is to investigate the mathematical explanations of various recent empirical observations. One reason for interest in cellular automata is that some of them exhibit self-organizing behavior. In mathematical terms this suggests the existence of attractors. A cellular automaton can be thought of as a map on doubly infinite sequences which commutes with shifts. Hurley will study the dynamics of such maps. Self-organization manifests itself in the observation that random sequences become more highly patterned under repeated iterations and the asymptotic pattern is independent of the original sequence. The two major goals of Hurley's research are to understand the hierarchy of the collection of attractors of an automaton and to describe the dynamics of its restriction to its interesting attractors.