Fractal dimension for Inhomogeneous graph-directed attractors

Abstract: In this paper, we define inhomogeneous Graph-Directed (GD) separation conditions for a given inhomogeneous GD Iterated Function Systems (IFS), and estimate the upper box dimension of attractors by the dimension of the condensation set and associated Mauldin-Williams graph dimension. Following some work of Fraser, we also estimate the lower box dimension of attractors generated by inhomogeneous GDIFS. In the end, we shed few lights on the continuity of dimensions for the attractors of inhomogeneous GDIFS.