3:00 p.m., Friday (September 16, 2005)

Math Annex 1100

Alexander Holroyd

The Bootstrap Percolation Cellular Automaton - a case study in Theory versus Experiment

See for a picture.

Cellular automata arise naturally in the study of physical systems, and exhibit a seemingly limitless range of intriguing behaviour. Such models lend themselves naturally to computer simulation, but rigorous analysis can be notoriously difficult, and can yield highly unexpected results.

Bootstrap percolation is a very simple model for nucleation and growth which turns out to hold many surprises. Sites in a square grid are initially declared ``infected" independently with some fixed probability. Subsequently, healthy sites become infected if they have at least two infected neighbours, while infected sites remain infected forever. The model undergoes a phase transition at a certain threshold whose asymptotic value differs from numerical predictions by more than a factor of two! This discrepancy points to a previously unsuspected phenomenon called ``crossover", and leads to further intriguing questions.

Refreshments will be served at 2:45 p.m. (MATX 1115, Faculty Lounge).

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