A stochastic adding machine and complex dynamics

This paper considers properties of a Markov chain on the natural numbers wh ich models a binary adding machine in which there is a non-zero probability of failure each time a register attempts to increment the succeeding regis ter 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 ope rators of these chains have a self-similar structure, and have a spectrum w hich is, variously, the Julia set or filled Julia set of a quadratic map of the complex plane. AMS classification scheme numbers: 37A30, 47A10, 37F50.