Sub Rosa, a system of quasiperiodic rhombic substitution tilings with n-fold rotational symmetry

Abstract

In this paper we prove the existence of quasiperiodic rhombic substitution tilings with 2n-fold rotational symmetry, for any n. The tilings are edge-to-edge and use [n/2] rhombic prototiles with unit length sides. We explicitly describe the substitution rule for the edges of the rhombuses, and prove the existence of the corresponding tile substitutions by proving that the interior can be tiled consistently with the given edge substitutions.

26 pages, 11 figures

References in corpus (1)

• A computer search for planar substitution tilings with n-fold rotational symmetry

Cited by in corpus (5)

• Cyclotomic Aperiodic Substitution Tilings
• Metallic mean Wang tiles I: self-similarity, aperiodicity and minimality
• Substitution discrete plane tilings with $2n$-fold rotational symmetry for odd n
• Planar Rosa : a family of quasiperiodic substitution discrete plane tilings with $2n$-fold rotational symmetry
• Substitution tilings with dense tile orientations and n-fold rotational symmetry