ArticleProceedings of the National Academy of Sciences of the United States of America2020
Multiscale structural complexity of natural patterns.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 9 papers.
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Who cites it
9 citing papers in PubMed.
- Article
- Spatial Scale Selection for Urban Systems: A Complexity-Heterogeneity Balancing Method.Entropy (Basel, Switzerland) · 2025Article
- Structural stability and thermodynamics of artistic composition.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- Predictive Complexity of Quantum Subsystems.Entropy (Basel, Switzerland) · 2024Article
- Long range segmentation of prokaryotic genomes by gene age and functionality.Nucleic acids research · 2024Article
- Complexity and entropy of natural patterns.PNAS nexus · 2024Article
- Long range segmentation of prokaryotic genomes by gene age and functionality.bioRxiv : the preprint server for biology · 2024Article
- Toward a theory of evolution as multilevel learning.Proceedings of the National Academy of Sciences of the United States of America · 2022Article
- Subgraphs of Interest Social Networks for Diffusion Dynamics Prediction.Entropy (Basel, Switzerland) · 2021Article
Corrections and comments
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Authors and funding
5 authors.
Funding
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Abstract
Complexity of patterns is 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-dimensional and three-dimensional patterns that can be straightforwardly generalized onto other classes of objects. It is based on multistep 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 nonequilibrium 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.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.