Graphs induced by iterated function systems
  For an iterated function system (IFS) of simillitidues, we define two graphs on the representing symbolic space. We show that if the self-similar set $K$ has positive Lebesgue measure or the IFS satisfies the weak separation condition, then the graphs are hyperbolic, moreover the hyperbolic boundaries are homeomorphic to the self-similar sets. 
Xiang-Yang Wang
math.FA