Local Interaction Rules Research Articles

Computation in artificially evolved, non-uniform cellular automata

Cellular automata are dynamical systems in which space and time are discrete, that operate according to local interaction rules. Designing such systems to exhibit a specific behavior or to perform a particular task is highly complicated, thus severely limiting their applications. We study non-uniform cellular automata, focusing on the evolution of such systems to perform computational tasks, via a parallel evolutionary algorithm, known as cellular programming. We present the algorithm and demonstrate that high-performance systems can be evolved to perform two non-trivial computational tasks, density and random number generation.

Density Delay and Organizational Survival: Computational Models and Empirical Comparisons

Research on the ecological dynamics of organizational populations has demonstrated that competitive conditions at the time of founding have enduring effects on organizational survival. According to ecological theories, organizational life chances are systematically affected by density (the number of organizations in a population) at the time of founding because the lower resource endowments that characterize organizations appearing in periods of high population density tend to become self-reinforcing, and—over time—amplify differences in mortality rates of organizations founded under different conditions. However, credible arguments have been offered that could justify both positive and negative effects of the delayed effects of population density on organizational mortality rates, and received empirical research in part reflects this ambiguity. To develop new insight into this issue and to explore the boundaries of received empirical results, in this study we present a computational model of organizational evolution according to which the global dynamics of organizational populations emerge from the iteration of simple rules of local interaction among individual organizations. We use the synthetic data produced by simulation to estimate event history models of organizational mortality, and compare the parameter estimates with those reported in the most recent empirical studies of actual organizational populations. The conclusions supported by the model qualify and extend received empirical results, and suggest that delayed effects of density are highly sensitive the details of local structure of connections among members of organizational populations.

Convergence to Uniformity in a Cellular Automaton via Local Coevolution

Cellular programming is a coevolutionary algorithm by which parallel cellular systems evolve to solve computational tasks. The evolving system is a massively parallel, locally interconnected grid of cells, where each cell operates according to a local interaction rule. If this rule is identical for all cells, the system is referred to as uniform, otherwise, it is non-uniform. This paper describes an experiment that addresses the following question: Employing a local coevolutionary process to solve a hard problem, known as density classification, can an optimal uniform solution be found? Since our approach involves the evolution of non-uniform CAs, where cellular rules are initially assigned at random, such convergence to uniformity cannot be a priori expected to easily emerge. The question is of both theoretical and practical interest. As for the latter, one major advantage of local evolutionary processes is their amenability to parallel implementation, using commercially available parallel machines or specialized hardware. Our experiment shows that when such local evolution is applied to the density problem, the optimal solution can be found.

Interacting Locally and Evolving Globally: A Computational Approach to the Dynamics of Organizational Populations

We present a computational model of organizational evolution according to which the global dynamics of organizational populations emerge from simple rules of local interaction among individual orga...

INTERACTING LOCALLY AND EVOLVING GLOBALLY: A COMPUTATIONAL APPROACH TO THE DYNAMICS OF ORGANIZATIONAL POPULATIONS.

We present a computational model of organizational evolution according to which the global dynamics of organizational populations emerge from simple rules of local interaction among individual orga...

Model for a self-repairing system of non-articulated coralline algae

We propose a perspective for living systems, emphasizing that living systems are organized through the recognition of themselves and their surroundings. Oscillator functions in Brownian Algebra are introduced, supposing that the oscillation can be regarded as metabolism of the living state. We illustrate the idea of the self-repairing model in non-articulated coralline algae. Since various cells of this plant are assumed to be identified with the periodic sequence of oscillations, the individual periodic sequence characterizing a cell is supposed to be determined by a local-interaction rule which can be regarded as the process of self-organization through the recognition of local shape. Owing to accidental injury the rule characterizing a cell's own state can be transformed, and it entails another periodic sequence. We express the oscillator as state flow diagrams, and analyze the relationship between the transformation of the period and the injury which is represented by the removal of transient in flow diagrams.

Adaptive stochastic cellular automata: Theory

The mathematical concept of cellular automata has been generalized to allow for the possibility that the uniform local interaction rules that govern conventional cellular automata are replaced by nonuniform local interaction rules which are drawn from the same probability distribution function, in order to guarantee the statistical homogeneity of the cellular automata system. Adaptation and learning in such a system can be accomplished by evolving the probability distribution function along the steepest descent direction of some objective function in a statistically unbiased way to ensure that the cellular automata's dynamical behavior approaches the desired behavior asymptotically. The proposed CA model has been shown mathematically to possess the requisite convergence property under general conditions.

Cylindrical cellular automata

A one-dimensional cellular automaton with periodic boundary conditions may be viewed as a lattice of sites on a cylinder evolving according to a local interaction rule. A technique is described for finding analytically the set of attractors for such an automaton. Given any one-dimensional automaton rule, a matrixA is defined such that the number of fixed points on an arbitrary cylinder size is given by the trace ofA n , where the powern depends linearly on the cylinder size. More generally, the number of strings of arbitrary length that appear in limit cycles of any fixed period is found as the solution of a linear recurrence relation derived from the characteristic equation of an associated matrix. The technique thus makes it possible, for any rule, to compute the number of limit cycles of any period on any cylinder size. To illustrate the technique, closed-form expressions are provided for the complete attractor structure of all two-neighbor rules. The analysis of attractors also identifies shifts as a basic mechanism underlying periodic behavior. Every limit cycle can be equivalently defined as a set of strings on which the action of the rule is a shift of sizes/h; i.e., each string cyclically shifts bys sites inh iterations of the rule. The study of shifts provides detailed information on the structure and number of limit cycles for one-dimensional automata.

Linear cellular automata and recurring sequences in finite fields

A one-dimensional linear cellular automaton with periodic boundary conditions consists of a lattice of sites on a cylinder evolving according to a linear local interaction rule. Limit cycles for such a system are studied as sets of strings on which the rule acts as a shift of sizes/h; i.e., each string in the limit cycle cyclically shifts bys sites inh iterations of the rule. For any given rule, the size of the shift varies with the cylinder sizen. The analysis of shifts establishes an equivalence between the strings of values appearing in limit cycles for these automata, and linear recurring sequences in finite fields. Specifically, it is shown that a string appears in a limit cycle for a linear automaton rule on a cylinder sizen iff its values satisfy a linear recurrence relation defined by the shift value for thatn. The rich body of results on recurring sequences and finite fields can then be used to obtain detailed information on periodic behavior for these systems. Topics considered here include the inverse problem of identifying the set of linear automata rules for which a given string appears in a limit cycle, and the structure under operations (such as addition and complementation) of sets of limit cycle strings.

Modeling seismic P‐Waves with cellular automata

Cellular automata are arrays of discrete variables that follow local interaction rules and are capable of modeling many physical systems. A successful recent application has been in fluid dynamics, in which the Navier‐Stokes equations are solved by creating a model in which space, time, and the velocity of particles are all discrete. Acoustic waves can be obtained from these fluid models when perturbations of the idealized fluid are small. Because seismic P‐waves can be approximated by the acoustic wave equation, cellular automata can be adapted for seismic wave computations. This study shows how to model P‐waves in two dimensions by using a modified form of the cellular‐automaton rules for fluids. Propagation, reflection, and the computation of synthetic seismograms are demonstrated. Because no arithmetic calculations are needed and each lattice site can be updated simultaneously, this method is well‐suited for implementation on massively parallel computers. Among the many potential advantages are unconditional stability, no round‐off errors, and the possibility for devising novel approaches for modeling waves in inhomogeneous media.