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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
Summary
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.
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.
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