A stochastic adding machine and complex dynamics.
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.
Killeen
Peter R
PR
Department of Psychology, Arizona State University, Tempe, AZ 85287, USA.
Taylor
Thomas J
TJ