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### Robust periodic solutions in multi-state cellular automata

**Student-Run Applied & Math Seminar**

Speaker: | Xiaochen Liu, UC Davis |

Related Webpage: | https://www.math.ucdavis.edu/~xchliu/ |

Location: | 2112 MSB |

Start time: | Fri, Sep 29 2017, 12:10PM |

In this talk, we first provide the background of the robust periodic solutions of cellular automata. These are the analogy of stable limit cycles of ordinary differential equations. Our goal is to investigate the asymptotic probabilistic behaviour of the existence of such solutions in our system, the one-dimensional one-sided range-1 multi-state cellular automata. We precisely define the periodic solutions and the robust ones, namely, those advance into any environment with positive velocity. We also introduce the useful tools and theorems that help us transform the problem to random graph problems. Finally we present some current results and several conjectures.

This is joint work with Professor Gravner.