### Abstract

The densest packings of N unit squares in a torus are studied using analytical methods as well as simulated annealing. A rich array of dense packing solutions are found: density-one packings when N is the sum of two square integers; a family of 'gapped bricklayer' Bravais lattice solutions with density N/(N + 1); and some surprising non-Bravais lattice configurations, including lattices of holes as well as a configuration for N = 23 in which not all squares share the same orientation. The entropy of some of these configurations and the frequency and orientation of density-one solutions as N → ∞ are discussed.

Original language | English (US) |
---|---|

Article number | P01018 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2012 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2012 |

### Keywords

- jamming and packing

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty

## Fingerprint Dive into the research topics of 'Packing squares in a torus'. Together they form a unique fingerprint.

## Cite this

Blair, D. W., Santangelo, C., & MacHta, J. (2012). Packing squares in a torus.

*Journal of Statistical Mechanics: Theory and Experiment*,*2012*(1), [P01018]. https://doi.org/10.1088/1742-5468/2012/01/P01018