## A Survey on Cellular Automata (2003)

Citations: | 18 - 0 self |

### BibTeX

@TECHREPORT{Ganguly03asurvey,

author = {Niloy Ganguly and Biplab K Sikdar and Andreas Deutsch and Geoffrey Canright and P Pal Chaudhuri},

title = {A Survey on Cellular Automata},

institution = {},

year = {2003}

}

### OpenURL

### Abstract

A cellular automaton is a decentralized computing model providing an excellent platform for performing complex computation with the help of only local information. Researchers, scientists and practitioners from different fields have exploited the CA paradigm of local information, decentralized control and universal computation for modeling different applications. This article provides a survey of available literature of some of the methodologies employed by researchers to utilize cellular automata for modeling purposes. The survey introduces the different types of cellular automata being used for modeling and the analytical methods used to predict its global behavior from its local configurations. It further gives a detailed sketch of the efforts undertaken to configure the local settings of CA from a given global situation; the problem which has been traditionally termed as the inverse problem. Finally, it presents the different fields in which CA have been applied. The extensive bibliography provided with the article will be of help to the new entrant as well as researchers working in this field.

### Citations

3030 | Graph-based algorithms for boolean function manipulation
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(Show Context)
Citation Context ...ashing [94], classification [187], designing easy and fully testable F SM [55], authentication [75] etc. Chattopadhyay et al. presented some interesting results showing that boolean decision diagrams =-=[28]-=- can be used for efficient characterization of non-group CA [43], [44]. Ganguly et. al. [90] showed that MACA - a special class of non-group CA - model a hash family termed as hamming hash family for ... |

3009 |
Genetic programming: On the programming of computers by the means of natural selection
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(Show Context)
Citation Context ...ules are based on evolutionary computation techniques namely genetic algorithms and simulated annealing. The initial work on CA evolution was reported by Packard and his colleagues [179], [194]. Koza =-=[126]-=- also applied genetic algorithms to generate simple random numbers. The first major publication responsible for making genetic algorithms a popular tool for evolving CA was due to Mitchell et al. [149... |

1660 |
Neural networks and physical systems with emergent collective computational abilities
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Citation Context ...ermined by some external control. She has also 16snoted several open problems regarding CA based simulation of different types of languages. The advent of neural net with the seminal work of Hopfield =-=[108]-=-, [109] popularized the use of machine intelligence techniques in recognizing patterns. However, the inherent dense structure of neural networks is not suitable for V LSI implementation. So, researche... |

768 |
The Evolution of Cooperation. Basic
- Axelrod
- 1984
(Show Context)
Citation Context ...els have been used more frequently in behavioral and social sciences. In economics, Keenan and O’Brien [124] introduced a one-dimensional CA to model and analyze pricing in a spatial setting. Axelrod =-=[13]-=- made the first step in analyzing the dynamics of cooperation within a CA framework. Nowak and May developed the idea and studied the dynamics of cooperation using a two-dimensional CA with two-person... |

652 |
Handbook of Stochastic Methods
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(Show Context)
Citation Context ...used for analysis of global behavior. The Chapman Kolmogorav Equation which is derived by using the concept of stationary Markov-chain predicts the probability distribution of CA states from CA rules =-=[95]-=-. Moreover, mean field approximation, which is based upon the assumption that at any time the states of sites are independent of states of other sites in the lattice [209], [256] has been recently use... |

540 | 2002 A new kind of science
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(Show Context)
Citation Context ...esearchers working in this field. I. Introduction From the days of Von Neumann and Ulam who first proposed the concept of cellular automata (CA), to the recent book of Wolfram ‘A New Kind of Science’ =-=[262]-=-, the simple structure of CA has attracted researchers from various disciplines. It has been subjected to rigorous mathematical and physical analysis for the last fifty years and its application has b... |

473 |
Growing Artificial Societies: Social Science from the Bottom Up
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Citation Context ...Messick and Liebrand who analyzed the dynamics of three different decision principles [132], [143]. A substantial number of artificial societies described in Epstein and Axtell are based on CA models =-=[84]-=-. Gaylord and D’Andra developed a toolkit for CA based modeling of social dynamics using MATHEMATICA [98]. Oomes used CA to model the effect of economic inequality in emerging markets [103]. Cellular ... |

