Random Dyadic Tilings of the Unit Square

Svante Janson, Dana Randall, Joel Spencer

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)225-251
Number of pages27
JournalRandom Structures and Algorithms
Volume21
Issue number3-4
StatePublished - Oct 2002

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Tiling
Rectangle
Sampling
Unit
Random Tilings
Union
Limiting
Non-negative
Integer

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Mathematics(all)
  • Applied Mathematics

Cite this

Random Dyadic Tilings of the Unit Square. / Janson, Svante; Randall, Dana; Spencer, Joel.

In: Random Structures and Algorithms, Vol. 21, No. 3-4, 10.2002, p. 225-251.

Research output: Contribution to journalArticle

Janson, S, Randall, D & Spencer, J 2002, 'Random Dyadic Tilings of the Unit Square', Random Structures and Algorithms, vol. 21, no. 3-4, pp. 225-251.
Janson, Svante ; Randall, Dana ; Spencer, Joel. / Random Dyadic Tilings of the Unit Square. In: Random Structures and Algorithms. 2002 ; Vol. 21, No. 3-4. pp. 225-251.
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