We introduce and study the number of tilings of unit height rectangles with irrational tiles. We prove that the class of sequences of these numbers coincides with the class of diagonals of N-rational generating functions and a class of certain binomial multisums. We then give asymptotic applications and establish connections to hypergeometric functions and Catalan numbers.

We give the inflation rules for the decorated Mosseri–Sadoc tiles in the projection class of tilings T . Dehn invariants related to the stone inflation of the Mosseri–Sadoc tiles provide eigenvectors of the inflation matrix with eigenvalues equal to τ = 1+ √ 5 2 and (−τ).

The Wang Tiles method is a successful and effective technique for the representation of 2D-texture or 3D-geometry. In this paper we present a new method to fill Wang tiles with a 2D-FON distribution or a 3D-geometry in order to achieve a more efficient runtime. We extend the Wang Tiles method to include information about their position. We further demonstrate how the individual tiles are filled...