Random dyadic tilings of the unit square

Abstract

AbstractA “dyadic rectangle” is a set of the form R = [a2−s, (a + 1)2−s] × [b2−t, (b + 1)2−t], where s and t are nonnegative integers. A dyadic tiling is a tiling of the unit square with dyadic rectangles. In this paper we study n‐tilings, which consist of 2n nonoverlapping 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 of n‐tilings, and study some limiting properties of random tilings. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 225–251, 2002