Less singular quasicrystals: life in low codimensions

The Rauzy tilings were proposed recently in a generalisation of the Fibonacci chain by Vidal and Mosseri. These tilings have a particularly simple theoretical description, making them appealing candidates for analytical solutions for electronic properties. We show by a numerical study of statistical properties of the tight-binding spectra that these tilings fall in an intermediate category between the crystal and the quasicrystal, i.e. in a class of almost integrable models.