A "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.
ASJC Scopus subject areas
- Computer Graphics and Computer-Aided Design
- Applied Mathematics