Limit-(quasi)periodic point sets as quasicrystals with<b><i>p</i></b>-adic internal spaces

Abstract

Model sets (or cut and project sets) provide a familiar and commonly used\nmethod of constructing and studying nonperiodic point sets. Here we extend this\nmethod to situations where the internal spaces are no longer Euclidean, but\ninstead spaces with p-adic topologies or even with mixed Euclidean/p-adic\ntopologies.\n We show that a number of well known tilings precisely fit this form,\nincluding the chair tiling and the Robinson square tilings. Thus the scope of\nthe cut and project formalism is considerably larger than is usually supposed.\nApplying the powerful consequences of model sets we derive the diffractive\nnature of these tilings.\n