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The one-dimensional Exactly 1 cellular automaton
Student-Run Research| Speaker: | Janko Gravner, UC Davis |
| Location: | 1147 MSB |
| Start time: | Wed, Mar 2 2011, 12:10PM |
Description
In the Exactly 1 cellular automaton (also known as Rule 22 ), every site of the one-dimensional
lattice is either in state 0 or in state 1, and a synchronous update rule dictates that a site is
in state 1 next time if and only if it sees a single 1 in its three-site neighborhood at the
current time. We analyze this rule started from finite seeds, i.e., those initial configurations
that have only finitely many 1’s. Three qualitatively different types of evolution are observed:
replication, periodicity, and chaos. The main focus of the talk will be on rigorous results,
assisted by algorithmic searches, for the first two behaviors. Joint work with David Griffeath.