Journal articles: 'Continuous cellular automata'

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Semenov, V. K. "Continuous media and cellular automata." Uspekhi Fizicheskih Nauk 160, no. 11 (1990): 204. http://dx.doi.org/10.3367/ufnr.0160.199011j.0204.

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Semenov, V. K. "Continuous media and cellular automata." Soviet Physics Uspekhi 33, no. 11 (November 30, 1990): 996. http://dx.doi.org/10.1070/pu1990v033n11abeh002663.

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SECK TUOH MORA, JUAN CARLOS, MANUEL GONZALEZ HERNANDEZ, NORBERTO HERNANDEZ ROMERO, AARON RODRIGUEZ TREJO, and SERGIO V. CHAPA VERGARA. "MODELING LINEAR DYNAMICAL SYSTEMS BY CONTINUOUS-VALUED CELLULAR AUTOMATA." International Journal of Modern Physics C 18, no. 05 (May 2007): 833–48. http://dx.doi.org/10.1142/s0129183107010589.

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This paper exposes a procedure for modeling and solving linear systems using continuous-valued cellular automata. The original part of this work consists on showing how the cells in the automaton may contain both real values and operators for carrying out numerical calculations and solve a desired problem. In this sense the automaton acts as a program, where data and operators are mixed in the evolution space for obtaining the correct calculations. As an example, Euler's integration method is implemented in the configuration space in order to achieve an approximated solution for a dynamical system. Three examples showing linear behaviors are presented.

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Heaton, Jeff. "Evolving continuous cellular automata for aesthetic objectives." Genetic Programming and Evolvable Machines 20, no. 1 (August 27, 2018): 93–125. http://dx.doi.org/10.1007/s10710-018-9336-1.

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Turney, Peter D. "Measuring Behavioral Similarity of Cellular Automata." Artificial Life 27, no. 1 (2021): 62–71. http://dx.doi.org/10.1162/artl_a_00337.

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Abstract Conway's Game of Life is the best-known cellular automaton. It is a classic model of emergence and self-organization, it is Turing-complete, and it can simulate a universal constructor. The Game of Life belongs to the set of semi-totalistic cellular automata, a family with 262,144 members. Many of these automata may deserve as much attention as the Game of Life, if not more. The challenge we address here is to provide a structure for organizing this large family, to make it easier to find interesting automata, and to understand the relations between automata. Packard and Wolfram (1985) divided the family into four classes, based on the observed behaviors of the rules. Eppstein (2010) proposed an alternative four-class system, based on the forms of the rules. Instead of a class-based organization, we propose a continuous high-dimensional vector space, where each automaton is represented by a point in the space. The distance between two automata in this space corresponds to the differences in their behavioral characteristics. Nearest neighbors in the space have similar behaviors. This space should make it easier for researchers to see the structure of the family of semi-totalistic rules and to find the hidden gems in the family.

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Bubak, Marian, and Przemys l. ̵. aw Czerwiński. "Traffic simulation using cellular automata and continuous models." Computer Physics Communications 121-122 (September 1999): 395–98. http://dx.doi.org/10.1016/s0010-4655(99)00363-x.

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Pérez-Terrazas, Jaime Enrique, Vrani Ibarra-Junquera, and Haret Codratian Rosu. "Cellular automata modeling of continuous stirred tank reactors." Korean Journal of Chemical Engineering 25, no. 3 (May 2008): 461–65. http://dx.doi.org/10.1007/s11814-008-0078-2.

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Evsutin, O. O., A. A. Shelupanov, V. D. Babishin, and K. A. Sosedko. "Continuous optimization using a hybrid model of cellular automata and learning automata." Proceedings of Tomsk State University of Control Systems and Radioelectronics 22, no. 1 (2019): 50–54. http://dx.doi.org/10.21293/1818-0442-2019-22-1-50-54.

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Zhenjun Zhu and Chang Liu. "Micromachining process simulation using a continuous cellular automata method." Journal of Microelectromechanical Systems 9, no. 2 (June 2000): 252–61. http://dx.doi.org/10.1109/84.846706.

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Seck-Tuoh-Mora, Juan Carlos, Norberto Hernandez-Romero, Pedro Lagos-Eulogio, Joselito Medina-Marin, and Nadia Samantha Zuñiga-Peña. "A continuous-state cellular automata algorithm for global optimization." Expert Systems with Applications 177 (September 2021): 114930. http://dx.doi.org/10.1016/j.eswa.2021.114930.

