## Larger than Life Parameter Space: Nonlinear Cellular Automaton Rules and Creatures of the Digital Kind |

**Kellie Evans**

York College of Pennsylvania

October 20, 1997

3:30 pm

Bailey Hall

Refreshments at 3:15

Math Department Common Room

Larger than Life is a four-parameter family of two-state cellular automaton rules that generalize John Conway's celebrated Game of Life. Two approaches to the analysis of the Larger than Life family will be discussed. One is from the perspective of probability theory and particle systems. The ergodic classifications of monotone Larger than Life rules will be described. Upper bounds will be given for invariant measures. The other approach is to think of the time evolutions of finite initial states as iterated maps. Various finite configurations such as replicators (which have space-time diagrams that are isomorphic to Pascal's Triangle Mod 2); and bugs (large-range analogues to Life's famous gliders) will be introduced and examples will be provided.

For additional information, send e-mail to math@union.edu or call (518) 388-6246.

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