Stripes on Penrose tilings
A Hizume, Yoshikazu Yamagishi · Journal of Physics A Mathematical and Theoretical · 2010
We study the existence of one-dimensional quasicrystal structures on the vertex set Λ P of a Penrose tiling, in an arbitrary direction . If , ζ = e 2πi/5 , then is a discrete family of lines that has a one-dimensional quasicrystal structure. Conversely, if w ≠ 0 and , is a dense subset of . We also have a weak analog of Kronecker's approximation theorem.