Inhomogeneous Self-Affine Carpets

We investigate the dimension theory of inhomogeneous self-affine carpets. Through the work of Olsen, Snigireva and Fraser, the dimension theory of inhomogeneous self similar sets is now relatively well understood, yet almost no progress has been made concerning more general non-conformal inhomogeneous attractors. If a dimension is countably stable, then the results are immediate, and so we focus on the upper and lower box dimensions and compute these explicitly for large classes of inhomogeneous self-affine carpets. Interestingly, we find that the "expected formula" for the upper box dimension can fail in the self-affine setting, and we thus reveal new phenomena, not occurring in the simpler self-similar case.