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ARRIGHI, PABLO, SIMON MARTIEL, and VINCENT NESME. "Cellular automata over generalized Cayley graphs." Mathematical Structures in Computer Science 28, no. 3 (May 29, 2017): 340–83. http://dx.doi.org/10.1017/s0960129517000044.

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It is well-known that cellular automata can be characterized as the set of translation-invariant continuous functions over a compact metric space; this point of view makes it easy to extend their definition from grids to Cayley graphs. Cayley graphs have a number of useful features: the ability to graphically represent finitely generated group elements and their relations; to name all vertices relative to an origin; and the fact that they have a well-defined notion of translation. We propose a notion of graphs, which preserves or generalizes these features. Whereas Cayley graphs are very regular, generalized Cayley graphs are arbitrary, although of a bounded degree. We extend cellular automata theory to these arbitrary, bounded degree, time-varying graphs. The obtained notion of cellular automata is stable under composition and under inversion.

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MEYEROVITCH, TOM. "Finite entropy for multidimensional cellular automata." Ergodic Theory and Dynamical Systems 28, no. 4 (August 2008): 1243–60. http://dx.doi.org/10.1017/s0143385707000855.

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AbstractLet $X=S^{\mathbb {G}}$ where $\mathbb {G}$ is a countable group and S is a finite set. A cellular automaton (CA) is an endomorphism T:X→X (continuous, commuting with the action of $\mathbb {G}$). Shereshevsky [Expansiveness, entropy and polynomial growth for groups acting on subshifts by automorphisms. Indag. Math. (N.S.)4(2) (1993), 203–210] proved that for $\mathbb {G}=\mathbb {Z}^d$ with d>1 no CA can be forward expansive, raising the following conjecture: for $G=\mathbb {Z}^d$, d>1, the topological entropy of any CA is either zero or infinite. Morris and Ward [Entropy bounds for endomorphisms commuting with K actions. Israel J. Math. 106 (1998), 1–11] proved this for linear CAs, leaving the original conjecture open. We show that this conjecture is false, proving that for any d there exists a d-dimensional CA with finite, non-zero topological entropy. We also discuss a measure-theoretic counterpart of this question for measure-preserving CAs.

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Terrazas Gonzalez, Jesus D., and Witold Kinsner. "A Modular Dynamical Cryptosystem Based on Continuous-Interval Cellular Automata." International Journal of Cognitive Informatics and Natural Intelligence 5, no. 4 (October 2011): 83–109. http://dx.doi.org/10.4018/jcini.2011100106.

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This paper presents a new cryptosystem based on chaotic continuous-interval cellular automata (CCA) to increase data protection as demonstrated by their flexibility to encrypt and decrypt information from distinct sources. Enhancements to cryptosystems are also presented including (i) a model based on a new chaotic CCA attractor, (ii) the dynamical integration of modules containing dynamical systems to generate complex sequences, and (iii) an enhancement for symmetric cryptosystems by allowing them to generate an unlimited number of keys. This paper also presents a process of mixing chaotic sequences obtained from cellular automata, instead of using differential equations, as a basis to achieve higher security and higher speed for the encryption and decryption processes, as compared to other recent approaches. The complexity of the mixed sequences is measured using the variance fractal dimension trajectory to compare them to the unmixed chaotic sequences to verify that the former are more complex. This type of polyscale measure and evaluation has never been done in the past outside this research group.

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Li, Wei Qiao, Qin Yu, and Li Xiang Ma. "Cellular Automata-Based WSN Energy Saving Technology." Advanced Materials Research 546-547 (July 2012): 1334–39. http://dx.doi.org/10.4028/www.scientific.net/amr.546-547.1334.

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Wireless sensor network is a new type of wireless network. IEEE 802.15.4 / Zigbee standards with low energy consumption, low speed characteristics has been widely used in wireless sensor network. As the wireless sensor nodes are often set in complex geographical environment and had not continuous power supply, thus saving energy has been one of the main directions of research at home and abroad. Cellular automata are a mimic biological cell reproduction form of dynamical system, with a simple rule to reveal the complex global characteristics. This paper presents a kind of cellular automata and Zigbee based wireless sensor network binding mechanism, so that the wireless node according to the communication state during hibernation and job switching between states in order to achieve the purpose of energy saving. Simulations show that the mechanism can reduce the network energy consumption, improve energy utilization rate, and prolong the survival time of the node.

