Multi-scale structural complexity of natural patterns
arXiv:2003.04632 · doi:10.1073/pnas.2004976117
Abstract
Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal machine method for estimating structural (effective) complexity of two- and three-dimensional patterns that can be straightforwardly generalized onto other classes of objects. It is based on multi-step renormalization of the pattern of interest and computing the overlap between neighboring renormalized layers. This way, we can define a single number characterizing the structural complexity of an object. We apply this definition to quantify complexity of various magnetic patterns and demonstrate that not only does it reflect the intuitive feeling of what is "complex" and what is "simple", but also can be used to accurately detect different phase transitions and gain information about dynamics of non-equilibrium systems. When employed for that, the proposed scheme is much simpler and numerically cheaper than the standard methods based on computing correlation functions or using machine learning techniques.
arXiv commentv2: major revision, author added; 11 pages, 13 figures, 4 new sections. Complexity of time dependent spin systems and the relations between the proposed complexity definition and quantum calculus are explored. To appear in PNAS
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