Stripes on Penrose tilings

A Hizume, Y Yamagishi
2010 Journal of Physics A: Mathematical and Theoretical  
We consider a class of cut-and-project sets Λ = Λ_F × in the plane. Let L=Λ+w, w∈^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 ^2, or (3) each connected component of the closure of L is homeomorphic to [0,1] ×.
doi:10.1088/1751-8113/44/1/015202 fatcat:4isfpfatcfa6rbbs2nd3jxdhme