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