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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 ...
A set of yellow truncated domes on the down-ramp in a parking lot. Tactile paving (also called tenji blocks, truncated domes, detectable warnings, tactile tiles, tactile ground surface indicators, tactile walking surface indicators, or detectable warning surfaces) is a system of textured ground surface indicators found at roadsides (such as at curb cuts), by and on stairs, and on railway ...
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 with rectangles is a tiling which uses rectangles as its parts. The domino tilings are tilings with rectangles of 1 × 2 side ratio. The tilings with straight polyominoes of shapes such as 1 × 3, 1 × 4 and tilings with polyominoes of shapes such as 2 × 3 fall also into this category.
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 labyrinth can be generated by tiles in the form of a white square with a black diagonal. As with the quarter-circle tiles, each such tile has two orientations. [3] The connectivity of the resulting labyrinth can be analyzed mathematically using percolation theory as bond percolation at the critical point of a diagonally-oriented grid.
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