Dimensional Cellular Automata Research Articles

Application and Reversibility of Three Dimensional Cellular Automata

In this study, we obtain the characteristic matrices of three-dimensional cellular automata under the null boundary condition. We examine the inverse of characteristic matrices. We obtain a recurrence equation to determine under what conditions the matrix is invertible. Thanks to this equation, we can calculate the inverse of large-dimensional matrices. Finally, we give some applications of cellular automata. We find the minimal polynomial of the characteristic matrix. We find the cycle length and transition length of the characteristic matrix with the help of minimal polynomials. We also find the attractive points of the characteristic matrix. Finally, we draw the State Transition diagram with the results we obtained.

CHARACTERIZATION OF ONE DIMENSIONAL PERIODIC BOUNDARY CELLULAR AUTOMATA

In this paper, we investigate one dimensional cellular automata under periodic boundary conditions. We use matrix algebra for calculating over on Zp. We obtain a formula for finding the reversibility of cellular automata. Finally, we give some important examples of cellular automata.

Dynamical features of rule sequences of one dimensional cellular automata with two states and three neighbors which realize the description of digital sound data

In the present paper, we investigate the dynamical features of the rule sequence at each time step which realize the description of digital sound data. From previous research, we have performed the description with the limited number of 256 rules of three-rules sets of one dimensional cellular automata with two states and three neighbors referred as to 1-2-3 CA hereafter for various digital sounds and Huffman coding, and have successfully achieved a fully compressed description of the target sound data without reproducing the error. In order to investigate the dynamical features of the rule sequences at each time step, we perform numerical Wolfram's classification method. From computer experiments, in Pronounced word data, all the rule sequences are composed with Wolfram's class1, 2 and 4, whereas in musical data, all the rule sequences are composed with Wolfram's class2 and 4. Thus, we have succeed to classify the rule sequences among the genres of data.

Grain refinement mechanism of metamorphic layers by abrasive grinding hardening

The abrasive grinding hardening is not only a high precision material removal process, but also generates metamorphic layers to improve surface strength, which is affected by surface material grain size. As the grain size is decided by dynamic recrystallization phenomenon under grinding thermal-stain coupling, the grain refinement mechanism should be studied. The full scale thermal-strain coupled finite element method (FEM) considering wheel's profile and abrasive distribution is established firstly. Afterwards, the governing equation on the increase of dislocation density is set up by three dimensional cellular automata (CA). And the refinement process of metamorphic layers is modeled. Meanwhile, the influence mechanism of dynamic thermal-strain effect on austenite grain in metamorphic layers is studied. Finally, with the help of grinding experiments, the variation regulation on austenite grain size and its content along the surface layers is compared and validated under different feeding rates and grinding depths. The obtained conclusion can not only improve the transformation mechanism of metamorphic layers in abrasive grinding hardening, but also give a parametric reference for grain refinement in actual machining process.

Design of a Hybrid Programmable 2-D Cellular Automata Based Pseudo Random Number Generator

This paper proposes a hybrid programmable two-dimensional Cellular Automata (CA) based pseudo-random number generator which includes a newly designed rule set. The properties and evolution of one and two dimensional CA are revisited. The various metrics for evaluating CA as a Pseudo-Random Number Generator (PRNG) are discussed. It is proved that the randomness is high irrespective of the initial seed by applying this newly designed rule set. The PRNG is tested against a popular statistical test called Diehard test suite and the results show that the PRNG is highly random. The chaotic measures like entropy, hamming distance and cycle length have been measured

Salt & Pepper Noise Reduction using Cellular Automata

In order to reduce salt & pepper noise in an MRI image of brain, in this paper we make algorithm using 2-dimensional Cellular Automata (CA). Image processing with CA has improved digital image processing in several years. Salt & Pepper noise can corrupt a picture via image transmission (atmospheric disturbance) or faulty sensors in camera or a computer system through hardware.

Retracted: Development of Bulk Metallic Glass Matrix Composites (BMGMC) by Additive Manufacturing: Modelling and Simulation – A Review: Part B

