Michael Baake et al 1998 J. Phys. A: Math. Gen. 31 5755 doi:10.1088/0305-4470/31/27/006
Limit-(quasi)periodic point sets as quasicrystals with p-adic internal spaces
Michael Baake
, Robert V Moody
and Martin Schlottmann
Model sets (or cut and project sets) provide a familiar and commonly used method of constructing and studying nonperiodic point sets. Here we extend this method to situations where the internal spaces are no longer Euclidean, but instead spaces with p-adic topologies or even with mixed Euclidean/p-adic topologies. We show that a number of well known tilings precisely fit this form, including the chair tiling and the Robinson square tilings. Thus the scope of the cut and project formalism is considerably larger than is usually supposed. Applying the powerful consequences of model sets we derive the diffractive nature of these tilings.
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Issue 27 (10 July 1998)
Received 26 February 1998
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Limit-(quasi)periodic point sets as quasicrystals with p-adic internal spaces
Michael Baake et al 1998 J. Phys. A: Math. Gen. 31 5755
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