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MATH 821

An Introduction to Cellular Automata
and Complex Random Systems

Instructor: David Griffeath
Time & Place: MWF 9:55 AM, B223 Van Vleck
Prerequisite: Consent of Instructor

We will explore theoretical and experimental approaches to the study of cellular automata and other spatially distributed complex systems. The course will be interdisciplinary in spirit, stressing the use of CA dynamics, deterministic and probabilistic, as paradigms for physical phenomena from across the spectrum of applied science. Included among the models covered will be lattice gases, percolation through porous media, self-organization in excitable media, and spatial distribution of competing species.

Where possible, we will develop techniques for the rigorous mathematical analysis of such models. Tools include path representations, convex analysis, contour methods, mean-field approximation, and large deviations. But the course will also stress computer simulation and dynamic, interactive visualization. Demonstrations and tutorials will make extensive use of our web site, the Primordial Soup Kitchen:,

our WinCA experimentation platform, and other Java-based CA software currently being developed under the auspices of a UW Web Grant.

Little advanced (graduate-level) mathematical background will be required. However a basic familiarity with aspects of probability theory, combinatorics, differential equations, and/or computer algorithms at the advanced undergraduate level is essential.

There will be no formal textbook. Reading materials for the course, which will be distributed, are likely to include:

  • Rick Durrett's "St. Flour Lecture Notes," and his
    Annals of Probability Special Invited Paper on "Oriented Percolation";

  • excerpts from Cellular Automaton Machines by Toffoli and Margolus, MIT Press, 1987;

  • Rudy Rucker's "Introduction to Cellular Automata"
    (text bundled with his CA-Lab software);

  • Several of my recent papers with J. Gravner,
    on Excitable CA dynamics and CA shape theory.

If interested in this seminar, please REGISTER at your earliest convenience and let me know by email that you plan to attend. We will need at least 10 registered students in order for the course to run. Based on initial feedback, it appears that there is sufficient interest.

Any questions, or requests for additional information, should be sent by email to


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