# Random Domino Tilings

Random Domino Tilings

Consider an rectangle and rectangular tiles of size 1×2 (dominoes). A domino tiling of the rectangle is a placement of dominoes that covers the rectangle completely without overlaps. A tiling exists if and only if and are not both odd, implying is even. One tiling can readily be found: suppose is even, place dominoes vertically in the first column and repeat for the next columns. This Demonstration generates random tilings of rectangles of chosen sizes and computes the total number of tilings possible.

m×n

m

n

mn

m

m/2

n