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B-tiles can be related to such A-tiles in two ways: If B S has the same size as A L then B L is an enlarged version φ A S of A S, with side lengths (φ, φ, φ 2 = 1 + φ) – this decomposes into an A L tile and A S tile joined along a common side of length 1.
Following Grünbaum and Shephard (section 1.3), a tiling is said to be regular if the symmetry group of the tiling acts transitively on the flags of the tiling, where a flag is a triple consisting of a mutually incident vertex, edge and tile of the tiling. This means that, for every pair of flags, there is a symmetry operation mapping the first ...
Any translation must be smaller than some size of square, and so cannot leave any such tiling invariant. A portion of tiling by the Robinson tiles. Robinson proves these tiles must form this structure inductively; in effect, the tiles must form blocks which themselves fit together as larger versions of the original tiles, and so on.
A tiling that cannot be constructed from a single primitive cell is called nonperiodic. If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic. [3] The tilings obtained from an aperiodic set of tiles are often called aperiodic tilings, though strictly speaking it is the tiles themselves that are ...
Vector tiles, tiled vectors or vectiles [1] are packets of geographic data, packaged into pre-defined roughly-square shaped "tiles" for transfer over the web. This is an emerging method for delivering styled web maps , combining certain benefits of pre-rendered raster map tiles with vector map data.
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