Formal Definitions of Unbounded Evolution and Innovation Reveal Universal Mechanisms for Open-Ended Evolution in Dynamical Systems
Alyssa M Adams, Hector Zenil, Paul CW Davies, Sara I Walker
One of the most remarkable features of the > 3.5 billion year history of life on Earth is the apparent trend of innovation and open-ended growth of complexity. Similar trends are apparent in artificial and technological systems. However, a general framework for understanding open-ended evolution as it might occur in biological or technological systems has not yet been achieved. Here, we cast the problem within the broader context of dynamical systems theory to uncover and characterize mechanisms for producing open-ended evolution (OEE). We present formal definitions of two hallmark features of OEE: unbounded evolution and innovation. We define unbounded evolution as patterns that are non-repeating within the expected Poincare\'e recurrence time of an equivalent isolated system, and innovation as trajectories not observed in isolated systems. As a case study, we test three new variants of cellular automata (CA) that implement time-dependent update rules against these two definitions. We find that each is capable of generating conditions for OEE, but vary in their ability to do so. Our results demonstrate that state-dependent dynamics, widely regarded as a hallmark feature of life, statistically out-perform other candidate mechanisms. It is also the only mechanism to produce OEE in a scalable manner, consistent with notions of OEE as ongoing production of complexity. Our results thereby suggest a new framework for unifying the mechanisms for generating OEE with features distinctive to life and its artifacts, with wide applicability to both biological and artificial systems.