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Multiscale structural complexity of natural patterns.

Andrey A Bagrov1,2, Ilia A Iakovlev2, Askar A Iliasov3

  • 1Department of Physics and Astronomy, Uppsala University, SE-75120 Uppsala, Sweden; andrey.bagrov@physics.uu.se.

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|November 19, 2020
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Summary
This summary is machine-generated.

We developed a universal machine method to quantify pattern complexity using renormalization. This approach is simpler and cheaper than existing methods for analyzing magnetic patterns and nonequilibrium systems.

Keywords:
complexityimage processingpattern formationrenormalization group

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Area of Science:

  • Physics
  • Materials Science
  • Computational Science

Background:

  • Human perception of pattern complexity is crucial for object differentiation but difficult to quantify.
  • Existing methods for complexity analysis can be computationally expensive and lack universality.

Purpose of the Study:

  • To propose a transparent and universal machine method for estimating the structural complexity of 2D and 3D patterns.
  • To demonstrate the method's applicability to magnetic patterns and nonequilibrium systems.
  • To offer a simpler and more numerically efficient alternative to current techniques.

Main Methods:

  • The proposed method involves multistep renormalization of a pattern.
  • It computes the overlap between neighboring renormalized layers to define a single complexity number.
  • The technique is designed for straightforward generalization across different object classes.

Main Results:

  • The method successfully quantifies structural complexity, aligning with intuitive perceptions of simple and complex patterns.
  • It accurately detects phase transitions in magnetic patterns.
  • It provides insights into the dynamics of nonequilibrium systems.

Conclusions:

  • The developed machine method offers a universal and efficient way to quantify structural complexity.
  • This approach simplifies the analysis of complex systems, including magnetic materials and nonequilibrium dynamics.
  • It presents a computationally cheaper alternative to correlation function and machine learning methods.