Adams, Alyssa M., Sara I. Walker, Hector Zenil, and P. C. W. Davies. “Quantifying Non-trivial Open-Ended Evolution Reveals Necessary and Sufficient Conditions.”
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One of the most remarkable features over the last ⇠ 3.5 billion years of life on Earth is the apparent trend of innovation and open-ended growth of complexity. However, this trend
does not have a satisfactory explanation in terms of currently known principles. Here, we demonstrate that a variant of CA are capable of open-ended evolution and innovation by implementing state-dependent dynamical rules. To quantitatively evaluate potential for open-ended evolution and innovation, we present formal definitions of open-ended evolution as patterns that are non-repeating within the expected Poincare re- ´currence time of an equivalent isolated system, and of innovation as trajectories not observed in isolated systems. We show that a small subset of state-dependent systems satisfy both definitions. We compare these systems to a set of controls including CA evolved according to fixed rules and randomly evolved rules and show that state-dependent systems are statistically more reliable at producing both open-ended evolution and innovation. We further show how state-dependent CA allow for sustained growth of complexity, demonstrating that both the complexity and percentage of open-ended cases increases with increasing environment size. Our results indicate that uncovering the principles governing open-ended evolution and innovation in the biosphere will likely require removing the segregation of states and (fixed) dynamic laws characteristic of the physical sciences in attempts to model biological complexity.