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A brief history of cellular automata
, 2000
"... Cellular automata are simple models of computation which exhibit fascinatingly complex behavior. They have captured the attention of several generations of researchers, leading to an extensive body of work. Here we trace a history of cellular automata from their beginnings with von Neumann to the pr ..."
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Cited by 46 (2 self)
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Cellular automata are simple models of computation which exhibit fascinatingly complex behavior. They have captured the attention of several generations of researchers, leading to an extensive body of work. Here we trace a history of cellular automata from their beginnings with von Neumann to the present day. The emphasis is mainly on topics closer to computer science and mathematics rather than physics, biology or other applications. The work should be of interest to both new entrants into the field as well as researchers working on particular aspects of cellular automata.
Emergent Phenomena and Complexity
 Artificial Life IV. Proceedings of the Fourth International Workshop on the Synthesis and Simulation of Living Systems
, 1994
"... I seek to define rigorously the concept of an emergent phenomenon in a complex system, together with its implications for explanation, understanding and prediction in such systems. I argue that in a certain fundamental sense, emergent systems are those in which even perfect knowledge and understandi ..."
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Cited by 24 (0 self)
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I seek to define rigorously the concept of an emergent phenomenon in a complex system, together with its implications for explanation, understanding and prediction in such systems. I argue that in a certain fundamental sense, emergent systems are those in which even perfect knowledge and understanding may give us no predictive information. In them the optimal means of prediction is simulation. I investigate the consequences of this for certain decidability and complexity issues, and then explain why these limitations do not preclude all means of doing interesting science in such systems. I touch upon some recent incorporation of this work into the investigation of selforganised criticalities. 1 Motivation and Objectives The calculations were so elaborate it was very difficult. Now, usually I was the expert at this; I could always tell you what the answer was going to look like, or when I got it I could explain why. But this thing was so complicated I couldn't explai...
Cellular automata as a paradigm for ecological modelling
 Applied Mathematics and Computation
, 1988
"... We review cellular automata as a modeling formalism and discuss how it can be used for modeling (spatial) ecological processes. The implications of this modeling paradigm for ecological observation are stressed. Finally we discuss some shortcomings of the cellularautomaton formalism and mention so ..."
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Cited by 20 (3 self)
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We review cellular automata as a modeling formalism and discuss how it can be used for modeling (spatial) ecological processes. The implications of this modeling paradigm for ecological observation are stressed. Finally we discuss some shortcomings of the cellularautomaton formalism and mention some extensions and generalizations which may remedy these shortcomings. 1.
Harmonic analysis of fractal measures
 Constr. Approx
, 1996
"... Abstract. We consider affine systems in Rn constructed from a given integral invertible and expansive matrix R, and a finite set B of translates, σbx: = R−1x + b; the corresponding measure µ on Rn is a probability measure and fixed by the selfsimilarity µ = B ..."
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Cited by 18 (12 self)
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Abstract. We consider affine systems in Rn constructed from a given integral invertible and expansive matrix R, and a finite set B of translates, σbx: = R−1x + b; the corresponding measure µ on Rn is a probability measure and fixed by the selfsimilarity µ = B
Predicting nonlinear cellular automata quickly by decomposing them into linear ones
 Physica D
, 1998
"... We show that a wide variety of nonlinear cellular automata (CAs) can be decomposed into a quasidirect product of linear ones. These CAs can be predicted by parallel circuits of depthO(log 2 t) using gates with binary inputs, orO(log t) depth if “sum mod p ” gates with an unbounded number of inputs ..."
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Cited by 18 (7 self)
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We show that a wide variety of nonlinear cellular automata (CAs) can be decomposed into a quasidirect product of linear ones. These CAs can be predicted by parallel circuits of depthO(log 2 t) using gates with binary inputs, orO(log t) depth if “sum mod p ” gates with an unbounded number of inputs are allowed. Thus these CAs can be predicted by (idealized) parallel computers much faster than by explicit simulation, even though they are nonlinear. This class includes any CA whose rule, when written as an algebra, is a solvable group. We also show that CAs based on nilpotent groups can be predicted in depth O(log t) or O(1) by circuits with binary or “sum mod p ” gates respectively. We use these techniques to give an efficient algorithm for a CA rule which, like elementary CA rule 18, has diffusing defects that annihilate in pairs. This can be used to predict the motion of defects in rule 18 in O(log 2 t) parallel time. PACS Keywords: 02.10, 02.70, 05.45, 46.10 1
A Survey on Cellular Automata
, 2003
"... 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 contr ..."
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Cited by 16 (0 self)
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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.
