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.
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