. Bulk metallic glasses (BMGs) and their composites (BMGMC) have emerged as competitive materials for structural engineering applications exhibiting superior tensile strength, hardness along with very high elastic strain limit. However, they suffer from a lack of ductility and subsequent low toughness due to the inherent brittleness of the glassy structure which render them to failure without appreciable yielding owing to mechanisms of rapid movement of shear bands all throughout the volume of the material. This severely limits their use in the manufacture of structural engineering parts. Various theories and mechanisms have been proposed to counter this effect. Introduction of secondary ductile phase in the form ofin-situnucleating and growing dendrites from melt during solidification have proved out to be best solution of this problem. Nucleation and growth of these ductile phases have been extensively studied over the last 16 years since their introduction for the first time in Zr-based BMGMC by Prof. Johnson at Caltech. Data about almost all types of phases appearing in different systems have been successfully reported. However, there is very little information available about the precise mechanism underlying their nucleation and growth during solidification in a copper mould during conventional vacuum casting and melt pool of additively manufactured parts. Various routes have been proposed to study this including experiments in microgravity, levitation in synchrotron light and modelling and simulation. In this report, which is Part B of two parts comprehensive overview, state of the art of development, manufacturing, characterisation and modelling and simulation of BMGMCs is described in detail. Evolution of microstructure in BMGMC during additive manufacturing have been presented with the aim to address fundamental problem of lack in ductility along with prediction of grain size and phase evolution with the help of advanced modelling and simulation techniques. It has been systematically proposed that 2 and 3 dimensional cellular automaton method combined with finite element (CAFE) tools programmed on MATLAB® and simulated on Ansys® would best be able to describe this phenomenon in most efficient way. Present part B focuses on methodology by which modelling and simulation can be adopted and applied to describe evolution of microstructure in this complex class of materials.

Retracted: Development of Bulk Metallic Glass Matrix Composites (BMGMC) by Additive Manufacturing: Modelling and Simulation – A Review: Part A

Bulk metallic glasses (BMGs) and their composites (BMGMC) have emerged as competitive materials for structural engineering applications exhibiting superior tensile strength, hardness along with very high elastic strain limit. However, they suffer from a lack of ductility and subsequent low toughness due to the inherent brittleness of the glassy structure which render them to failure without appreciable yielding owing to mechanisms of rapid movement of shear bands all throughout the volume of the material. This severely limits their use in fabricating structural and machinery parts. Various mechanisms have been proposed to counter this effect. Introduction of secondary ductile phase in the form ofin-situnucleating and growing dendrites from melt during solidification have proved out to be best solution of this problem. Nucleation and growth of these ductile phases have been extensively studied over the last 16 years since their introduction for the first time in Zr-based BMGMC by Prof. Johnson at Caltech. Data about almost all types of phases appearing in different systems have been successfully reported. However, there is very little information available about the precise mechanism underlying their nucleation and growth during solidification in a copper mould during conventional vacuum casting and melt pool of additively manufactured parts. Various routes have been proposed to study this including experiments in microgravity, levitation in synchrotron light and modelling and simulation. In this report consisting of two parts which is a preamble of author’s PhD Project, a concise review about evolution of microstructure in BMGMC during additive manufacturing have been presented with the aim to address fundamental problem of lack in ductility along with prediction of grain size and phase evolution with the help of advanced modelling and simulation techniques. It has been systematically proposed that 2 and 3 dimensional cellular automaton method combined with finite element (CAFE) tools programmed on MATLAB® and simulated on Ansys® would best be able to describe this phenomenon in most efficient way. Present part consists of general introduction of bulk metallic glass matrix composites (BMGMC), problem of lack of ductility in them, measures to counter it, success stories and their additive manufacturing.

Classification of Two Dimensional Cellular Automata Rules for Symmetric Pattern Generation

Cellular automata (CA) are parallel computational models that comprise of a grid of cells. CA is mainly used for modeling complex systems in various fields, where the geometric structure of the lattices is different. In the absence of a CA model to accommodate different types of lattices in CA, an angle-based CA model is proposed to accommodate various lattices. In the proposed model, the neighborhood structure in a two dimensional cellular automata (2D-CA) is viewed as a star graph. The vertices of the proposed graph are determined by a parameter, angle ( θ ) . Based on the angle ( θ ) , the neighborhood of the CA, which is treated as the vertices of the graph, varies. So this model is suitable for the representation of different types of two dimensional lattices such as square lattice, rectangular lattice, hexagonal lattice, etc. in CA. A mathematical model is formulated for representing CA rules which suit for different types of symmetric lattices. The star graph representation helps to find out the internal symmetries exists in CA rules. Classification of CA rules based on the symmetry exists in the rules, which generates symmetric patterns are discussed in this work.

A parallel implementation of a cloud dynamics model with cellular automaton

The construction of computational models to simulate real systems enables their dynamics to be understood and analyzed, and the future evolution of these systems to be predicted. The benefits of using computational simulations are that they are more secure, save cost and time, since systems that do not already exist can be created without incurring the costs of building them, securely, and in less time than real ones. However, the simulation of complex systems needs a lot of calculations, usually run in high performance platforms which rely extensively on parallel computing. Atmospheric models are examples of complex systems, since they consist of a large number of variables, many differential equations, and space-temporal evolution. A cellular automaton (CA) is a numerical method used in simulations of systems represented by a matrix of cells where the state transitions depend on the state of neighboring cells. This work sets out a proposal for the parallel implementation of a two dimensional CA, using an atmospheric model of cloud dynamics as a case study. The tests were performed in a shared memory architecture with a 12-core processor and a 192-core GPU. Several experiments were performed in order to assess stability, precision, and performance in an isolated atmospheric area. The experiments evaluated the performance of the parallel model relative to the sequential one, using runtime and speedup as metrics. The results showed that the parallel model is stable from the point of view of thermal equilibrium. Moreover, the performance tests showed that the runtime decreases as the number of threads increases until the limit of the number of computing cores, reaching a performance gain of up to 6.5 times better than the sequential version.

