A measure of state transition of collective of stateless automata in discrete environment

TL;DR

This paper introduces a geometric approach to defining the state of a collective of stateless automata in a discrete environment, aiming to measure their state transitions as a dynamic computational object.

Contribution

It proposes a novel geometric method for defining state and measuring transitions in a collective of stateless automata, advancing understanding of their computational dynamics.

Findings

Defined a geometric measure of state transition

Characterized the collective automata as a dynamic computational object

Provided a framework for analyzing stateless automata interactions

Abstract

In this work a collective of interacting stateless automata in a discrete geometric environment is considered as an integral automata-like computational dynamic object. For such distributed on the environment object different approaches to definition of the measure of state transition are possible. We propose a geometric approach for defining what a state is.