Measuring complexity through average symmetry

Roberto C. Alamino*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different) complexity to either deterministic or random homogeneous densities and higher complexity to the intermediate cases. This new measure is easily computable, breaks the coarse graining paradigm and can be straightforwardly generalized, including to continuous cases and general networks. By applying this measure to a series of objects, it is shown that it can be consistently used for both small scale structures with exact symmetry breaking and large scale patterns, for which, differently from similar measures, it consistently discriminates between repetitive patterns, random configurations and self-similar structures

Original languageEnglish
Article number275101
Number of pages16
JournalJournal of Physics A: Mathematical and Theoretical
Issue number27
Early online date12 Jun 2015
Publication statusPublished - 10 Jul 2015

Bibliographical note



  • average symmetry
  • complexity
  • entropy


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