Local information transfer as a spatiotemporal filter for complex systems

TL;DR

This paper introduces local transfer entropy, a new spatiotemporal measure for analyzing information flow in complex systems, demonstrated on cellular automata to identify coherent structures and their role as information transfer agents.

Contribution

It develops a local transfer entropy measure from existing information theory, enabling detailed spatiotemporal analysis and revealing the role of particles in cellular automata.

Findings

Local transfer entropy profiles reveal coherent structures in cellular automata.

Particles such as gliders and domain walls are confirmed as primary information transfer agents.

The method provides a quantitative tool for analyzing emergent structures in complex systems.

Abstract

We present a measure of local information transfer, derived from an existing averaged information-theoretical measure, namely transfer entropy. Local transfer entropy is used to produce profiles of the information transfer into each spatiotemporal point in a complex system. These spatiotemporal profiles are useful not only as an analytical tool, but also allow explicit investigation of different parameter settings and forms of the transfer entropy metric itself. As an example, local transfer entropy is applied to cellular automata, where it is demonstrated to be a novel method of filtering for coherent structure. More importantly, local transfer entropy provides the first quantitative evidence for the long-held conjecture that the emergent traveling coherent structures known as particles (both gliders and domain walls, which have analogues in many physical processes) are the dominant information transfer agents in cellular automata.