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Makarenko, Alexander. "Cellular automata models with complex valued transition functions." System research and information technologies, no. 4 (December 29, 2020): 141–47. http://dx.doi.org/10.20535/srit.2308-8893.2020.4.11.

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The new class of mathematical models for computation theory is considered — namely cellular automata (CA) with branching complex-valued transition functions. The key point is possible multivaluedness of cell’s states with such transition functions. Different cases with complex-value transition functions had been considered. Dynamics CA on one branch and on different isolated branches are described. Also the case of transitions of states between branches is proposed. The case of continuous-valued CA and their finite-valued approximations are discussed. The problem of approximation of multivalued CA is stated.

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UGUZ, SELMAN, HASAN AKIN, and IRFAN SIAP. "REVERSIBILITY ALGORITHMS FOR 3-STATE HEXAGONAL CELLULAR AUTOMATA WITH PERIODIC BOUNDARIES." International Journal of Bifurcation and Chaos 23, no. 06 (June 2013): 1350101. http://dx.doi.org/10.1142/s0218127413501010.

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This paper presents a study of two-dimensional hexagonal cellular automata (CA) with periodic boundary. Although the basic construction of a cellular automaton is a discrete model, its global level behavior at large times and on large spatial scales can be a close approximation to a continuous system. Meanwhile CA is a model of dynamical phenomena that focuses on the local behavior which depends on the neighboring cells in order to express their global behavior. The mathematical structure of the model suggests the importance of the algebraic structure of cellular automata. After modeling the dynamical behaviors, it is sometimes an important problem to be able to move backwards on CAs in order to understand the behaviors better. This is only possible if cellular automaton is a reversible one. In the present paper, we study two-dimensional finite CA defined by hexagonal local rule with periodic boundary over the field ℤ3 (i.e. 3-state). We construct the rule matrix corresponding to the hexagonal periodic cellular automata. For some given coefficients and the number of columns of hexagonal information matrix, we prove that the hexagonal periodic cellular automata are reversible. Moreover, we present general algorithms to determine the reversibility of 2D 3-state cellular automata with periodic boundary. A well known fact is that the determination of the reversibility of a two-dimensional CA is a very difficult problem, in general. In this study, the reversibility problem of two-dimensional hexagonal periodic CA is resolved completely. Since CA are sufficiently simple to allow detailed mathematical analysis, also sufficiently complex to produce chaos in dynamical systems, we believe that our construction will be applied many areas related to these CA using any other transition rules.

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Andrecut, M. "A Simple Three-States Cellular Automaton for Modelling Excitable Media." International Journal of Modern Physics B 12, no. 05 (February 20, 1998): 601–7. http://dx.doi.org/10.1142/s0217979298000363.

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Wave propagation in excitable media provides an important example of spatiotemporal self-organization. The Belousov–Zhabotinsky (BZ) reaction and the impulse propagation along nerve axons are two well-known examples of this phenomenon. Excitable media have been modelled by continuous partial differential equations and by discrete cellular automata. Here we describe a simple three-states cellular automaton model based on the properties of excitation and recovery that are essential to excitable media. Our model is able to reproduce the dynamics of patterns observed in excitable media.

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Gosálvez, M. A., Y. Xing, K. Sato, and R. M. Nieminen. "Discrete and continuous cellular automata for the simulation of propagating surfaces." Sensors and Actuators A: Physical 155, no. 1 (October 2009): 98–112. http://dx.doi.org/10.1016/j.sna.2009.08.012.

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Liu, Weibin, and Jihua Ma. "Limit averages of continuous functions under the action of cellular automata." Monatshefte für Mathematik 181, no. 4 (January 4, 2016): 869–74. http://dx.doi.org/10.1007/s00605-015-0869-6.

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Dembowski, Marcin, Barbara Wolnik, Witold Bołt, Jan M. Baetens, and Bernard De Baets. "Affine continuous cellular automata solving the fixed-length density classification problem." Natural Computing 17, no. 3 (July 24, 2017): 467–77. http://dx.doi.org/10.1007/s11047-017-9631-4.

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Zhikharevich, V. V., and G. D. Tymchyk. "Development of a continuous asynchronous cellular automata method for simulating turbulent flows." Prikladnaya diskretnaya matematika, no. 18 (December 1, 2012): 73–81. http://dx.doi.org/10.17223/20710410/18/6.

