A new simple proof of the Aztec diamond theorem

The Aztec diamond of order $n$ is the union of lattice squares in the plane intersecting the square $\mathrm{\mid }x\mathrm{\mid }+\mathrm{\mid }y\mathrm{\mid }<n$. The Aztec diamond theorem states that the number of domino tilings of this shape is $2^{n(n+1)\mathrm{/}2}$. It was first proved by Elkies, Kuperberg, Larsen and Propp in 1992. We give a new simple proof of this theorem.