### 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 2^{n} 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 language | English (US) |
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Pages (from-to) | 225-251 |

Number of pages | 27 |

Journal | Random Structures and Algorithms |

Volume | 21 |

Issue number | 3-4 |

DOIs | |

State | Published - 2002 |

### ASJC Scopus subject areas

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

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## Cite this

Janson, S., Randall, D., & Spencer, J. (2002). Random Dyadic Tilings of the Unit Square.

*Random Structures and Algorithms*,*21*(3-4), 225-251. https://doi.org/10.1002/rsa.10051