401 |
Dynamic Models of Segregation
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(Show Context)
Citation Context ...in his unpublished dissertation of 1949. The central goal of his model was to understand group formation. Another early example of CA based modeling was provided by Thomas Schelling. Schelling [203], =-=[204]-=- analyzed segregation processes among individuals belonging to two different classes : black and white. Neither Sakoda nor Schelling ever referred to CA. The formal concept of CA was obviously not kno... |

245 |
Cellular neural networks: theory
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- 1988
(Show Context)
Citation Context ...rse network structure of cellular automata for relevant applications. The hybridization of cellularity and neural network has given rise to the popular concept of cellular neural networks [12], [57], =-=[58]-=-. There are some earlier theoretical works by CA researchers which have not directly dealt with pattern recognition, but gave important insights in developing the pattern recognition applications. Not... |

236 |
Universality and complexity in cellular automata
- Wolfram
- 1984
(Show Context)
Citation Context ...re termed as Von Neumann and Moore neighborhood, respectively. There are extended generalizations of these two neighborhoods configurations - the Rradial and R-axial neighborhoods respectively [100], =-=[257]-=-, [268]. (For both Von Neumann and Moore neighborhood, R = 1.) Because of its inherent simplicity, the one-dimensional CA with two states per cell became the most studied variant of CA [256]. The neig... |

236 |
Theory and Applications of Cellular Automata
- Wolfram
- 1986
(Show Context)
Citation Context ... function. On the other hand, the machine (CA) becomes as complex as the function it tries to simulate. This very theoretical dichotomy has since driven research on CA [17], [29], [46], [129], [149], =-=[259]-=-, [261]. Based on the theoretical concept of universality, researchers have tried to develop simpler and more practical architectures of CA which can be used to model widely divergent application area... |

229 |
Statistical mechanics of cellular automata
- Wolfram
- 1983
(Show Context)
Citation Context ...ly [100], [257], [268]. (For both Von Neumann and Moore neighborhood, R = 1.) Because of its inherent simplicity, the one-dimensional CA with two states per cell became the most studied variant of CA =-=[256]-=-. The neighborhood generally varies from three [46] to five [131] or seven cells [149]. In another type of CA, the states are assumed to be a string of elements in a Galois field GF(q), where q is the... |

189 |
Pattern recognition computation using action potential timing for stimulus representation. Nature, 376:33--36
- Hopfield
- 1995
(Show Context)
Citation Context ... by some external control. She has also 16snoted several open problems regarding CA based simulation of different types of languages. The advent of neural net with the seminal work of Hopfield [108], =-=[109]-=- popularized the use of machine intelligence techniques in recognizing patterns. However, the inherent dense structure of neural networks is not suitable for V LSI implementation. So, researchers in t... |

175 |
The fantastic combinations of John Conway's new solitaire game \life
- Gardner
- 1970
(Show Context)
Citation Context ...el widely divergent application areas. In this respect, two notable developments can be credited to Conway and Wolfram. In the 1970, the mathematician John Conway proposed his now famous game of life =-=[96]-=- which received widespread interest among researchers. In the beginning of the eighties, Stephen Wolfram has studied in much detail a family of simple one-dimensional cellular automata rules (now famo... |

170 |
Cellular Automata Machines: a New Environment for Modeling, the
- Toffoli, Margolus
- 1987
(Show Context)
Citation Context ... These CAMs operate in autonomous mode. The structure of such machines having a high degree of parallelism (with local and uniform interconnection) is ideally suited for simulation of complex systems =-=[242]-=-. A CAM can achieve simulation performance of at least several orders of magnitude higher than that can be achieved with a conventional computer at comparable cost. CAMs were developed as a result of ... |

160 |
Cellular Automata Modeling of Physical Systems
- Chopard, Droz
- 1998
(Show Context)
Citation Context ...ing to the design requirements of the applications. Also there are some standard rule sets which have been used across different applications - Wolfram rules [259], linear rules [46], diffusion rules =-=[49]-=- etc. The next state, in almost all cases, depends upon the output of the previous state. However, there are some time-dependent rules, for example in the problem of directed percolation Chopard and D... |

