Patch frequencies in Penrose rhombic tilings

Abstract

This short exposition presents an algorithm for an exact calculation of patch frequencies for the rhombic Penrose tiling. We recall a construction of Penrose tilings via dualisation, and by extending the known method for obtaining vertex configurations, we obtain the desired algorithm. It is then used to determine the frequencies of several particular large patches which appear in the literature. The analogous approach is also explained for the Ammann-Beenker tiling.

30 pages, 26 figures, 2 tables (minor changes)

References in corpus (3)

• Strictly localized states in the octagonal Ammann-Beenker quasicrystal
• Statistical mechanics of dimers on quasiperiodic Ammann-Beenker tilings
• Localized States in Local Isomorphism Classes of Pentagonal Quasicrystals

Cited by in corpus (1)

• Geometrical Penrose Tilings are characterized by their 1-atlas