Cellular automata-based efficient method for the removal of high-density impulsive noise from digital images

Cellular automata (CA) are simple dynamical systems used for solving simple as well as complex problems. It uses a discrete space, like the space used in spatial domain for image processing, to store the values of the input data. Then, the input data can be processed according to the transition rules, functions, or, programmes, for the required output. This research work presents an efficient algorithm based on two dimensional cellular automata (2D CA), with hybrid rules under null and periodic boundary conditions, for filtering high-density impulsive noise from corrupted digital images. The most important advantage of the proposed method is that, it can be applied on all types of digital images (binary, greyscale, or, true color). The paper is organized as follows: Sect. 1 gives a brief introduction towards the problem of noise in digital images with emphasis on its solution. Further, this section presents a brief review of existing standard noise filtering methods based on general image processing and CA techniques. Section 2 discusses the basic concept of CA with special emphasis on 2D CA and related concepts. Section 3 presents the proposed algorithm for the removal of high-density impulsive noise from corrupted digital images. Section 4 discusses, in detail, the experimental results using both mathematical and subjective analysis; and, the extensive experimentation reveals that the proposed 2D CA based algorithm yields better results than the standard noise filtering algorithms. And, then finally Sect. 5 presents the conclusions and future scope.

Modelling and Simulation of Solidification Phenomena during Additive Manufacturing of Bulk Metallic Glass Matrix Composites (BMGMC)—A Brief Review and Introduction of Technique

Despite a wealth of experimental studies focused on determining and improving mechanical properties and development of fundamental understanding of underlying mechanisms behind nucleation and growth of ductile phase precipitates from melt in glassy matrix, still, there is dearth of knowledge about how these ductile phases nucleate during solidification. Various efforts have been made to address this problem such as experiments in microgravity, high resolution electron microscopy and observation in synchrotron light after levitation but none have proved out to be satisfactory. In this study, an effort has been made to address this problem by modelling and simulation. Current state of the art of development, manufacturing, characterisation and modelling and simulation of bulk metallic glass matrix composites is described in detail. Evolution of microstructure in bulk metallic glass matrix composites during solidification in additive manufacturing has been presented with the aim to address fundamental problem of evolution of solidification microstructure as a result of solute partitioning, diffusion and capillary action. An overview is also presented to explain the relation of microstructure evolution to hardness and fracture toughness. This is aimed at overcoming fundamental problem of lack of ductility and toughness in this diverse class of materials. Quantitative prediction of solidification microstructure is done with the help of advanced part scale modelling and simulation techniques. It has been systematically proposed that 2-dimensional cellular automaton (CA) method combined with finite element (for thermal modelling) tools (CA-FE) programmed on FORTRAN? and parallel simulated on ABAQUS? would best be able to describe this complicated multiphysics phenomenon in most efficient way. Focus is laid on quantification of methodology by which modelling and simulation can be adopted and applied to describe evolution of microstructure in this important class of materials. It is found that proposed methodology is meritorious.

A Symbolic Dynamics Perspective of Conway’s Game of Life

An interesting question is whether the intrinsic complexity of the gliders in [Formula: see text]-dimensional cellular automata could be quantitatively analyzed in rigorously mathematical sense. In this paper, by introducing the [Formula: see text]-dimensional symbolic space, some fundamental dynamical properties of [Formula: see text]-dimensional shift map are explored in a subtle way. The purpose of this article is to present an accurate characterization of complex symbolic dynamics of gliders in Conway’s game of life. A series of dynamical properties of gliders on their concrete subsystems are investigated by means of the directed graph representation and transition matrix. More specifically, the gliders here are topologically mixing and possess the positive topological entropy on their subsystems. Finally, it is worth mentioning that the method presented in this paper is also applicable to other gliders in different [Formula: see text] dimensions.

Cellular automata: a decision support system for stock market trading

This study focuses on the implementation of moving average technical indicator on a one dimensional cellular automata. The moving average is an indicator that shows the average price of a security at a given period of time and it is the oldest and most widely used technical analysis tool. Each cell in the automata compares the relationship between moving averages of the security's price with the security price itself. During the simulation each cell in the automata produces two output states either BUY or SELL, that will help the traders to take better decision on stocks. A Buy signal is generated by the cellular automata when the security price rises above its moving average, and a Sell signal is generated when the security price falls below its moving average.