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Wolnik, Barbara, Marcin Dembowski, Witold Bołt, Jan M. Baetens, and Bernard De Baets. "Density-conserving affine continuous cellular automata solving the relaxed density classification problem." Journal of Physics A: Mathematical and Theoretical 50, no. 34 (July 31, 2017): 345103. http://dx.doi.org/10.1088/1751-8121/aa7d86.

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Helgason, Cathy M., and Thomas H. Jobe. "Fuzzy logic and continuous cellular automata in warfarin dosing of stroke patients." Current Treatment Options in Cardiovascular Medicine 7, no. 3 (June 2005): 211–18. http://dx.doi.org/10.1007/s11936-005-0049-4.

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Silva, E., F. H. Pereira, and P. H. T. Schimit. "Information spreading in a population modeled by continuous asynchronous probabilistic cellular automata." Computer Communications 154 (March 2020): 288–97. http://dx.doi.org/10.1016/j.comcom.2020.02.074.

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Gravner, Janko. "Recurrent ring dynamics in two-dimensional excitable cellular automata." Journal of Applied Probability 36, no. 2 (June 1999): 492–511. http://dx.doi.org/10.1239/jap/1032374467.

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TheGreenberg–Hastings model(GHM) is a simple cellular automaton which emulates two properties of excitable media: excitation by contact and a refractory period. We study two ways in which external stimulation can makeringdynamics in the GHM recurrent. The first scheme involves the initial placement of excitation centres which gradually lose strength, i.e. each time they become inactive (and then stay inactive forever) with probability 1 −pf. In this case, the density of excited sites must go to 0; however, their long–term connectivity structure undergoes a phase transition aspfincreases from 0 to 1. The second proposed rule utilizes continuous nucleation in that new rings are started at every rested site with probabilityps. We show that, for smallps, these dynamics make a site excited about everyps−1/3time units. This result yields some information about the asymptotic shape of a closely related random growth model.

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Duarte, J. A. M. S. "Bushfire Automata and Their Phase Transitions." International Journal of Modern Physics C 08, no. 02 (April 1997): 171–89. http://dx.doi.org/10.1142/s0129183197000175.

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Cellular automata for heterogeneous bushfire propagation are introduced and their critical properties studied. The underlying models assume continuous fuel with variable moisture characterized by either a fixed value or a random choice of extinction determined by the moisture level. Elliptical (circular) propagation from a single ignition point is assumed. Classes of universality are very stably identified to be those of directed and undirected percolation, despite a significant range of variation of the many parameters involved.

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Xu, Haiyun, Fangyue Chen, and Weifeng Jin. "Topological Conjugacy Classification of Elementary Cellular Automata with Majority Memory." International Journal of Bifurcation and Chaos 27, no. 14 (December 30, 2017): 1750217. http://dx.doi.org/10.1142/s0218127417502170.

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The topological conjugacy classification of elementary cellular automata with majority memory (ECAMs) is studied under the framework of symbolic dynamics. In the light of the conventional symbolic sequence space, the compact symbolic vector space is identified with a feasible metric and topology. A slight change is introduced to present that all global maps of ECAMs are continuous functions, thereafter generating the compact dynamical systems. By exploiting two fundamental homeomorphisms in symbolic vector space, all ECAMs are furthermore grouped into 88 equivalence classes in the sense that different mappings in the same global equivalence are mutually topologically conjugate.

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Gravner, Janko. "Recurrent ring dynamics in two-dimensional excitable cellular automata." Journal of Applied Probability 36, no. 02 (June 1999): 492–511. http://dx.doi.org/10.1017/s0021900200017277.

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The Greenberg–Hastings model (GHM) is a simple cellular automaton which emulates two properties of excitable media: excitation by contact and a refractory period. We study two ways in which external stimulation can make ring dynamics in the GHM recurrent. The first scheme involves the initial placement of excitation centres which gradually lose strength, i.e. each time they become inactive (and then stay inactive forever) with probability 1 − p f. In this case, the density of excited sites must go to 0; however, their long–term connectivity structure undergoes a phase transition as p f increases from 0 to 1. The second proposed rule utilizes continuous nucleation in that new rings are started at every rested site with probability p s . We show that, for small p s , these dynamics make a site excited about every p s −1/3 time units. This result yields some information about the asymptotic shape of a closely related random growth model.

