This book is based on the author’s doctoral dissertation at the University of Sydney, and presents a novel approach to quantifying the dynamics of distributed computation in complex systems. The central idea behind the approach is that the dynamics of complex systems, ranging from ant colonies to human brains, can be better understood by examining the computations performed by these systems. Given the heterogeneous nature of the systems under investigation, the author puts forward a broad view of computation and divides it into three components: information storage, transfer, and modification. Through the application of several measures derived from information theory, the author is able to quantify the temporal and spatial dynamics of information within complex systems at both a local and a global level. Therefore, his analysis goes significantly beyond the scope of other known techniques that are used for describing the behavior of complex systems.

The book is structured into nine chapters. Chapter 1 sets the stage for the new approach, specifying that the author’s interest is in quantifying operations on information (and their interplay) in complex systems. More specifically, the author seeks to develop a comprehensive framework for studying information dynamics, and to employ the resulting framework to gain a better understanding of distributed computation. For generality and applicability, the approach makes use of information theoretic tools (various forms of entropy) and focuses mainly on computation within cellular automata (CA). Chapter 2 introduces complex systems, information theory, and CA, with an emphasis on the choice of CA as a formalism for exploring aspects of distributed computation.

The next three chapters constitute the core of the author’s approach, and contain a quantitative description of information storage, transfer, and modification. The author shows that quantitative evaluation is strongly compatible with the qualitative view on information dynamics within CA, expressed in terms of blinkers, background domains, particles, and particle collisions. Chapter 3 deals with information storage and illustrates how the measures of excess entropy, active information storage, and entropy rate can be used to determine the total storage available to the system, the amount of storage in use, and the amount of uncertainty complementary to storage, respectively. Chapter 4 is concerned with information transfer (that is, communication) and employs five types of transfer entropy measures (apparent, conditional, complete, collective, and multivariate) to compute the amount of information transferred from one or more sources to one or more destinations. Moreover, this chapter makes explicit the difference between information transfer and causality, the latter being captured by information flow, and explains it at length. Chapter 5 focuses on information processing, seen as a combination of information storage and transfer. The author uses the measure of separable information as an indicator of the (nontrivial) modification of information, while highlighting the distinction between modification and deletion, as estimated by the measure of information destruction.

The next three chapters apply the aforementioned framework to systems other than CA. In chapter 6, an information theoretic analysis of random Boolean networks (RBN) and other complex systems provides evidence to support the “edge of chaos” conjecture, which predicts that information storage and transfer are maximized around the transition from ordered to chaotic system behavior. Chapter 7 examines the use of state-space diagrams as visual tools to discover coherent information structures in CA and RBN, by graphically representing local information dynamics. Chapter 8 demonstrates how studying the temporal dynamics of information transfer can better account for phenomena such as the interaction between heart and breathing rate in sleep apnea, and how investigating the spatial dynamics of information transfer can link the activation of brain regions to the performance of a visuomotor tracking task. Finally, chapter 9 reviews the proposed approach and hints at possible avenues for further development of the theory.

All in all, this volume introduces a new and thorough approach for analyzing the dynamics of computation in complex systems, while acknowledging the pioneering work done by previous researchers in devising an information theoretic framework for reasoning about distributed computation.