Action and perception for spatiotemporal patterns
  This is a contribution to the formalization of the concept of agents in
multivariate Markov chains. Agents are commonly defined as entities that act,
perceive, and are goal-directed. In a multivariate Markov chain (e.g. a
cellular automaton) the transition matrix completely determines the dynamics.
This seems to contradict the possibility of acting entities within such a
system. Here we present definitions of actions and perceptions within
multivariate Markov chains based on entity-sets. Entity-sets represent a
largely independent choice of a set of spatiotemporal patterns that are
considered as all the entities within the Markov chain. For example, the
entity-set can be chosen according to operational closure conditions or
complete specific integration. Importantly, the perception-action loop also
induces an entity-set and is a multivariate Markov chain. We then show that our
definition of actions leads to non-heteronomy and that of perceptions
specialize to the usual concept of perception in the perception-action loop.
