Hausdorff and box dimension bounds for subfractals induced by S-gap shifts

In this paper, we consider subsets of an attractor of an iterated function system in which each point is associated with an allowable word from an S-gap shift. The main result shows that bounds for the box dimension and Hausdorff dimension of a subfractal induced by an S-gap shift are given by the zeros of the upper and lower topological pressure functions.