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Uguz, Selman, Uḡur Sahin, Hasan Akin, and Irfan Siap. "Self-Replicating Patterns in 2D Linear Cellular Automata." International Journal of Bifurcation and Chaos 24, no. 01 (January 2014): 1430002. http://dx.doi.org/10.1142/s021812741430002x.

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This paper studies the theoretical aspects of two-dimensional cellular automata (CAs), it classifies this family into subfamilies with respect to their visual behavior and presents an application to pseudo random number generation by hybridization of these subfamilies. Even though the basic construction of a cellular automaton is a discrete model, its macroscopic behavior at large evolution times and on large spatial scales can be a close approximation to a continuous system. Beyond some statistical properties, we consider geometrical and visual aspects of patterns generated by CA evolution. The present work focuses on the theory of two-dimensional CA with respect to uniform periodic, adiabatic and reflexive boundary CA (2D PB, AB and RB) conditions. In total, there are 512 linear rules over the binary field ℤ2for each boundary condition and the effects of these CA are studied on applications of image processing for self-replicating patterns. After establishing the representation matrices of 2D CA, these linear CA rules are classified into groups of nine and eight types according to their boundary conditions and the number of neighboring cells influencing the cells under consideration. All linear rules have been found to be rendering multiple self-replicating copies of a given image depending on these types. Multiple copies of any arbitrary image corresponding to CA find innumerable applications in real life situation, e.g. textile design, DNA genetics research, statistical physics, molecular self-assembly and artificial life, etc. We conclude by presenting a successful application for generating pseudo numbers to be used in cryptography by hybridization of these 2D CA subfamilies.

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Slavova, Angela. "Dynamic properties of cellular neural networks." Journal of Applied Mathematics and Stochastic Analysis 6, no. 2 (January 1, 1993): 107–16. http://dx.doi.org/10.1155/s1048953393000103.

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Dynamic behavior of a new class of information-processing systems called Cellular Neural Networks is investigated. In this paper we introduce a small parameter in the state equation of a cellular neural network and we seek for periodic phenomena. New approach is used for proving stability of a cellular neural network by constructing Lyapunov's majorizing equations. This algorithm is helpful for finding a map from initial continuous state space of a cellular neural network into discrete output. A comparison between cellular neural networks and cellular automata is made.

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Zhao, Ruifeng, Yue Zhai, Lu Qu, Ruhao Wang, Yaoying Huang, and Qi Dong. "A continuous floor field cellular automata model with interaction area for crowd evacuation." Physica A: Statistical Mechanics and its Applications 575 (August 2021): 126049. http://dx.doi.org/10.1016/j.physa.2021.126049.

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Wani, Shahi, and Fasel Qadir. "Cellular Automata Based Study of Spectral Signatures of Dal_Lake Infrared Imagery." Oriental journal of computer science and technology 10, no. 2 (May 18, 2017): 276–81. http://dx.doi.org/10.13005/ojcst/10.02.04.

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Among all the water bodies in Jammu & Kashmir Dal Lake has a peculiar significance due to its location in the heart of the capital city Srinagar. Historical studies over last fifteen hundred years indicate a continuous squeezing of the Lake due to different natural and manmade interventions. Over this long period, the governance of the land has passed through various wise and ugly human plans besides some slow natural processes. The mathematical modelling of such a dynamics is not an easy task because of the many intervening variables and the difficulty which implies their measurements. On the other hand, during the last decades, the use of Cellular Automata (CA) techniques to simulate the behaviour of linear or non-linear systems is becoming of great interest. This fact is mainly due to the fact that this approach depends largely on local relations and a series of rules instead of precise mathematical formulae. The infrared (IR) satellite imagery can be helpful in identifying the different areas of interest using CA as a tool of image processing. The study will not only separate the areas of interest but also pave a way towards a comprehensive study of all the identified zones using spectral signatures received from the continuous IR imagery of both pre-monsoon and post-monsoon periods in future.

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Kuc, D., and J. Gawąd. "Modelling of Microstructure Changes During Hot Deformation Using Cellular Automata." Archives of Metallurgy and Materials 56, no. 2 (June 1, 2011): 523–32. http://dx.doi.org/10.2478/v10172-011-0056-2.