156 |
Cellular Automata and Complexity
- Wolfram
- 1994
(Show Context)
Citation Context ...on. On the other hand, the machine (CA) becomes as complex as the function it tries to simulate. This very theoretical dichotomy has since driven research on CA [17], [29], [46], [129], [149], [259], =-=[261]-=-. Based on the theoretical concept of universality, researchers have tried to develop simpler and more practical architectures of CA which can be used to model widely divergent application areas. In t... |

154 |
Life at the edge of chaos
- Langton
- 1991
(Show Context)
Citation Context ... emergent global behavior based upon the rule configuration of the CA cells for non-linear CA is provided next. The most important parameter derived out of the rule structure is Langton’s λ parameter =-=[130]-=-. If the CA consists of two states 0 and 1, then the λ parameter is defined as the probability that a particular CA cell will have its next state as 1, that is, it indicates the fraction of 1’s in the... |

126 |
Self-reproduction in cellular automata
- Langton
- 1984
(Show Context)
Citation Context ... any arbitrary function. On the other hand, the machine (CA) becomes as complex as the function it tries to simulate. This very theoretical dichotomy has since driven research on CA [17], [29], [46], =-=[129]-=-, [149], [259], [261]. Based on the theoretical concept of universality, researchers have tried to develop simpler and more practical architectures of CA which can be used to model widely divergent ap... |

121 |
CeZIular Automata
- CODD
- 1968
(Show Context)
Citation Context ...CA have been proposed to ease the design and behavioral analysis of the CA as well as make it versatile for modeling purposes. The CA structure introduced by Von Neumann uses 29 states per cell. Codd =-=[59]-=- introduced a machine with 8 states per cell. Arbib provided a simple description of self-reproducing CA in [8], whereas Banks worked with a CA having 4 states per cell [18]. All these two-dimensional... |

97 | The evolution of emergent computation
- Mitchell, Crutchfield
- 1994
(Show Context)
Citation Context ...has been refined and reaffirmed by a series of works on Density Classification 1 and Synchronization 2 by their group - the EVCA (evolutionary algorithm cellular automata) group of Santa Fe Institute =-=[64]-=-, [73], [74]. The sampling error which arises from random selection of an initial configuration often reduces efficiency of the evolutionary process. In order to circumvent this, Paredis [181] propose... |

92 |
Cellular neural networks: Applications
- Chua, Yang
- 1988
(Show Context)
Citation Context ...he sparse network structure of cellular automata for relevant applications. The hybridization of cellularity and neural network has given rise to the popular concept of cellular neural networks [12], =-=[57]-=-, [58]. There are some earlier theoretical works by CA researchers which have not directly dealt with pattern recognition, but gave important insights in developing the pattern recognition application... |

89 |
Turtles, Termites, and Traffic Jams
- Resnick
- 1994
(Show Context)
Citation Context ...ection [199], on developing CA models of Tumor Development [155], and on detecting genetic disorders of cancerous cells [152], [153]. In ecology, it has been used to model the predator-prey ecosystem =-=[193]-=-, to detect the nature of fish migration in rivers [207], and to model the growth of vegetable population [16], [269]. The chemotaxis CA modeled by Resnik [193] has been used to determine the random w... |

81 |
Toward a quantitative theory of self-generated complexity
- Grassberger
(Show Context)
Citation Context ... been to study the CA dynamics as it evolves in successive time steps. A detailed analysis of CA dynamics enables us to understand the emergent behavior and computational capacity of the system [65], =-=[102]-=-. CA classification based on the study of its dynamics has been a major focus for the researchers. Borrowing concepts from the field of continuous dynamical systems, W olfram [257] first classified CA... |

77 |
Essays on Cellular Automata
- Burks
- 1968
(Show Context)
Citation Context ... to simulate any arbitrary function. On the other hand, the machine (CA) becomes as complex as the function it tries to simulate. This very theoretical dichotomy has since driven research on CA [17], =-=[29]-=-, [46], [129], [149], [259], [261]. Based on the theoretical concept of universality, researchers have tried to develop simpler and more practical architectures of CA which can be used to model widely... |

