Monomial Cellular Automata
Ron Bartlett
Max Garzon
Department of Mathematical Sciences,
The University of Memphis,
Memphis, Tennessee 38152, USA
Abstract
We investigate the dynamics of monomial cellular automata, whose next-state is given as a product of the neighboring states. Monomial cellular automata provide a multiplicative analogue of additive cellular automata with novel dynamical features. Phase portraits are given for monomials of degree two and three, along with general methods to obtain them. Monomials of higher degree are analyzed via a superposition principle.
