We present results from experiments in which a genetic algorithm (GA) was used to evolve cellular automata (CAs) to perform a particular computational task—one-dimensional density classification. We look in detail at the evolutionary mechanisms producing the GA’s behavior on this task and the impediments faced by the GA. In particular, we identify four “epochs of innovation ” in which new CA strategies for solving the problem are discovered by the GA, describe how these strategies are implemented in CA rule tables, and identify the GA mechanisms underlying their discovery. The epochs are characterized by a breaking of the task’s symmetries on the part of the GA. The symmetry breaking results in a short-term fitness gain but ultimately prevents the discovery of the most highly fit strategies. We discuss the extent to which symmetry breaking and other impediments are general phenomena in any GA search. 1.

We present results from an experiment similar to one performed by Packard [24], 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 λ parameter [17], 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 ” λ 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 λ 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 λ, 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.

This paper reports the application of new methods for detecting computation in nonlinear processes to a simple evolutionary model that allows us to directly address these questions. The main result is the evolutionary discovery of methods for emergent global computation in a spatially distributed system consisting of locally interacting processors. We use the general term "emergent computation" to describe the appearance of global information-processing in such systems (cf. (6,7)). Our goal is to understand the mechanisms by which evolution can discover methods of emergent computation. We are studying this question in a theoretical framework that, while simplified, still captures the essence of the phenomena of interest. This framework requires (i) an idealized class of decentralized system in which global information-processing can arise from the actions of simple, locally-connected units; (ii) a computational task that necessitates global information processing; and (iii) an idealized computational model of evolution. One of the simplest systems in which emergent computation can be studied is a onedimensional binary-state cellular automaton (CA) (8) --- a one-dimensional spatial lattice of

Defining structure and detecting the emergence of complexity in nature are inherently subjective, though essential, scientific activities. Despite the difficulties, these problems can be analyzed in terms of how model-building observers infer from measurements the computational capabilities embedded in nonlinear processes. An observer’s notion of what is ordered, what is random, and what is complex in its environment depends directly on its computational resources: the amount of raw measurement data, of memory, and of time available for estimation and inference. The discovery of structure in an environment depends more critically and subtlely, though, on how those resources are organized. The descriptive power of the observer’s chosen (or implicit) computational model class, for example, can be an overwhelming determinant in finding regularity in data. This paper presents an overview of an inductive framework — hierarchical-machine reconstruction — in which the emergence of complexity is associated with the innovation of new computational model classes. Complexity metrics for detecting structure and quantifying emergence, along with an analysis of the constraints on the dynamics of innovation, are outlined. Illustrative examples are drawn from the onset of unpredictability in nonlinear systems, finitary nondeterministic processes, and

Abstract. How does evolution produce sophisticated emergent computation in systems composed of simple components limited to local interactions? To model such a process, we used a genetic algorithm (GA) to evolve cellular automata to perform a computational task requiring globally-coordinated information processing. On most runs a class of relatively unsophisticated strategies was evolved, but on a subset of runs a number of quite sophisticated strategies was discovered. We analyze the emergent logic underlying these strategies in terms of information processing performed by “particles ” in space-time, and we describe in detail the generational progression of the GA evolution of these strategies. Our analysis is a preliminary step in understanding the general mechanisms by which sophisticated emergent computational capabilities can be automatically produced in decentralized multiprocessor systems. 1.

CA rules can be classied automatically for a spectrum of ordered, complex and chaotic dynamics, by a measure of the variance of input-entropy over time. Rules that support interacting gliders and related complex dynamics can be identied, giving an unlimited source for further study. The distribution of rule classes in rule-space can be shown. A byproduct of the method allows the automatic \ltering" of CA space-time patterns to show up gliders and related emergent congurations more clearly. The classication seems to correspond to our subjective judgment of space-time dynamics. There are also approximate correlations with global measures on convergence in attractor basins, characterized by the distribution of in-degree sizes in their branching structure, and to the rule parameter, Z. Based on computer experiments using the software Discrete Dynamics Lab (DDLab)[22], this paper explains the methods and presents results for 1d CA. 1 Introduction Cellular automata (CA) are a much stud...

We illustrate and extend the techniques of computational mechanics in explicating the structures that emerge in the space-time behavior of elementary one-dimensional cellular automaton rule 54. The CA's dominant regular domain is identified and a domain filter is constructed to locate and classify defects in the domain. The primary particles are identified and a range of interparticle interactions is studied. The deterministic equation of motion of the filtered spacetime behavior is derived. Filters of increasing sophistication are constructed for the efficient gathering of particle statistics and for the identification of higher-level defects, particle interactions, and secondary domains. We define the emergence time at which the space-time behavior condenses into configurations consisting only of domains, particles, and particle interactions. Taken together, these techniques serve as the basis for the investigation of pattern evolution and self-organization in this representative sys...

Cellular automata (CAs) are decentralized spatially extended systems consisting of large numbers of simple identical components with local connectivity. Such systems have the potential to perform complex computations with a high degree of efficiency and robustness, as well as to model the behavior of complex systems in nature. For these reasons CAs and related architectures have

. We introduce a class of embedded-particle models for describing the emergent computational strategies observed in cellular automata (CAs) that were evolved for performing certain computational tasks. The models are evaluated by comparing their estimated performances with the actual performances of the CAs they model. The results show, via a close quantitative agreement, that the embedded-particle framework captures the main information processing mechanisms of the emergent computation that arise in these evolved CAs. 1 Introduction In previous work we have used genetic algorithms (GAs) to evolve cellular automata (CAs) to perform computational tasks that require global coordination. The evolving cellular automata framework has provided a direct approach to studying how evolution (natural or artificial) can create dynamical systems that perform emergent computation; that is, how it can find dynamical systems in which the interaction of simple components with local information storage...

Abstract not found