Interaction spaces: towards a universal mathematical theory of complex systems

TL;DR

This paper introduces interaction spaces, a universal mathematical framework designed to unify various models of complex systems such as cellular automata, neural networks, and genetic algorithms, facilitating a comprehensive mathematical theory.

Contribution

It proposes the first steps towards a universal mathematical theory of complex systems by defining interaction spaces that embed diverse modeling frameworks.

Findings

Interaction spaces can embed cellular automata and neural networks.

The framework unifies stochastic and deterministic models.

It provides a common language for complex systems modeling.

Abstract

We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous or discrete dynamical systems, networked dynamical models, artificial neural networks and genetic algorithms in a single notion. Therefore, interaction spaces represent a common mathematical language that can be used to describe several complex systems modeling frameworks. This is the first step to start a mathematical theory of complex systems. Every notion is introduced both using an intuitive description by listing lots of examples, and using a modern mathematical language.