74 |
Adaptation toward the edge of chaos
- Packard
- 1988
(Show Context)
Citation Context ...ed to characterize CA dynamics. It has been shown by Langton that with the increase of the λ value, the CA changes from ‘order to chaos’. There have been several interesting works and polemics [149], =-=[179]-=- regarding the critical value of λ, termed as λc - the value of λ around which the CA behavior changes from ‘order’ to ‘chaos’ [130]. Besides λ, several other local parameters have been proposed. Nota... |

65 |
Evolution of Parallel Cellular Machines, The Cellular Programming Approach
- Sipper
- 1997
(Show Context)
Citation Context ...ps. 9sthe genetic algorithms. In light of these problems, parallel genetic algorithms have been proposed for CA evolution [32]. Specifically, Sipper proposed schemes for evolution of hybrid CA [228], =-=[229]-=-. The cellular algorithm proposed by Sipper presented a novel technique of optimization by assigning fitness to each individual cell. Similar cellular programming schemes are also proposed in [238], [... |

63 | A Summary of Research on Parallel Genetic Algorithms
- Cantú-Paz
- 1995
(Show Context)
Citation Context ... time steps that oscillates between all 0’s and all 1’s in successive time steps. 9sthe genetic algorithms. In light of these problems, parallel genetic algorithms have been proposed for CA evolution =-=[32]-=-. Specifically, Sipper proposed schemes for evolution of hybrid CA [228], [229]. The cellular algorithm proposed by Sipper presented a novel technique of optimization by assigning fitness to each indi... |

61 |
The spatial dilemmas of evolution
- May, Nowak
- 1993
(Show Context)
Citation Context ... which provide insights into the synchronization problems - for example, the firing squad [151], firing mob [66], and queen bee [232]. A CA simulation of the famous game of iterated prisoners dilemma =-=[173]-=-, [210] has also been proposed. B. CA as Parallel Computing Machine In machine design, the application of CA was proposed for building parallel multipliers [11], [60], prime number sieves [85], parall... |

59 |
Decision procedures for surjectivity and injectivity of parallel maps for tesselation structures
- Amoroso, Patt
- 1972
(Show Context)
Citation Context ...th reference to the ‘Garden of Eden’ (that is, non-reachable states), attractor basins, entropy of the evolved patterns etc. Investigation based on ‘Garden of Eden’ states was initiated in the 1970’s =-=[7]-=-, [162]; further developments in this direction are described in [121], [122]. Kaneko [119] introduced an information theoretic approach to characterize the complexity of ‘Garden of Eden’ states in te... |

58 | Evolving globally synchronized cellular automata
- Das, Crutchfield, et al.
- 1995
(Show Context)
Citation Context ...en refined and reaffirmed by a series of works on Density Classification 1 and Synchronization 2 by their group - the EVCA (evolutionary algorithm cellular automata) group of Santa Fe Institute [64], =-=[73]-=-, [74]. The sampling error which arises from random selection of an initial configuration often reduces efficiency of the evolutionary process. In order to circumvent this, Paredis [181] proposed the ... |

57 | Algebraic Properties of Cellular Automata
- Martine, Odlyzko
- 1984
(Show Context)
Citation Context ...ries from three [46] to five [131] or seven cells [149]. In another type of CA, the states are assumed to be a string of elements in a Galois field GF(q), where q is the number of states of a CA cell =-=[140]-=- . Additive and linear CA gained popularity in the V LSI era, due to local interaction of simple cells, each having two states ‘0’ or ‘1’ - the elements of the field GF(2). The next state logic of lin... |

54 | Evolving cellular automata with genetic algorithms: A review of recent work
- Mitchell, Crutchfield, et al.
- 1996
(Show Context)
Citation Context ... the local rules/initial conditions from a given prescribed global behavior. Good historical overviews highlighting works to achieve this basic goal up to the late 1990s are available in [46], [147], =-=[148]-=-, [200], [232], [253]. In line with such surveys, we outline a concise up-to-date survey of the theory and applications of this computing model in different disciplines. We try to bring out the rich d... |

