Attractors of directed graph IFSs that are not standard IFS attractors   and their Hausdorff measure
  For directed graph iterated function systems (IFSs) defined on R, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of standard (1-vertex directed graph) IFSs, with or without separation conditions. We also calculate their exact Hausdorff measure. Thus we are able to identify a new class of attractors for which the exact Hausdorff measure is known. 
G. C. Boore and K. J. Falconer
math.MG