Stripes on rectangular tilings

Abstract

We consider a class of cut-and-project sets $Λ= Λ_F \times \zahl$ in the plane. Let $L=\Lambda +w\Re$, $w\in {\Re }^2$, be a countable union of parallel lines. Then either (1) $L$ is a discrete family of lines, (2) $L$ is a dense subset of ${\Re }^2$, or (3) each connected component of the closure of $L$ is homeomorphic to $[0,1]\times \Re$.

6 pages, 2 figures

References in corpus (2)

• Discrete Tomography of Penrose Model Sets
• Stripes on rectangular tilings

Cited by in corpus (1)

• Stripes on rectangular tilings