54 |
Cellular Automata as an Alternative to (Rather than an Approximation of
- Toffoli
- 1984
(Show Context)
Citation Context ...ogists. C. CA For Modeling Physical and Biological Systems It is from the physicists the drive for developing cellular automata as an alternative to differential equations in modeling laws of physics =-=[241]-=-, [174] began. This has resulted in investigation of CA models 12sfor physical systems with an emphasis on spin systems [63], [134], [188], [252], models for various forms of regular, dendritic, and r... |

53 |
Simulating physics with cellular automata
- Vichniac
(Show Context)
Citation Context ... to differential equations in modeling laws of physics [241], [174] began. This has resulted in investigation of CA models 12sfor physical systems with an emphasis on spin systems [63], [134], [188], =-=[252]-=-, models for various forms of regular, dendritic, and random growth based on two-dimensional CA [178], models for pattern formation in reaction-diffusion systems [135], [175], [255], modeling of hydro... |

50 |
A class of optimal minimum odd-weight-column SEC-DED codes IBM
- Hsiao
- 1970
(Show Context)
Citation Context ...es: Chowdhury et al. introduced the CA based error correcting codes (CAECC) [54]. The encoder/decoder circuit complexity for CAECC has been shown to be lower than that of the 15swell known Hsiao code =-=[112]-=-. The CA based single byte error correcting and double byte error detecting code proposed in [54] was found to be superior to other schemes in terms of throughput and silicon area. The scheme has been... |

49 |
Theory of Self-Reproducing Automata
- Neumann, Burks
- 1966
(Show Context)
Citation Context ...ral times produces complex patterns displaying the potential to simulate different sophisticated natural phenomena. The concept of CA was initiated in the early 1950’s by J. Von Neumann and Stan Ulam =-=[168]-=-. Von Neumann showed that a cellular automaton can be universal. He devised a CA, each cell of which has a state space of 29 states, and showed that the devised CA can execute any computable operation... |

49 | Coevolving cellular automata: Be aware of the Red Queen
- Paredis
- 1997
(Show Context)
Citation Context ...nstitute [64], [73], [74]. The sampling error which arises from random selection of an initial configuration often reduces efficiency of the evolutionary process. In order to circumvent this, Paredis =-=[181]-=- proposed the co-evolution process in which both the CA and the initial configuration (IC) are simultaneously evolved. Juille and Pollack changed the co-evolutionary setup by introducing a limit on th... |

49 | A Brief History of Cellular automata
- Sarkar
- 2000
(Show Context)
Citation Context ...cal rules/initial conditions from a given prescribed global behavior. Good historical overviews highlighting works to achieve this basic goal up to the late 1990s are available in [46], [147], [148], =-=[200]-=-, [232], [253]. In line with such surveys, we outline a concise up-to-date survey of the theory and applications of this computing model in different disciplines. We try to bring out the rich diversit... |

48 |
equicontinuity and attractors in cellular automata, Ergodic Theory and Dynamical Systems 17
- K˚urka, Languages
- 1997
(Show Context)
Citation Context ...examined a family of sparsely connected Boolean nets to characterize the CA machines. A classification of CA into five disjoint groups based on the structure of their attractors was proposed by Kurka =-=[127]-=-. Various order/chaos measures are used to globally characterize CA dynamics. The topology of CA state space has played a very important role for this analysis. For example, a characterization has bee... |

46 | Classifying cellular automata automatically: Finding gliders, filtering, and relating space-time patterns, attractor basins, and the Z parameter
- Wuensche
- 1999
(Show Context)
Citation Context ... information theoretic approach to characterize the complexity of ‘Garden of Eden’ states in terms of their volumes, stability against noise, information storage capacity etc. Recent work by Wuensche =-=[266]-=- shows that CA can be classified into ordered, complex or chaotic based on the parameters - G-Density (that is, bushiness of Garden of Eden), In-Degree Frequency etc. In order to accurately model disc... |

