  We introduce a construction to embed a quasiperiodic lattice of obstacles
into a single unit cell of a higher-dimensional space, with periodic boundary
conditions. This construction transparently shows the existence of channels in
these systems,in which particles may travel without colliding, up to a critical
obstacle radius. It provides a simple and efficient algorithm for numerical
simulation of dynamics in quasiperiodic structures, as well as giving a natural
notion of uniform distribution (measure) and averages. As an application, we
simulate diffusion in a two-dimensional quasicrystal, finding three different
regimes, in particular atypical weak super-diffusion in the presence of
channels, and sub-diffusion when obstacles overlap.
