Stripes on rectangular tilings

Akio Hizume, Yoshikazu Yamagishi

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 di…