セルオートマトンによる塗膜下腐食シミュレーション手法に関する研究（第1報：スクライブ塗装鋼板の解析）

An underfilm corrosion simulation method for epoxy coated steel panels in ship’s water ballast tanks (WBT) has been developed. The incubation and extension of coating failure are simulated by using 2-dimensional cellular automaton method, and the steel diminution is simulated by modifying the corrosion model proposed by Kawamura et al. (2015). Analysis parameters are determined by using the results of onboard exposure and cyclic corrosion tests performed by Shiotani et al. (2014). The change in corroded surface shape of epoxy coated and scribed steel panels made of conventional steel and corrosion resistant steel (CRS) exposed in an ore carrier’s WBT for 4.8 years is simulated. The simulated coating deterioration (blister) area and the corroded surface profile agree well with those measured. This demonstrates the effectiveness of the developed simulation method and the determined parameters. The differences in analysis parameters between conventional steel and CRS suggest that CRS can reduce the harmful effect of the active corrosion region on the remaining coating life at the blister’s frontline and the corrosion under the blister.

Selection of Optimum Rule Set of Two Dimensional Cellular Automata for Some Morphological Operations

The cellular automaton paradigm is very appealing and its inherent simplicity belies its potential complexity. Two dimensional cellular automata are significantly applying to image processing operations. This paper describes the application of cellular automata (CA) to various morphological operations such as thinning and thickening of binary images. The description about the selection of the optimum rule set of two dimensions cellular automata for thinning and thickening of binary images is illustrated by this paper. The selection of the optimum rule set from large search space has been performed on the basis of sequential floating forward search method. The misclassification error between the images obtained by the standard function and the one obtained by cellular automata rule is used as the fitness function. The proposed method is also compared with some standard methods and found suitable for the purpose of morphological operations.

Self-organized criticality in a two-dimensional cellular automaton model of a magnetic flux tube with background flow

We investigate the transition to Self Organized Criticality in a two-dimensional model of a flux tube with a background flow. The magnetic induction equation, represented by a partial differential equation with a stochastic source term, is discretized and implemented on a two dimensional cellular automaton. The energy released by the automaton during one relaxation event is the magnetic energy. As a result of the simulations we obtain the time evolution of the energy release, of the system control parameter, of the event lifetime distribution and of the event size distribution, respectively, and we establish that a Self Organized Critical state is indeed reached by the system. Moreover, energetic initial impulses in the magnetohydrodynamic flow can lead to one dimensional signatures in the magnetic two dimensional system, once the Self Organized Critical regime is established. The applications of the model for the study of Gamma Ray Bursts is briefly considered, and it is shown that some astrophysical parameters of the bursts, like the light curves, the maximum released energy, and the number of peaks in the light curve can be reproduced and explained, at least on a qualitative level, by working in a framework in which the systems settles in a Self Organized Critical state via magnetic reconnection processes in the magnetized Gamma Ray Burst fireball.

Cellular automata simulation of saltwater intrusion in coastal aquifer

The wasteful consumption of freshwater in heavily populated coastal areas usually consist the basic reason for the intrusion of saltwater into the coastal aquifers. In order to avoid such catastrophic scenarios, their prediction is of utter significance. Underground water systems are highly complex and the water flow is extremely dynamic, thus making the prediction of this phenomenon a difficult task. For this reason, a two dimensional Cellular Automaton (CA) was designed enabling both the qualitative and quantitative simulation and illustration of the saltwater intrusion into an unconfined coastal aquifer. The presented results ensure the robustness of the proposed CA model taking full advantage of its inherent parallelism and local connectivity.

Three-rules set of one dimensional cellular automata with two states and three neighbors improves description ability

Three-rules set of one dimensional cellular automata with two states and three neighbors improves description ability

Cellular Automata-based Anthropogenic Heat Simulation 1

Abstract Cellular automata (CA) models have been for several years, employed to describe urban phenomena like growth of human settlements, changes in land use and, more recently, dispersion of air pollutants. We propose to adapt CA to study the dispersion of anthropogenic heat emissions on the micro scale. Three dimensional cubic CA with a constant cell size of 0.15 m have been implemented. Simulations suggest an improvement in processing speed compared to conventional computational fluid dynamics (CFD) models, which are limited in scale and yet incapable of solving simulations on local or larger scale. Instead of solving the Navier- Stokes equations, as in CFD, only temperature and heat differences for the CA are modeled. Radiation, convection and turbulence have been parameterized according to scale. This CA- based approach can be combined with an agent-based traffic simulation to analyse the effect of driving behavior and other microscopic factors on urban heat.