A framework for the local information dynamics of distributed computation in complex systems

The nature of distributed computation has often been described in terms of the component operations of universal computation: information storage, transfer and modification. We review the first complete framework that quantifies each of these individual information dynamics on a local scale within a system, and describes the manner in which they interact to create non-trivial computation where "the whole is greater than the sum of the parts". We describe the application of the framework to cellular automata, a simple yet powerful model of distributed computation. This is an important application, because the framework is the first to provide quantitative evidence for several important conjectures about distributed computation in cellular automata: that blinkers embody information storage, particles are information transfer agents, and particle collisions are information modification events. The framework is also shown to contrast the computations conducted by several well-known cellular automata, highlighting the importance of information coherence in complex computation. The results reviewed here provide important quantitative insights into the fundamental nature of distributed computation and the dynamics of complex systems, as well as impetus for the framework to be applied to the analysis and design of other systems.Comment: 44 pages, 8 figure

Automatic Filters for the Detection of Coherent Structure in Spatiotemporal Systems

Most current methods for identifying coherent structures in spatially-extended systems rely on prior information about the form which those structures take. Here we present two new approaches to automatically filter the changing configurations of spatial dynamical systems and extract coherent structures. One, local sensitivity filtering, is a modification of the local Lyapunov exponent approach suitable to cellular automata and other discrete spatial systems. The other, local statistical complexity filtering, calculates the amount of information needed for optimal prediction of the system's behavior in the vicinity of a given point. By examining the changing spatiotemporal distributions of these quantities, we can find the coherent structures in a variety of pattern-forming cellular automata, without needing to guess or postulate the form of that structure. We apply both filters to elementary and cyclical cellular automata (ECA and CCA) and find that they readily identify particles, domains and other more complicated structures. We compare the results from ECA with earlier ones based upon the theory of formal languages, and the results from CCA with a more traditional approach based on an order parameter and free energy. While sensitivity and statistical complexity are equally adept at uncovering structure, they are based on different system properties (dynamical and probabilistic, respectively), and provide complementary information.Comment: 16 pages, 21 figures. Figures considerably compressed to fit arxiv requirements; write first author for higher-resolution version

Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform Computations

We present results from an experiment similar to one performed by Packard (1988), in which a genetic algorithm is used to evolve cellular automata (CA) to perform a particular computational task. Packard examined the frequency of evolved CA rules as a function of Langton's lambda parameter (Langton, 1990), and interpreted the results of his experiment as giving evidence for the following two hypotheses: (1) CA rules able to perform complex computations are most likely to be found near ``critical'' lambda values, which have been claimed to correlate with a phase transition between ordered and chaotic behavioral regimes for CA; (2) When CA rules are evolved to perform a complex computation, evolution will tend to select rules with lambda values close to the critical values. Our experiment produced very different results, and we suggest that the interpretation of the original results is not correct. We also review and discuss issues related to lambda, dynamical-behavior classes, and computation in CA. The main constructive results of our study are identifying the emergence and competition of computational strategies and analyzing the central role of symmetries in an evolutionary system. In particular, we demonstrate how symmetry breaking can impede the evolution toward higher computational capability.Comment: 38 pages, compressed .ps files (780Kb) available ONLY thru anonymous ftp. (Instructions available via `get 9303003' .

Local Causal States and Discrete Coherent Structures

Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate dynamics. Phenomenologically, they appear as key components that organize the macroscopic behaviors in such systems. Despite a century of effort, they have eluded rigorous analysis and empirical prediction, with progress being made only recently. As a step in this, we present a formal theory of coherent structures in fully-discrete dynamical field theories. It builds on the notion of structure introduced by computational mechanics, generalizing it to a local spatiotemporal setting. The analysis' main tool employs the \localstates, which are used to uncover a system's hidden spatiotemporal symmetries and which identify coherent structures as spatially-localized deviations from those symmetries. The approach is behavior-driven in the sense that it does not rely on directly analyzing spatiotemporal equations of motion, rather it considers only the spatiotemporal fields a system generates. As such, it offers an unsupervised approach to discover and describe coherent structures. We illustrate the approach by analyzing coherent structures generated by elementary cellular automata, comparing the results with an earlier, dynamic-invariant-set approach that decomposes fields into domains, particles, and particle interactions.Comment: 27 pages, 10 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/dcs.ht

What Is a Macrostate? Subjective Observations and Objective Dynamics

We consider the question of whether thermodynamic macrostates are objective consequences of dynamics, or subjective reflections of our ignorance of a physical system. We argue that they are both; more specifically, that the set of macrostates forms the unique maximal partition of phase space which 1) is consistent with our observations (a subjective fact about our ability to observe the system) and 2) obeys a Markov process (an objective fact about the system's dynamics). We review the ideas of computational mechanics, an information-theoretic method for finding optimal causal models of stochastic processes, and argue that macrostates coincide with the ``causal states'' of computational mechanics. Defining a set of macrostates thus consists of an inductive process where we start with a given set of observables, and then refine our partition of phase space until we reach a set of states which predict their own future, i.e. which are Markovian. Macrostates arrived at in this way are provably optimal statistical predictors of the future values of our observables.Comment: 15 pages, no figure

Continuum percolation theory of epimorphic regeneration

A biophysical model of epimorphic regeneration based on a continuum percolation process of fully penetrable disks in two dimensions is proposed. All cells within a randomly chosen disk of the regenerating organism are assumed to receive a signal in the form of a circular wave as a result of the action/reconfiguration of neoblasts and neoblast-derived mesenchymal cells in the blastema. These signals trigger the growth of the organism, whose cells read, on a faster time scale, the electric polarization state responsible for their differentiation and the resulting morphology. In the long time limit, the process leads to a morphological attractor that depends on experimentally accessible control parameters governing the blockage of cellular gap junctions and, therefore, the connectivity of the multicellular ensemble. When this connectivity is weakened, positional information is degraded leading to more symmetrical structures. This general theory is applied to the specifics of planaria regeneration. Computations and asymptotic analyses made with the model show that it correctly describes a significant subset of the most prominent experimental observations, notably anterior-posterior polarization (and its loss) or the formation of four-headed planaria.Comment: This author wish to retract the paper arXiv:1705.06720 because it began as part of a collaboration that later fell apart and it was published without the consent from the collaborators. Furthermore, the collaborators have managed to provide a better solution to this proble