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Modelling of Microstructure Changes During Hot Deformation Using Cellular AutomataThe paper is focused on an application of the cellular automata (CA) method to description of microstructure changes in continuous deformation condition. The model approach consists of Cellular Automata model of microstructure development and the thermal-mechanical finite element (FE) code. Dynamic recrystallization phenomenon is taken into account in 2D CA model which takes advantage of explicit representation of microstructure, including individual grains and grain boundaries. Flow stress is the main material parameter in mechanical part of FE and is calculated on the basis of average dislocation density obtained from the CA model. The results obtained from the model were validated with the experimental data. In the present study, austenitic steel X3CrNi18-10 was investigated. The examination of microstructure for the initial and final microstructures was carried out, using light microscopy, transmission electron microscopy and EBSD technique. Compression forces were recorded during the tests and flow stresses were determined using the inverse method.

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MAES, CHRISTIAN. "COUPLING INTERACTING PARTICLE SYSTEMS." Reviews in Mathematical Physics 05, no. 03 (September 1993): 457–75. http://dx.doi.org/10.1142/s0129055x93000139.

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We consider random processes (probabilistic cellular automata or interacting particle systems) defined through the interaction of an infinite number of components. We show how coupling arguments yield simple yet quite general ergodicity theorems. The relation between discrete time and continuous time versions is analyzed via similar techniques and the explicit convergence rate of discrete time approximations to the continuous time process is obtained.

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Yeldan, Öznur, Alberto Colorni, Alessandro Luè, and Emanuele Rodaro. "A Stochastic Continuous Cellular Automata Traffic Flow Model with a Multi-agent Fuzzy System." Procedia - Social and Behavioral Sciences 54 (October 2012): 1350–59. http://dx.doi.org/10.1016/j.sbspro.2012.09.849.

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Monshat, H., and S. Serajzadeh. "Simulation of austenite decomposition in continuous cooling conditions: a cellular automata-finite element modelling." Ironmaking & Steelmaking 46, no. 6 (November 30, 2017): 513–21. http://dx.doi.org/10.1080/03019233.2017.1405178.

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CHAU, H. F., HAO XU, K. M. LEE, L. W. SIU, and K. K. YAN. "FINDING THE SIGN OF A FUNCTION VALUE BY BINARY CELLULAR AUTOMATON." International Journal of Modern Physics C 13, no. 10 (December 2002): 1347–64. http://dx.doi.org/10.1142/s0129183102003929.

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Given a continuous function f(x), suppose that the sign of f has only finitely many discontinuous points in the interval [0, 1]. We show how to use a sequence of one-dimensional deterministic binary cellular automata to determine the sign of f(ρ) where ρ is the (number) density of 1s in an arbitrarily given bit string of finite length provided that f satisfies certain technical conditions.

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Zhang, Yaofeng, and Renbin Xiao. "Modeling and Simulation of Polarization in Internet Group Opinions Based on Cellular Automata." Discrete Dynamics in Nature and Society 2015 (2015): 1–15. http://dx.doi.org/10.1155/2015/140984.

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Hot events on Internet always attract many people who usually form one or several opinion camps through discussion. For the problem of polarization in Internet group opinions, we propose a new model based on Cellular Automata by considering neighbors, opinion leaders, and external influences. Simulation results show the following: (1) It is easy to form the polarization for both continuous opinions and discrete opinions when we only consider neighbors influence, and continuous opinions are more effective in speeding the polarization of group. (2) Coevolution mechanism takes more time to make the system stable, and the global coupling mechanism leads the system to consensus. (3) Opinion leaders play an important role in the development of consensus in Internet group opinions. However, both taking the opinion leaders as zealots and taking some randomly selected individuals as zealots are not conductive to the consensus. (4) Double opinion leaders with consistent opinions will accelerate the formation of group consensus, but the opposite opinions will lead to group polarization. (5) Only small external influences can change the evolutionary direction of Internet group opinions.

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Uguz, Selman, Ecem Acar, and Shovkat Redjepov. "2D Triangular von Neumann Cellular Automata with Periodic Boundary." International Journal of Bifurcation and Chaos 29, no. 03 (March 2019): 1950029. http://dx.doi.org/10.1142/s0218127419500299.

