  Consider the basic algorithm to perform the transformation n--> n+1 changing
digits of the d-adic expansion of n one by one. We obtain a family of Markov
chains on the non-negative integers through sucessive and independent
applications of the algorithm modified by a parametrized stochastic rule that
randomly prevents one of the steps in the algorithm to finish. The objects of
study in this paper are the spectra of the transition operators of these Markov
chains. The spectra of these Markov chains turn out to be fibered Julia sets of
fibered polynomials. This enable us to analyze their topological and analytical
properties with respect to the underlying parameters of the Markov chains.
