AbstractA “dyadic rectangle” is a set of the formR= [a2−s, (a+ 1)2−s] × [b2−t, (b+ 1)2−t], wheresandtare nonnegative integers. A dyadic tiling is a tiling of the unit square with dyadic rectangles. In this paper we studyn‐tilings, which consist of 2nnonoverlapping dyadic rectangles, each of area 2−n, whose union is the unit square. We discuss some of the underlying combinatorial structures, provide some efficient methods for uniformly sampling from the set ofn‐tilings, and study some limiting properties of random tilings. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 225–251, 2002