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A self-tiling tile set, or setiset, of order n is a set of n shapes or pieces, usually planar, each of which can be tiled with smaller replicas of the complete set of n shapes. That is, the n shapes can be assembled in n different ways so as to create larger copies of themselves, where the increase in scale is the same in each case.
The tiles in the square tiling have only one shape, and it is common for other tilings to have only a finite number of shapes. These shapes are called prototiles, and a set of prototiles is said to admit a tiling or tile the plane if there is a tiling of the plane using only these shapes.
A kitchen backsplash gets splattered with grease from the stove top and rarely gets the good scrub it so badly requires But some clever, kitschy ideas are turning this often neglected space into a ...
Guastavino tile vaulting in the City Hall station of the New York City Subway Guastavino ceiling tiles on the south arcade of the Manhattan Municipal Building. The Guastavino tile arch system is a version of Catalan vault introduced to the United States in 1885 by Spanish architect and builder Rafael Guastavino (1842–1908). [1]
Rep-tiles can be used to create fractals, or shapes that are self-similar at smaller and smaller scales. A rep-tile fractal is formed by subdividing the rep-tile, removing one or more copies of the subdivided shape, and then continuing recursively.
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