LIMIT-(QUASI)PERIODIC POINT SETS AS QUASI-CRYSTALS WITH P-ADIC INTERNAL SPACES

Model sets (or cut and project sets) provide a familiar and commonly u sed method of constructing and studying nonperiodic point sets. Here w e extend this method to situations where the internal spaces are no lo nger Euclidean, but instead spaces with p-adic topologies or even with mixed Euclidean/p-adic topologies. We show that a number of well know n tilings precisely fit this form, including the chair tiling and the Robinson square tilings. Thus the scope of the cut and project formali sm is considerably larger than is usually supposed. Applying the power ful consequences of model sets we derive the diffractive nature of the se tilings.