# Action and perception for spatiotemporal patterns

## TL;DR

This paper formalizes the concepts of action and perception for agents within multivariate Markov chains, addressing how entities can be defined and understood in such deterministic systems.

## Contribution

It introduces definitions of actions and perceptions based on entity-sets, reconciling agent concepts with the dynamics of multivariate Markov chains.

## Key findings

- Definitions of actions and perceptions are formalized within multivariate Markov chains.
- The perception-action loop induces an entity-set consistent with the chain's dynamics.
- Actions are shown to lead to non-heteronomy, aligning with traditional perception concepts.

## Abstract

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.