Pseudo-self-affine tilings in $\mathbb R^d$

It is proved that every pseudo-self-affine tiling in $\mathbb R^d$ is mutually locally derivable with a self-affine tiling. A characterization of pseudo-self-similar tilings in terms of derived Voronoï tessellations is a corollary. Previously, these results were obtained in the planar case, jointly with Priebe Frank. The new approach is based on the theory of graph-directed iterated function systems and substitution Delone sets developed by Lagarias and Wang.