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Sci Rep. 2017 Apr 20;7(1):997. doi: 10.1038/s41598-017-00810-8.

Formal Definitions of Unbounded Evolution and Innovation Reveal Universal Mechanisms for Open-Ended Evolution in Dynamical Systems.

Adams A1,2,3, Zenil H3,4,5, Davies PCW1, Walker SI6,7,8,9.

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Beyond Center for Fundamental Concepts in Science, Arizona State University, Tempe, AZ, USA.
Department of Physics, Arizona State University, Tempe, AZ, USA.
Algorithmic Nature Group, LABORES, Paris, France.
Department of Computer Science, University of Oxford, Oxford, UK.
Information Dynamics Lab, SciLifeLab, Department of Medicine Solna, Karolinska Institute, Stockholm, Sweden.
Beyond Center for Fundamental Concepts in Science, Arizona State University, Tempe, AZ, USA.
School of Earth and Space Exploration, Arizona State University, Tempe, AZ, USA.
ASU-SFI Center for Biosocial Complex Systems, Arizona State University, Tempe, AZ, USA.
Blue Marble Space Institute of Science, Seattle, WA, USA.


Open-ended evolution (OEE) is relevant to a variety of biological, artificial and technological systems, but has been challenging to reproduce in silico. Most theoretical efforts focus on key aspects of open-ended evolution as it appears in biology. We recast the problem as a more general one in dynamical systems theory, providing simple criteria for open-ended evolution based on two hallmark features: unbounded evolution and innovation. We define unbounded evolution as patterns that are non-repeating within the expected Poincare recurrence time of an isolated system, and innovation as trajectories not observed in isolated systems. As a case study, we implement novel variants of cellular automata (CA) where the update rules are allowed to vary with time in three alternative ways. Each is capable of generating conditions for open-ended evolution, but vary in their ability to do so. We find that state-dependent dynamics, regarded as a hallmark of life, statistically out-performs other candidate mechanisms, and is the only mechanism to produce open-ended evolution in a scalable manner, essential to the notion of ongoing evolution. This analysis suggests a new framework for unifying mechanisms for generating OEE with features distinctive to life and its artifacts, with broad applicability to biological and artificial systems.

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