- 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:
http://psoup.math.wisc.edu/kitchen.html,
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
griffeat@math.wisc.edu.
Thanks,
DG
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