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Cellular automata (CA) theory is a very rich and useful model of a discrete dynamical system that focuses on their local information relying on the neighboring cells to produce CA global behaviors. Although the main structure of CA is a discrete special model, the global behaviors at many iterative times and on big scales can be close to nearly a continuous system. The mathematical points of the basic model imply the computable values of the mathematical structure of CA. After modeling the CA structure, an important problem is to be able to move forwards and backwards on CA to understand their behaviors in more elegant ways. This happens in the possible case if CA is a reversible one. In this paper, we investigate the structure and the reversibility cases of two-dimensional (2D) finite, linear, and triangular von Neumann CA with periodic boundary case. It is considered on ternary field [Formula: see text] (i.e. 3-state). We obtain the transition rule matrices for each special case. It is known that the reversibility cases of 2D CA is generally a very challenging problem. For given special triangular information (transition) rule matrices, we prove which triangular linear 2D von Neumann CA is reversible or not. In other words, the reversibility problem of 2D triangular, linear von Neumann CA with periodic boundary is resolved completely over ternary field. However, the general transition rule matrices are also presented to establish the reversibility cases of these special 3-states CA. Since the main CA structures are sufficiently simple to investigate in mathematical ways and also very complex for obtaining chaotic models, we believe that these new types of CA can be found in many different real life applications in special cases e.g. mathematical modeling, theoretical biology and chemistry, DNA research, image science, textile design, etc. in the near future.

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DE JONG, HANS, and CHRISTIAN MAES. "EXTENDED APPLICATION OF CONSTRUCTIVE CRITERIA FOR ERGODICITY OF INTERACTING PARTICLE SYSTEMS." International Journal of Modern Physics C 07, no. 01 (February 1996): 1–18. http://dx.doi.org/10.1142/s0129183196000028.

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We discuss computational aspects of verifying constructive criteria for ergodicity of interacting particle systems. Both discrete time (probabilistic cellular automata) and continuous time spin flip dynamics are considered. We also investigate how the criteria have to be adapted if stirring is added to the dynamics.

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Jamal, Ade. "A Continuous Topography Approach for Agent Based Traffic Simulation, Lane Changing Model." JURNAL Al-AZHAR INDONESIA SERI SAINS DAN TEKNOLOGI 2, no. 1 (June 19, 2014): 35. http://dx.doi.org/10.36722/sst.v2i1.96.

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Traffic simulation has been being an interesting research subject for transport engineer and scientist, mathematicians and informatics scientist for different point of view. Transport scientists study the traffic complexity and behaviour of traffic participants by using statistical experiment or simulation. The earlier approach was based on macroscopic model deducted from hydrodynamics kinematic wave analogy. Later on the microscopic model was introduced first by invoking cellular automata and then agent based model takes important role in the traffic simulation world. Most of microscopic model are based on a multi-grid element topography model which is a natural environment of cellular automata. Just recently a software engineer started an ambitious work to develop a multipurpose framework for complex traffic simulation. The ingenious idea is to replace the traditional grid based element topography with a continuous two dimensional one from which a region of traffic road or street is built up. Traffic participant is modelled as agent whose physical properties such as its coordinate position, speed, and direction are governed by the kinematic Newtonian law. This article will present this new concept and show how the simple movement of lane changing model that is very well known from the beginning era of traffic simulation become a quite complex movement in the new continuous topography

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Bloomfield, J. M., J. A. Sherratt, K. J. Painter, and G. Landini. "Cellular automata and integrodifferential equation models for cell renewal in mosaic tissues." Journal of The Royal Society Interface 7, no. 52 (April 7, 2010): 1525–35. http://dx.doi.org/10.1098/rsif.2010.0071.

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Mosaic tissues are composed of two or more genetically distinct cell types. They occur naturally, and are also a useful experimental method for exploring tissue growth and maintenance. By marking the different cell types, one can study the patterns formed by proliferation, renewal and migration. Here, we present mathematical modelling suggesting that small changes in the type of interaction that cells have with their local cellular environment can lead to very different outcomes for the composition of mosaics. In cell renewal, proliferation of each cell type may depend linearly or nonlinearly on the local proportion of cells of that type, and these two possibilities produce very different patterns. We study two variations of a cellular automaton model based on simple rules for renewal. We then propose an integrodifferential equation model, and again consider two different forms of cellular interaction. The results of the continuous and cellular automata models are qualitatively the same, and we observe that changes in local environment interaction affect the dynamics for both. Furthermore, we demonstrate that the models reproduce some of the patterns seen in actual mosaic tissues. In particular, our results suggest that the differing patterns seen in organ parenchymas may be driven purely by the process of cell replacement under different interaction scenarios.