Quasilinear Cellular Automata
 Physica D
, 1997
"... Simulating a cellular automaton (CA) for t timesteps into the future requires t 2 serial computation steps or t parallel ones. However, certain CAs based on an Abelian group, such as addition mod 2, are termed linear because they obey a principle of superposition. This allows them to be predicted e ..."
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Cited by 14 (4 self)
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Simulating a cellular automaton (CA) for t timesteps into the future requires t 2 serial computation steps or t parallel ones. However, certain CAs based on an Abelian group, such as addition mod 2, are termed linear because they obey a principle of superposition. This allows them to be predicted efficiently, in serial timeO(t) orO(log t) in parallel. In this paper, we generalize this by looking at CAs with a variety of algebraic structures, including quasigroups, nonAbelian groups, Steiner systems, and others. We show that in many cases, an efficient algorithm exists even though these CAs are not linear in the previous sense; we term them quasilinear. We find examples which can be predicted in serial time proportional to t, t log t, t log 2 t and t α for α < 2, and parallel time log t, log t log log t and log 2 t. We also discuss what algebraic properties are required or implied by the existence of scaling relations and principles of superposition, and exhibit several novel “vectorvalued ” CAs. 1 Introduction: CAs
Observing Complexity and the Complexity of Observation
, 1993
"... in nonlinear systems. Physica, 7D:16, 1983. [52] J.P. Crutchfield. Reconstructing language hierarchies. In H. A. Atmanspracher and H. Scheingraber, editors, Information Dynamics, page 45, New York, 1991. Plenum. [19] J.P. Crutchfield. Knowledge and meaning ... chaos and complexity. In L. Lam and V ..."
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Cited by 13 (3 self)
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in nonlinear systems. Physica, 7D:16, 1983. [52] J.P. Crutchfield. Reconstructing language hierarchies. In H. A. Atmanspracher and H. Scheingraber, editors, Information Dynamics, page 45, New York, 1991. Plenum. [19] J.P. Crutchfield. Knowledge and meaning ... chaos and complexity. In L. Lam and V. Naroditsky, editors, Modeling Complex Phenomena, page 66, Berlin, 1992. SpringerVerlag. [20] J.P. Crutchfield. Semantics and thermodynamics. In M. Casdagli and S. Eubank, editors, Nonlinear Modeling and Forecasting, volume XII of Santa Fe Institute Studies in the Sciences of Complexity, page 317, Reading, Massachusetts, 1992. AddisonWesley. [21] P. E. Caines. Linear Stochastic Systems. Wiley, New York, 1988. [22] B. Kitchens and S. Tuncel. Finitary measures for sub shifts of finite type and sofic systems. Memoirs' of the AMS, 58:no. 338, 1985. [23] I. P. Cornfeld, S. V. Fomin, and Ya. G. Sinai. Ergodic Theory. SpringerVerlag, Berlin, 1982. [24] J. E. Hopcroft and J. D. Ullman. Intr
An experimental study of robustness to asynchronism for elementary cellular automata
 COMPLEX SYSTEMS
, 2005
"... Cellular Automata (CA) are a class of discrete dynamical systems that have been widely used to model complex systems in which the dynamics is specified at local cellscale. Classically, CA are run on a regular lattice and with perfect synchronicity. However, these two assumptions have little chance ..."
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Cited by 8 (5 self)
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Cellular Automata (CA) are a class of discrete dynamical systems that have been widely used to model complex systems in which the dynamics is specified at local cellscale. Classically, CA are run on a regular lattice and with perfect synchronicity. However, these two assumptions have little chance to truthfully represent what happens at the microscopic scale for physical, biological or social systems. One may thus wonder whether CA do keep their behavior when submitted to small perturbations of synchronicity. This work focuses on the study of onedimensional (1D) asynchronous CA with two states and nearestneighbors. We define what we mean by “the behavior of CA is robust to asynchronism ” using a statistical approach with macroscopic parameters. and we present an experimental protocol aimed at finding which are the robust 1D elementary CA. To conclude, we examine how the results exposed can be used as a guideline for the research of suitable models according to robustness criteria.
An introduction to Cellular Automata
, 1998
"... We give basic definitions necessary to understand what are cellular automata, as well as to work with. Some efficient but sometimes problematic concepts as signal, simulation and universality, are pointed out. In particular, different notions of universality are put to light. ..."
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Cited by 7 (0 self)
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We give basic definitions necessary to understand what are cellular automata, as well as to work with. Some efficient but sometimes problematic concepts as signal, simulation and universality, are pointed out. In particular, different notions of universality are put to light.