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In combinatorial mathematics,
an Aztec diamond of order n consists of all squares of a square lattice
whose centers (x,y) satisfy |x| + |y| ≤ n.
Here n is a fixed integer, and the square lattice consists of unit squares with
the origin as a vertex of 4 of them, so that both x and y are half-integers.[1]

The Aztec diamond theorem states that the number of domino tilings of the
Aztec diamond of order n is 2n(n+1)/2.[2]
The Arctic Circle theorem says that a random tiling of a large Aztec diamond
tends to be frozen outside a certain circle.[3]