### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Matthew Russell**, Rutgers University, russell2 {at} math [dot] rutgers [dot] edu)
** Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: On the No. of ON Cells in Cellular Automata

Speaker: **Neil J. A. Sloane**, Rutgers University and The OEIS Foundation

Date: Thursday, February 5, 2015 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

A cellular automaton (or CA) is started with a single ON cell; how many cells are ON after n generations? A general theorem will be presented which applies to a certain class of "odd-rule" CAs, including Rule 150, Rule 614, and Fredkin's Replicator, although to get an explicit answer in the last two requires delicate surgical techniques. A number of other CAs can be analyzed by ad hoc methods, although most two-dimensional CAs seem beyond reach. The difficulty of analysis is strongly correlated with the beauty of the resulting patterns.

See: http://www.math.rutgers.edu/~russell2/expmath/