The Organization of Intrinsic Computation: Complexity-Entropy Diagrams and the Diversity of Natural Information Processing

TL;DR

This paper uses complexity-entropy diagrams to analyze and compare the intrinsic computation of various dynamical systems, revealing diverse types of information processing and their relation to phase transitions.

Contribution

It introduces a broad application of complexity-entropy diagrams to different classes of systems, highlighting their ability to compare intrinsic computation without system-specific details.

Findings

Complexity-entropy diagrams reveal diverse intrinsic computation types.

High information processing often occurs near phase transitions.

Different systems exhibit distinct complexity-entropy diagram patterns.

Abstract

Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display the range and different kinds of intrinsic computation across an entire class of system. Here, we use complexity-entropy diagrams to analyze intrinsic computation in a broad array of deterministic nonlinear and linear stochastic processes, including maps of the interval, cellular automata and Ising spin systems in one and two dimensions, Markov chains, and probabilistic minimal finite-state machines. Since complexity-entropy diagrams are a function only of observed configurations, they can be used to compare systems without reference to system coordinates or parameters. It has been known for some time that in special cases complexity-entropy diagrams reveal that high degrees of information processing are associated with phase transitions in the underlying process space, the so-called ``edge of chaos''. Generally, though, complexity-entropy diagrams differ substantially in character, demonstrating a genuine diversity of distinct kinds of intrinsic computation.