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Shumylyak, L. M., V. V. Zhykharevych, and S. E. Ostapov. "MODELING OF IMPURITIES SEGREGATION PHENOMENON IN THE MELT CRYSTALLIZATION PROCESS BY CONTINUOUS CELLULAR AUTOMATA METHOD." Prikladnaya diskretnaya matematika, no. 31(1) (March 1, 2016): 104–18. http://dx.doi.org/10.17223/20710410/31/10.

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Afshar, M. H., and M. Rohani. "Optimal design of sewer networks using cellular automata-based hybrid methods: Discrete and continuous approaches." Engineering Optimization 44, no. 1 (January 2012): 1–22. http://dx.doi.org/10.1080/0305215x.2011.557071.

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Rezvankhah, Mohamad Amin, Mohsen Shayan, Amir Reza Merati, and Mohsen Pahlevani. "Step flow model in continuous cellular automata method for simulation of anisotropic etching of silicon." Journal of Micro/Nanolithography, MEMS, and MOEMS 12, no. 2 (April 26, 2013): 023004. http://dx.doi.org/10.1117/1.jmm.12.2.023004.

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SANCHEZ, JUAN R. "COMPLEX BEHAVIOR OF FUZZY LOGISTIC RULE 90 AUTOMATON." International Journal of Modern Physics C 16, no. 09 (September 2005): 1449–59. http://dx.doi.org/10.1142/s0129183105008047.

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A dynamical system falling in between the elementary binary cellular automata and the coupled map lattices is presented. It is composed by a one-dimensional cellular automaton in which the values within each cell are continuous instead of discrete. However, in this case, the coupling between cells is made through a logistic map instead of making the fuzzification of the disjunctive normal form describing the corresponding Boolean rule. The system resembles the CA rule 90 evolution, since the future value of a cell depends only on a combination of the values of the nearest neighbors cells. The basic dynamical and stability properties of the system are analyzed. The system displays different types from attractors (fixed points, cycles and chaotic attractors), depending on the growth rate parameter used for the logistic map coupling. If the cell values are binary, i.e., only values 0 and 1 are allowed within each cell, the dynamical evolution of the rule 90 automaton is recovered.

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Kitakawa, A. "On a segregation intensity parameter in continuous-velocity lattice gas cellular automata for immiscible binary fluid." Chemical Engineering Science 59, no. 14 (July 2004): 3007–12. http://dx.doi.org/10.1016/j.ces.2004.04.032.

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Shumylyak, Liliya, Vladimir Zhikharevich, and Sergiy Ostapov. "Modeling of impurities segregation phenomenon in the melt crystallization process by the continuous cellular automata technique." Applied Mathematics and Computation 290 (November 2016): 336–54. http://dx.doi.org/10.1016/j.amc.2016.06.012.

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Liu, Lei, Yunxin Wu, and Abdulrahaman Shuaibu Ahmad. "A novel simulation of continuous dynamic recrystallization process for 2219 aluminium alloy using cellular automata technique." Materials Science and Engineering: A 815 (May 2021): 141256. http://dx.doi.org/10.1016/j.msea.2021.141256.

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Sahin, Uḡur, Selman Uguz, and Hasan Akin. "The Transition Rules of 2D Linear Cellular Automata Over Ternary Field and Self-Replicating Patterns." International Journal of Bifurcation and Chaos 25, no. 01 (January 2015): 1550011. http://dx.doi.org/10.1142/s021812741550011x.

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In this paper we start with two-dimensional (2D) linear cellular automata (CA) in relation with basic mathematical structure. We investigate uniform linear 2D CA over ternary field, i.e. ℤ3. Present work is related to theoretical and imaginary investigations of 2D linear CA. Even though the basic construction of a CA is a discrete model, its macroscopic level behavior at large times and on large scales could be a close approximation to a continuous system. Considering some statistical properties, someone may also study geometrical aspects of patterns generated by cellular automaton evolution. After iteratively applying the linear rules, CA have been shown capable of producing interesting complex behaviors. Some examples of CA produce remarkably regular behavior on finite configurations. Using some simple initial configurations, the produced pattern can be self-replicating regarding some linear rules. Here we deal with the theory 2D uniform periodic, adiabatic and reflexive boundary CA (2D PB, AB and RB) over the ternary field ℤ3and the applications of image processing for patterns generation. From the visual appearance of the patterns, it is seen that some rules display sensitive dependence on boundary conditions and their rule numbers.

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Journal articles on the topic 'Continuous cellular automata'

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