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Physical interactions enable energy-efficient Turing patterns

Cathelijne ter Burg and David Zwicker*

  • *Contact author: david.zwicker@ds.mpg.de
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Phys. Rev. Research 7, L042070 – Published 30 December, 2025

DOI: https://doi.org/10.1103/vtnv-2hw6

Abstract

Patterns are ubiquitous in nature, but how they form is often unclear. Turing developed a seminal theory to explain patterns based on reactions that counteract the equalizing tendency of diffusion. These reactions require continuous energy input since the system otherwise would proceed to equilibrium, but what systems are energy-efficient is currently unclear. To address this question, we introduce a thermodynamically consistent model of a Turing system. We reveal that repulsive interactions between the stereotypical activator and inhibitor reduce energy requirements significantly. Interestingly, efficient patterns occur for weak activity, albeit at reduced amplitude. Our results suggest that physical interactions might be central in forming natural patterns.

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Phys. Rev. Research 7, L042070– Published 30 December, 2025
  • Received 4 September 2025
  • Accepted 19 November 2025
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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. Open access publication funded by Max Planck Society.

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