Graph-Directed Iterated Function Systems with Overlaps
Indiana University Mathematics Journal
We extend the finite type condition to graph-directed iterated function systems with overlaps. Under this condition, we describe algorithms to compute the box dimension and Hausdorff dimension of the corresponding graph self-similar sets and show that these dimensions agree; moreover, the Hausdorff measure of these sets is shown to be strictly positive.
Das, Manav, Sze-Man Ngai.
"Graph-Directed Iterated Function Systems with Overlaps."
Indiana University Mathematics Journal, 53 (1): 109-134.