Similarity and complexity of the shapes of square-cell configurations
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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 wordsShape analysis Lattice animals Similarity Complexity
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