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  • Open Access

Characterizing how order gives way to spatiotemporal chaos in two-dimensional pattern-forming systems

Eduardo A. Droguett-Mora1,*, Cristina Masoller2, and Marcel G. Clerc1

  • *Contact author: eduardo.droguett@ug.uchile.cl
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Phys. Rev. Research 8, 013308 – Published 23 March, 2026

DOI: https://doi.org/10.1103/rdhb-x2gv

Abstract

Systems with energy injection and dissipation are characterized by self-organization through spontaneous breaking of translational symmetry, giving rise to the formation of patterns. Depending on the energy injection, patterns can be regular in space and stationary, or exhibit irregular spatial distributions and complex temporal dynamics. The emergence of complexity in two-dimensional patterns is not yet fully understood nor characterized. Based on a liquid crystal light valve with optical feedback, we characterize experimentally the formation of a pattern in the presence of noise and the route to the spatiotemporal complexity. A universal model of pattern formation, valid close to nascent bistability and spatial bifurcation, is also numerically simulated and studied. In the experimental and in the simulated data, the spatiotemporal complexity is characterized via several complexity measures that provide complementary information. We find that, when varying the control parameter, from the homogeneous state, a stationary pattern emerges, which then becomes chaotic, with characteristic temporal dynamics and spatial irregularities. These transitions were correctly identified by a clustering algorithm. Our results pave the way for future studies of other pattern-forming complex systems.

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Phys. Rev. Research 8, 013308– Published 23 March, 2026
  • Received 15 December 2025
  • Accepted 4 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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