James E. Hanson -- Computational Mechanics

Dynamics of patterns in spatial systems

My published work to date has dealt with applying computational mechanics to cellular automata.

What is computational mechanics?

Investigating dynamical systems in the context of information theory--i.e., of information transmission--has proved extremely fruitful in recent years. Information theory has been used with great success to characterize the diversity of behavior of a system, its instability to perturbations, and the rate at which predictability of or information about the system's state decays. Our understanding of deterministic chaos, disordered systems, and turbulent flow (to name a few examples) has benefited immeasurably.

But this does not exhaust the story by any means. In addition to the simple transmission of information, most systems also exhibit nontrivial information processing. This shows up as some kind of emergent structure or pattern in the record of the system's behavior--structure that may be embedded in apparent randomness due to simple information transmission. The notion of ``information'' is insufficient to help identify or describe such structural features. This gap is precisely what computational mechanics is designed to fill.

The program of computational mechanics therefore focuses on structural features or patterns in the behavior of dynamical systems, effecting a very general characterization of them by means of computation-theoretic and automata-theoretic models. The term ``computational mechanics'' was chosen to highlight its connection to statistical mechanics and information theory on the one hand, and computation theory on the other. It is arguably the natural next step beyond the use of information-theoretic ideas in dynamics.

Why computation theory?

Why is computation theory an appropriate springboard for analyzing structure in natural processes? The answer lies in the close analogy between structures or patterns and algorithms. A pattern consists of a structural feature or complex of features common to a set of examples (such as data sets from an experiment). Formulating an explicit representation a pattern is equivalent to specifying a method of reproducing examples of it: in other words, of designing an algorithm. Computational mechanics exploits this analogy by investigating structure in natural processes in terms of algorithms--that is, in terms of computation theory.

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This page last updated January 22, 2004