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 $\mathcal{R}$, ${\dim }_B(\mathcal{R})$, exists and satisfies ${\dim }_B(\mathcal{R})={\dim }_H(\mathcal{R})\in [1.6196,1.7415].$

26 pages, 9 figures