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Open-ended evolution (OEE) is relevant to a variety of biological, artificialand technological systems, but has been challenging to reproduce in silico.Most theoretical efforts focus on key aspects of open-ended evolution as itappears in biology. We recast the problem as a more general one in dynamicalsystems theory, providing simple criteria for open-ended evolution based on twohallmark features: unbounded evolution and innovation. We define unboundedevolution as patterns that are non-repeating within the expected Poincarerecurrence time of an equivalent isolated system, and innovation astrajectories not observed in isolated systems. As a case study, we implementnovel variants of cellular automata (CA) in which the update rules are allowedto vary with time in three alternative ways. Each is capable of generatingconditions for open-ended evolution, but vary in their ability to do so. Wefind that state-dependent dynamics, widely regarded as a hallmark of life,statistically out-performs other candidate mechanisms, and is the onlymechanism to produce open-ended evolution in a scalable manner, essential tothe notion of ongoing evolution. This analysis suggests a new framework forunifying mechanisms for generating OEE with features distinctive to life andits artifacts, with broad applicability to biological and artificial systems.

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