A formula for the upper box-counting dimension of self-projective sets

Abstract

We prove a packing exponent formula for the upper box-counting dimension of attractors of certain projective iterated function systems. This partially affirms a conjecture of De Leo, and gives that the box-counting dimension of the Rauzy gasket $\mathcal R$, $\operatorname{dim}_B(\mathcal R)$, exists and satisfies $\operatorname{dim}_B(\mathcal R) = \operatorname{dim}_H(\mathcal R) \in [1.6196,1.7415].$