  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 equivalent isolated system, and innovation as
trajectories not observed in isolated systems. As a case study, we implement
novel variants of cellular automata (CA) in which 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, widely 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.
