Juan Carlos Seck-Tuoh-Mora

Invertible behavior in elementary cellular automata with memory

Elementary cellular automata (ECAs) have been studied for their ability to generate complex global behavior, despite their simplicity. One variation of ECAs is obtained by adding memory to each cell in a neighborhood. This process generates a provisional configuration in which the application of an evolution rule establishes the dynamics of the system. This version is known as an ECA with memory (ECAM). Most previous work on ECAMs analyzed the complex behavior taking chaotic ECAs. However, the present paper investigates reversible ECAMs as obtained from reversible and permutative ECAs. These ECAs have at least one ancestor for every configuration; thus, the correct permutation of states may specify the memory function to obtain reversible ECAMs. For permutative ECAs, which are often irreversible, we demonstrate that the use of a quiescent state and the correct manipulation of de Bruijn blocks produce reversible ECAMs.

Simple Networks on Complex Cellular Automata: From de Bruijn Diagrams to Jump-Graphs

We overview networks which characterise dynamics in cellular automata. These networks are derived from one-dimensional cellular automaton rules and global states of the automaton evolution: de Bruijn diagrams, subsystem diagrams, basins of attraction, and jump-graphs. These networks are used to understand properties of spatially-extended dynamical systems: emergence of non-trivial patterns, self-organisation, reversibility and chaos. Particular attention is paid to networks determined by travelling self-localisations, or gliders.

Distributed Control of a Manufacturing System with One-Dimensional Cellular Automata

We present a distributed control modeling approach for an automated manufacturing system based on the dynamics of one-dimensional cellular automata. This is inspired by the fact that both cellular automata and manufacturing systems are discrete dynamical systems where local interactions given among their elements (resources) can lead to complex dynamics, despite the simple rules governing such interactions. The cellular automaton model developed in this study focuses on two states of the resources of a manufacturing system, namely, busy or idle. However, the interaction among the resources such as whether they are shared at different stages of the manufacturing process determines the global dynamics of the system. A procedure is shown to obtain the local evolution rule of the automaton based on the relationships among the resources and the material flow through the manufacturing process. The resulting distributed control of the manufacturing system appears to be heterarchical, and the evolution of the cellular automaton exhibits a Class II behavior for some given disordered initial conditions.

Modeling of Throughput in Production Lines Using Response Surface Methodology and Artificial Neural Networks

The problem of assigning buffers in a production line to obtain an optimum production rate is a combinatorial problem of type NP-Hard and it is known as Buffer Allocation Problem. It is of great importance for designers of production systems due to the costs involved in terms of space requirements. In this work, the relationship among the number of buffer slots, the number of work stations, and the production rate is studied. Response surface methodology and artificial neural network were used to develop predictive models to find optimal throughput values. 360 production rate values for different number of buffer slots and workstations were used to obtain a fourth-order mathematical model and four hidden layers’ artificial neural network. Both models have a good performance in predicting the throughput, although the artificial neural network model shows a better fit ( ) against the response surface methodology ( ). Moreover, the artificial neural network produces better predictions for data not utilized in the models construction. Finally, this study can be used as a guide to forecast the maximum or near maximum throughput of production lines taking into account the buffer size and the number of machines in the line.

Welch sets for random generation and representation of reversible one-dimensional cellular automata !

Abstract Reversible one-dimensional cellular automata are studied from the perspective of Welch Sets. This paper presents an algorithm to generate random Welch sets that define a reversible cellular automaton. Then, properties of Welch sets are used in order to establish two bipartite graphs describing the evolution rule of reversible cellular automata. The first graph gives an alternative representation for the dynamics of these systems as block mappings and shifts. The second graph offers a compact representation for the evolution rule of reversible cellular automata. Both graphs and their matrix representations are illustrated by the generation of random reversible cellular automata with 6 and 18 states.

Complex dynamics in a hexagonal cellular automaton

Hexagonal cellular automata (CA) were studied with interest as a variation of the famous Game of Life CA, mainly for spiral phenomena simulations; where the most interesting constructions are related to the Belousov-Zhabotinsky reaction. In this paper, we study a special kind of hexagonal CA known as the Spiral rule. Such automaton displays a non-trivial complex behaviour related to discrete models of reaction-diffusion chemical media, dominated by spiral guns that easily emerge from random initial conditions. Computing abilities of Spiral rule automata are shown by means of logic gates, defined by collisions between mobile self-localizations. Also, a more extended classification of complex self-localization patterns is presented, including some self-organized patterns.

A fuzzy control for optimizing the design of passive electrical circuits

This paper exposes a fuzzy control to determine independent parameters of a passive circuit in order to obtain a desired output established by the design requirements. This is achieved using a vector representation of the circuit and varying the independent parameters by a fuzzy control based on three inference rules according to the output voltage. An analysis about the behavior of the control is explained and some examples of this procedure are depicted.

MODELING A NONLINEAR LIQUID LEVEL SYSTEM BY CELLULAR NEURAL NETWORKS

This paper presents the analogue simulation of a nonlinear liquid level system composed by two tanks; the system is controlled using the methodology of exact linearization via state feedback by cellular neural networks (CNNs). The relevance of this manuscript is to show how a block diagram representing the analogue modeling and control of a nonlinear dynamical system, can be implemented and regulated by CNNs, whose cells may contain numerical values or arithmetic and control operations. In this way the dynamical system is modeled by a set of local-interacting elements without need of a central supervisor.

Elementary cellular automaton Rule 110 explained as a block substitution system: Rule 110 as a block substitution system

This paper presents the characterization of Rule 110 as a block substitution system of three symbols. Firstly, it is proved that the dynamics of Rule 110 is equivalent to cover the evolution space with triangles formed by the cells of the automaton. It is hence demonstrated that every finite configuration can be partitioned in several blocks of symbols and, that the dynamics of Rule 110 can be reproduced by a set of production rules applied to them. The shape of the blocks in the current configuration can be used for knowing the number of them in the next one; with this, the evolution of random configurations, ether and gliders can be modeled.