Three classes of one-dimensional, two-tile Penrose tilings and the Fibonacci Kronig-Penney model as a generic case

We generalize the Fibonacci Penrose tiling to three classes of one-dimensional, two-tile Penrose tilings which can be obtained geometrically as well as recursively. From a numerical study of their spectral properties, we conclude that the Fibonacci case has the generic features of all three classes. As a model of epitaxial quasiperiodic superlattices we consider a Fibonacci Kronig-Penney model and give a physical picture relating structural to spectral properties.