# Mathematics Colloquia and Seminars

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### The one-dimensional Exactly 1 cellular automaton

**Student-Run Applied & Math Seminar**

Speaker: | Janko Gravner, UC Davis |

Location: | 1147 MSB |

Start time: | Wed, Mar 2 2011, 12:10PM |

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.