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  1. Home
  3. Characterizing Open-ended Evolution Through Undecidability Mechanisms In Random Boolean Networks.
  1. Home
  3. Characterizing Open-ended Evolution Through Undecidability Mechanisms In Random Boolean Networks.

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Characterizing open-ended evolution through undecidability mechanisms in random Boolean networks.

Amahury J López-Díaz1, Pedro Juan Rivera Torres2,3, Gerardo L Febres4,5

  • 1School of Systems Science and Industrial Engineering, Binghamton University, Binghamton, NY, USA. alpez@binghamton.edu.

NPJ Systems Biology and Applications
|June 23, 2026

View abstract on PubMed

Summary
This summary is machine-generated.

We developed a new metric, Omega (Ω), to detect signatures of open-ended evolution (OEE) in dynamical systems. This metric quantifies recurrent novelty, distinguishing it from simple cycles or random behavior, aiding in biological modeling.

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Area of Science:

  • Systems Biology
  • Theoretical Biology
  • Computational Biology

Background:

  • Discrete dynamical models are crucial in systems biology.
  • Current diagnostics struggle to identify signatures of open-ended evolution (OEE) like sustained novelty.
  • Distinguishing recurrent novelty from rapid settling or noise is a key challenge.

Purpose of the Study:

  • To introduce a model-independent metric, Omega (Ω), for quantifying dynamical signatures relevant to OEE.
  • To assess Ω's utility in identifying sustained novelty in various dynamical systems.
  • To explore mechanisms that support OEE in biological modeling.

Main Methods:

  • Developed Ω, a metric summarizing residence-time-weighted attractor cycle lengths across recurrent episodes.
  • Utilized Random Boolean Networks (RBNs) as a testbed to compare classical and non-classical dynamics.
  • Investigated mechanisms including probabilistic context switching, rule mutation, paraconsistent logic, and quantum-inspired dynamics.

    • Main Results:

    • Ω quantifies the contribution of multiple cyclic phenotypes to sustained novelty.
    • Undecidability-adjacent, state-dependent mechanisms (e.g., probabilistic switching, paraconsistent logic) promote sustained novelty.
    • Ω is zero for single-attractor dynamics or pure novelty without recurrence.

    Conclusions:

    • Ω serves as a portable proxy for OEE in biological modeling.
    • Specific non-classical dynamical mechanisms are enabling conditions for sustained novelty and OEE.
    • The metric can guide the engineering of evolvable synthetic circuits and is extendable to hybrid state spaces.