Tilings Encyclopedia | MLD Class Chair

MLD Class Chair

The chair tiling, as most tilings presented here, is nonperiodic. But there is a strong resemblance to periodic tiling. For instance, the set of vertex points in the tiling obviously spans a square lattice. Moreover, it is possible to detect large subsets in the tiling which are fully periodic. For instance, consider the pattern of white crosses (consisting of four tiles each) in the tiling. In fact, the chair tiling is the union of a countable set of fully periodic tile sets $L_{1}, L_{2}, L_{3}$…, where each $L_{i}$ possesses period vectors of length $2 \times 2^{i}$.

Finite Rotations P Adic Windowed Tiling Polytopal Tiles Rep Tiles Self Similar Substitution Mld Class Chair

Square Chair

MLD to the more popular chair tiling, this version allows a simple translation into a coloured lattice: Replace each square of type i (1,2,3, or 4) with its midpoint, and assign to it colour i. Then each set of all points of colour i is a model set with internal p-adic space with p=2. This was first shown in [BMS98], a general framework is given in [LMS03].

With Decoration Finite Rotations P Adic Windowed Tiling Polytopal Tiles Self Similar Substitution Parallelogram Tiles Rhomb Tiles Mld Class Chair