Geodesic
Pseudo-self-affine tilings in~$\mathbb R^d$
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIII, Tome 326 (2005), pp. 198-213

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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. 
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     title = {Pseudo-self-affine tilings in~$\mathbb R^d$},
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B. Solomyak. Pseudo-self-affine tilings in~$\mathbb R^d$. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIII, Tome 326 (2005), pp. 198-213. http://geodesic.mathdoc.fr/item/ZNSL_2005_326_a10/