Classification of Complex Systems Based on Transients

TL;DR

This paper introduces a new classification method for deterministic dynamical systems based on their transient behaviors, which correlates well with existing classifications and can be applied to complex models like cellular automata.

Contribution

A novel, general classification technique for deterministic systems based on asymptotic transient behaviors, applicable to cellular automata and potentially aiding in modeling complex structures.

Findings

Classification results align with Wolfram's manual classification

Method successfully applied to 2D cellular automata

Technique is adaptable to complex models of computation

Abstract

In order to develop systems capable of modeling artificial life, we need to identify, which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical systems. The method distinguishes between different asymptotic behaviors of a system's average computation time before entering a loop. When applied to elementary cellular automata, we obtain classification results, which correlate very well with Wolfram's manual classification. Further, we use it to classify 2D cellular automata to show that our technique can easily be applied to more complex models of computation. We believe this classification method can help to develop systems, in which complex structures emerge.