Theoretica chimica acta

, Volume 79, Issue 5, pp 379–387 | Cite as

Similarity and complexity of the shapes of square-cell configurations

  • Frank Harary
  • Paul G. Mezey


An equivalence relation on square-cell configurations, which we call animals, is formulated precisely, using the similarity criterion of “seeing” parts of the shape of the animal from its interior, and an operation called “squashing”, leading to a smaller animal. It is noted that there is a unique smallest animal in each resulting equivalence class, called the canonical animal of its class. It is proposed that the number of cells in a canonical animalA serves as a measure of complexity of any animal similar toA. The formulation of the canonical animal is suggested as a tool for characterizing shapes of monolayer clusters of adsorbed molecules on square lattices, a problem of importance in chemical catalysis.

Key words

Shape analysis Lattice animals Similarity Complexity 


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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Frank Harary
    • 1
  • Paul G. Mezey
    • 2
  1. 1.Department of Computer ScienceNew Mexico State UniversityLas CrucesUSA
  2. 2.Department of Chemistry and Department of MathematicsUniversity of SaskatchewanSaskatoonCanada

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