38 |
Symbolic dynamics of noisy chaos
- Crutchfield, Packard
- 1983
(Show Context)
Citation Context ...ch has been to study the CA dynamics as it evolves in successive time steps. A detailed analysis of CA dynamics enables us to understand the emergent behavior and computational capacity of the system =-=[65]-=-, [102]. CA classification based on the study of its dynamics has been a major focus for the researchers. Borrowing concepts from the field of continuous dynamical systems, W olfram [257] first classi... |

38 |
Reversibility and surjectivity problems of cellular automata
- Kari
- 1994
(Show Context)
Citation Context ...ctor basins, entropy of the evolved patterns etc. Investigation based on ‘Garden of Eden’ states was initiated in the 1970’s [7], [162]; further developments in this direction are described in [121], =-=[122]-=-. Kaneko [119] introduced an information theoretic approach to characterize the complexity of ‘Garden of Eden’ states in terms of their volumes, stability against noise, information storage capacity e... |

36 |
Picture Languages
- Rosenfeld
- 1979
(Show Context)
Citation Context ... sorting machines [170]. The CA 11sas a fault-tolerant computing machine has been projected in [167], [171]. Two-dimensional CA have been used extensively for image processing and pattern recognition =-=[196]-=-, [235]. The MP P (Massively Parallel Processor) of Goodyear Aerospace Corporation [81], was one of the fastest computers of the early 1980s. CA based machines termed as CAMs (CA Machines) have been d... |

35 |
Theory and Applications of Cellular Automata in Cryptography
- Nandi, Kar, et al.
- 1994
(Show Context)
Citation Context ... been further enhanced by Paul by using the concept of the extension field [183]. Design of CA based cipher system: Nandi et al. presented an elegant low cost scheme for CA based cipher system design =-=[166]-=-. Both block ciphering and stream ciphering strategies designed with programmable cellular automata (P CA) have been reported. Recently, an improved version of the cipher system has been proposed [213... |

34 |
Real-time language recognition by one-dimensional cellular automata
- Smith
- 1972
(Show Context)
Citation Context ...ge acceptor by considering initial configuration as the input string and acceptance or rejection is determined by a specific cell of the CA. It has been shown that CA can accept context-free language =-=[234]-=-, non context-free language [113], and also context-sensitive language [83]. Mahajan’s thesis work provides some exciting insights into the potential of CA to act as a language recognizer [136]. She h... |

32 |
Additive Cellular Automata: Theory and Applications
- Chaudhuri, Chowdhury, et al.
- 1997
(Show Context)
Citation Context ...mulate any arbitrary function. On the other hand, the machine (CA) becomes as complex as the function it tries to simulate. This very theoretical dichotomy has since driven research on CA [17], [29], =-=[46]-=-, [129], [149], [259], [261]. Based on the theoretical concept of universality, researchers have tried to develop simpler and more practical architectures of CA which can be used to model widely diver... |

32 |
Cellular automaton modeling of biological pattern formation
- Deutsch, Dormann
- 2005
(Show Context)
Citation Context ...equations by cellular automata as an analytical tool. Good theoretical overviews and insights highlighting the possibilities of CA replacing partial differential equations can be found in [14], [49], =-=[79]-=-, [211]. The subsequent two sections provide a sketch of the models proposed by physicists, chemists, theoretical biologists, economists and sociologists. C. CA For Modeling Physical and Biological Sy... |

32 |
Reversability of 2D cellular automata is undecidable
- Kari
- 1990
(Show Context)
Citation Context ...ls have been also studied in [117], [267]. While the next state function (rule) in general is deterministic in nature, there are variations in which the rule sets are probabilistic [22], [25], [104], =-=[121]-=-, [136], [243], or fuzzy [35], [86], [263]. The nature of next state functions also varies significantly; researchers have defined the rule set according to the design requirements of the applications... |

31 |
Modern cellular automata—Theory and applications
- Preston, Duff
- 1984
(Show Context)
Citation Context ...ted in [167], [171]. Two-dimensional CA have been used extensively for image processing and pattern recognition [196], [235]. The MP P (Massively Parallel Processor) of Goodyear Aerospace Corporation =-=[81]-=-, was one of the fastest computers of the early 1980s. CA based machines termed as CAMs (CA Machines) have been developed by Toffoli and others [240]. These CAMs operate in autonomous mode. The struct... |