Theory and applications of cellular automata and iterated systems

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Cellular automata and iterated systems are discrete dynamical systems that can be used to model many processes of interest in a variety of sciences. They have been used, for example, to construct models of crystal growth, chemical reactions, spiral galaxies, social interactions, and vehicle traffic. They are used in applications in computer chip design, cryptography, and as pseudo-random number generators. The program set forth in this proposal involves both analytic studies of the mathematical properties of cellular automata and iterated systems and their application in construction of simple models that illustrate general principles of complex systems. For example, recent work has considered the trade-off between stability and flexibility and shown that in environments where random fluctuations occur that preferentially select for one or another of two stable types, an unstable type (that is, one which through self-monitoring and adaptive control remains "balanced" between distinct behavioral responses) can come to dominate, even if it pays a cost in terms of increased mortality. Another study proposed for continued work will consider the trade-off between quickness of response and accuracy in perception of threat situations: a quick response increases the likelihood of escaping danger, but also increases the likelihood of missing opportunity that might be perceived with more careful consideration. Simple models of cases like these are important for research on complex adaptive systems since the complexity of real world systems often masks general underlying principles.