To understand an aperiodic tiling (or a quasicrystal modeled on an aperiodic tiling), we construct a space of similar tilings, on which the group of translations acts naturally. This space is then an (abstract) dynamical system. Dynamical properties of the space (such as mixing, or the spectrum of the translation operator) are closely related to bulk properties of individual tilings (such as th...

This paper fully develops Diamond Tiling, a technique to partition the computations of stencil applications such as FDTD. The Diamond Tiling technique is the result of optimizing the amount of useful computations that can be executed when a region of memory is loaded to the local memory of a multiprocessor chip. Diamond Tiling contributes to the state of the art on time tiling techniques in tha...

A tiling of a subset A of R is a countable set T of tiles in R such that: (1) ∪T = A, (2) whenever S, T belong to T and are distinct we have intS ∩ intT = ∅. Part of a pentagonal tiling is shown in Figure 2. A patch is a tiling by finitely many tiles of a connected, simply connected subset of R which cannot be disconnected by removing one point. To say that a patch A belongs to a tiling T means...

Parametric tiling is a well-known transformation which is widely used to improve locality, parallelism and granularity. However, parametric tiling is also a non-linear transformation and this prevents polyhedral analysis or further polyhedral transformation after parametric tiling. It is therefore generally applied during the code generation phase. In this paper, we present a method to remain p...