Generating Self-Affine Tiles and Their Boundaries
نویسنده
چکیده
A tile is a bounded subset of the plane, copies of which may be used to cover the whole plane without gaps or overlap. There are many sources (such as [1]) of beautiful images involving tiling, from medieval Islamic art, through Escher, to more modern work. Perhaps the simplest example of a tile, though, is a solid square, which may tile the plane in a familiar checkerboard pattern. The square is also an example of an important subclass of tiles called the self-affine tiles. A tile T is self-affine if there is an expanding matrix A and a collection of vectors (called the digit set) such that
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