An Exploration of Rule Clustering in Cellular Automata Rule Spaces

The study of complex systems examines the global behavior of a system and how the individual parts of the system affect that behavior [1]. The study of complex systems spans across many fields of science like biology, physics, engineering, and computer science. One area of complex systems that has not been fully explored is cellular automata. Since its discovery by John von Neumann, there have been no consistent ways of categorizing similarities between cellular automata rules or collecting similar rules for observation. This thesis introduces an approach to identifying clusters of similar rules and extracting rules from that cluster. Several similarity measures were developed to establish similarity between rules. All similarity measure approaches are outlined in this thesis, but only one was selected for determining similarity in this approach. Based on a partitioning of the rule space, this approach uses lo and h with their inherent primitives p0 and pi to obtain a cluster identification string [5], The cluster Id. is determined by the output of the surrounding neighbors of any rule in the cluster. This cluster Id. can be used to produce a set of rules, all yielding the same or similar output

A statistical approach to the identification of diploid cellular automata based on incomplete observations

In this paper, the identification problem of diploid cellular automata is considered, in which, based on a series of incomplete observations, the underlying cellular automaton rules and the states of missing cell states are to be uncovered. An algorithm for identifying the rule, based on a statistical parameter estimation method using a normal distribution approximation, is presented. In addition, an algorithm for filling the missing cell states is formulated. The accuracy of these methods is examined in a series of computational experiments

The identification of cellular automata

Although cellular automata have been widely studied as a class of the spatio temporal systems, very few investigators have studied how to identify the CA rules given observations of the patterns. A solution using a polynomial realization to describe the CA rule is reviewed in the present study based on the application of an orthogonal least squares algorithm. Three new neighbourhood detection methods are then reviewed as important preliminary analysis procedures to reduce the complexity of the estimation. The identification of excitable media is discussed using simulation examples and real data sets and a new method for the identification of hybrid CA is introduced

An evolutionary approach to the identification of Cellular Automata based on partial observations

In this paper we consider the identification problem of Cellular Automata (CAs). The problem is defined and solved in the context of partial observations with time gaps of unknown length, i.e. pre-recorded, partial configurations of the system at certain, unknown time steps. A solution method based on a modified variant of a Genetic Algorithm (GA) is proposed and illustrated with brief experimental results.Comment: IEEE CEC 201

Identification of cellular automata based on incomplete observations with bounded time gaps

In this paper, the problem of identifying the cellular automata (CAs) is considered. We frame and solve this problem in the context of incomplete observations, i.e., prerecorded, incomplete configurations of the system at certain, and unknown time stamps. We consider 1-D, deterministic, two-state CAs only. An identification method based on a genetic algorithm with individuals of variable length is proposed. The experimental results show that the proposed method is highly effective. In addition, connections between the dynamical properties of CAs (Lyapunov exponents and behavioral classes) and the performance of the identification algorithm are established and analyzed

Identification of the neighborhood and CA rules from spatio-temporal CA patterns

Extracting the rules from spatio-temporal patterns generated by the evolution of cellular automata (CA) usually produces a CA rule table without providing a clear understanding of the structure of the neighborhood or the CA rule. In this paper, a new identification method based on using a modified orthogonal least squares or CA-OLS algorithm to detect the neighborhood structure and the underlying polynomial form of the CA rules is proposed. The Quine-McCluskey method is then applied to extract minimum Boolean expressions from the polynomials. Spatio-temporal patterns produced by the evolution of 1D, 2D, and higher dimensional binary CAs are used to illustrate the new algorithm, and simulation results show that the CA-OLS algorithm can quickly select both the correct neighborhood structure and the corresponding rule

Extracting Boolean rules from CA patterns

A multiobjective genetic algorithm (GA) is introduced to identify both the neighborhood and the rule set in the form of a parsimonious Boolean expression for both one- and two-dimensional cellular automata (CA). Simulation results illustrate that the new algorithm performs well even when the patterns are corrupted by static and dynamic nois

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

Análisis de sistemas complejos usando machine learning

Nowadays, we can find complex systems in a great variety of fields, such as biology, physics, engineering or social systems. From fluid dynamics to biomolecular interactions, we can find complex systems everywhere, and it is not an easy task to predict their behaviour. Cellular automata are considered great techniques of modelling complex systems. In cellular automata, some simple rules lead sometimes to emergent chaotic or complex behaviours that are interesting in the context of some real-life complex models. Machine Learning algorithms are well known for identifying underlaying patterns in complex structures. In this paper, cellular automata and some Machine Learning algorithms, such as Neural Networks or k-Nearest Neighbours are introduced, and after that some of them are used to analyze cellular automata. The aim of this paper is to define a way of working with cellular automata and machine learning that can be expanded later with new algorithms, new automata or more data.Universidad de Sevilla. Grado en Matemática