Fractals, vol.23, no.3, 2015 (SCI-Expanded)
© 2015 World Scientific Publishing Company.In this paper, first we equip the automorphism group of the p-ary rooted tree X∗with a natural metric and define a family of contractions on Aut(X∗). Then, we construct an iterated function system (IFS) whose attractor is the closure of the adding machine group on Aut(X∗). Finally, we show that this group is a strong self-similar group in the sense of IFS.