Packing squares in a torus

D. W. Blair, C. Santangelo, J. MacHta

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 languageEnglish (US)
Article numberP01018
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number1
StatePublished - Jan 2012
Externally publishedYes


  • jamming and packing

ASJC Scopus subject areas

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


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