Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure

"GCB was supported by an EPSRC Doctoral Training Grant whilst undertaking this work"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.PreprintPeer reviewe