title: A stochastic adding machine and complex dynamics.
abstract: This paper considers properties of a Markov chain on the natural numbers which models a binary adding machine in which there a non-zero probability of failure each time a register attempts to increment the succeeding register and resets. This chain has a family of natural quotient Markov chains, and extends naturally to a chain on the 2-adic integers. The transition operators of these chains have a self-similar structure, and have a spectrum which is, variously, the Julia set or filled Julia set of a quadratic map of the complex plane.
authors.affiliation: Department of Psychology, Arizona State University, Tempe, AZ 85287, USA.
authors.forename: Peter R
authors.initials: PR
authors.lastname: Killeen
authors.forename: Thomas J
authors.initials: TJ
authors.lastname: Taylor