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Domino tiling. In geometry, a domino tiling of a region in the Euclidean plane is a tessellation of the region by dominoes, shapes formed by the union of two unit squares meeting edge-to-edge. Equivalently, it is a perfect matching in the grid graph formed by placing a vertex at the center of each square of the region and connecting two ...
One of 1024 possible domino tilings of an order 4 Aztec diamond A domino tiling of an order-50 Aztec diamond, chosen uniformly at random. The four corners of the diamond outside of the roughly circular area are "frozen". The Aztec diamond theorem states that the number of domino tilings of the Aztec diamond of order n is 2 n(n+1)/2. [2]
The mutilated chessboard problem is an instance of domino tiling of grids and polyominoes, also known as "dimer models", a general class of problems whose study in statistical mechanics dates to the work of Ralph H. Fowler and George Stanley Rushbrooke in 1937. [1] Domino tilings also have a long history of practical use in pavement design and ...
Domino toppling. Domino toppling is the activity of standing up dominoes in sequence known as a domino run and then knocking down the first one in line to strike the next, which knocks that down to strike the next, and so on, creating a chain reaction also called the domino effect. A competition between two or more players to be first to have ...
Dominoes is a family of tile-based games played with gaming pieces. Each domino is a rectangular tile, usually with a line dividing its face into two square ends. Each end is marked with a number of spots (also called pips or dots) or is blank. The backs of the tiles in a set are indistinguishable, either blank or having some common design.
Polyomino. The 18 one-sided pentominoes, including 6 mirrored pairs. A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling. Polyominoes have been used in popular puzzles since at least 1907 ...
Wang tiles (or Wang dominoes), first proposed by mathematician, logician, and philosopher Hao Wang in 1961, are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them.
There are two uncompleted hexagons of five tiles, also with corner values of 1 at the center. One could be completed with the 1-1-3 tile, and the other cannot be completed, as the required tile would be 0-2-1, which does not exist. Triominoes is a variant of dominoes using triangular tiles published in 1965.