In this work we define a stochastic adding machine associated to a quadratic base (n)n≥0 formed by recurrent sequences of order 2. We obtain a Markov chain with states in ℤ+ and we prove that the spectrum of the transition operator associated to this Markov chain is connected to the filled Julia sets for a class of endomorphisms in ℂ2 of which we study topological properties. © 2010 Mathematics Subject Classification.