Results 1  10
of
171
Algebraic Properties of Cellular Automata
, 1984
"... This paper details and extends the discussion of global proper72 L a T E X filename: Algebraic.tex (Paper: 1.2 [2]) 12:08 p.m. October 20, 1993 Algebraic Properties of Cellular Automata (1984) Figure 2. Global state transition diagrams for finite cellular automata with size N and periodic boundary c ..."
Abstract

Cited by 58 (1 self)
 Add to MetaCart
This paper details and extends the discussion of global proper72 L a T E X filename: Algebraic.tex (Paper: 1.2 [2]) 12:08 p.m. October 20, 1993 Algebraic Properties of Cellular Automata (1984) Figure 2. Global state transition diagrams for finite cellular automata with size N and periodic boundary conditions evolving according to the rule Ö(x) = x + x
Evolutionary games on graphs
, 2007
"... Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to ..."
Abstract

Cited by 54 (0 self)
 Add to MetaCart
Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in nonequilibrium statistical physics. This review gives a tutorialtype overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by nonmeanfieldtype social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner’s Dilemma, the Rock–Scissors–Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
Nonequilibrium critical phenomena and phase transitions into absorbing states
 ADVANCES IN PHYSICS
, 2000
"... ..."
Turbulent Pattern Bases for Cellular Automata
 Physica D
, 1993
"... Unpredictable patterns generated by cellular automata (CA) can be decomposed with respect to a turbulent, positive entropy rate pattern basis. The resulting filtered patterns uncover significant structural organization in a CA's dynamics and information processing capabilities. We illustrate the dec ..."
Abstract

Cited by 46 (14 self)
 Add to MetaCart
Unpredictable patterns generated by cellular automata (CA) can be decomposed with respect to a turbulent, positive entropy rate pattern basis. The resulting filtered patterns uncover significant structural organization in a CA's dynamics and information processing capabilities. We illustrate the decomposition technique by analyzing a binary, range2 cellular automaton having two invariant chaotic domains of different complexities and entropies. Once identified, the domains are seen to organize the CA's state space and to dominate its evolution. Starting from the domains' structures, we show how to construct a finitestate transducer that performs nonlinear spatial filtering such that the resulting spacetime patterns reveal the domains and the intervening walls and dislocations. To show the statistical consequences of domain detection, we compare the entropy and complexity densities of each domain with the globally averaged quantities. A more graphical comparison uses difference patter...
Classifying Cellular Automata Automatically; Finding gliders, filtering, and relating spacetime patterns, attractor basins, and the Z parameter
 Complexity
, 1998
"... CA rules can be classied automatically for a spectrum of ordered, complex and chaotic dynamics, by a measure of the variance of inputentropy over time. Rules that support interacting gliders and related complex dynamics can be identied, giving an unlimited source for further study. The distribution ..."
Abstract

Cited by 45 (3 self)
 Add to MetaCart
CA rules can be classied automatically for a spectrum of ordered, complex and chaotic dynamics, by a measure of the variance of inputentropy over time. Rules that support interacting gliders and related complex dynamics can be identied, giving an unlimited source for further study. The distribution of rule classes in rulespace can be shown. A byproduct of the method allows the automatic \ltering" of CA spacetime patterns to show up gliders and related emergent congurations more clearly. The classication seems to correspond to our subjective judgment of spacetime dynamics. There are also approximate correlations with global measures on convergence in attractor basins, characterized by the distribution of indegree sizes in their branching structure, and to the rule parameter, Z. Based on computer experiments using the software Discrete Dynamics Lab (DDLab)[22], this paper explains the methods and presents results for 1d CA. 1 Introduction Cellular automata (CA) are a much stud...
Computation in cellular automata: A selected review
 Nonstandard Computation
, 1996
"... Cellular automata (CAs) are decentralized spatially extended systems consisting of large numbers of simple identical components with local connectivity. Such systems have the potential to perform complex computations with a high degree of efficiency and robustness, as well as to model the behavior o ..."
Abstract

Cited by 36 (2 self)
 Add to MetaCart
Cellular automata (CAs) are decentralized spatially extended systems consisting of large numbers of simple identical components with local connectivity. Such systems have the potential to perform complex computations with a high degree of efficiency and robustness, as well as to model the behavior of complex systems in nature. For these reasons CAs and related architectures have
Transition Phenomena in Cellular Automata Rule Space
 Physica D
, 1990
"... We define several qualitative classes of cellular automata (CA) behavior, based on various statistical measures, and describe how the space of all cellular automata is organized. As a cellular automaton... ..."
Abstract

Cited by 30 (7 self)
 Add to MetaCart
We define several qualitative classes of cellular automata (CA) behavior, based on various statistical measures, and describe how the space of all cellular automata is organized. As a cellular automaton...
The Structure of the Elementary Cellular Automata Rule Space
 Complex Systems
, 1990
"... The structure of the elementary cellular automata rule space is investigated. The probabilities for a rule to be connected to other rules in the same class #intraclass#, as well as rules in di#erent classes #interclass#, are determined. The intraclass connection probabilities vary from around ..."
Abstract

Cited by 28 (6 self)
 Add to MetaCart
The structure of the elementary cellular automata rule space is investigated. The probabilities for a rule to be connected to other rules in the same class #intraclass#, as well as rules in di#erent classes #interclass#, are determined. The intraclass connection probabilities vary from around 0.3 to 0.5, an indication of the strong tendency for rules with the similar behavior to be next to each other. Rules are also grouped according to the mean #eld descriptions. The mean#eld clusters are classi#ed into three classes #nonlinear, linear, and inversely linear# according to the #hot bits" in the rule table. It is shown that such classi#cation provides another easy way to describe the rule space.
Coevolving NonUniform Cellular Automata to Perform Computations
, 1996
"... A major impediment of cellular automata (CA) stems from the difficulty of utilizing their complex behavior to perform useful computations. Recent studies by [ Packard, 1988, Mitchell et al., 1994b ] have shown that CAs can be evolved to perform a computational task. In this paper nonuniform CAs are ..."
Abstract

Cited by 25 (5 self)
 Add to MetaCart
A major impediment of cellular automata (CA) stems from the difficulty of utilizing their complex behavior to perform useful computations. Recent studies by [ Packard, 1988, Mitchell et al., 1994b ] have shown that CAs can be evolved to perform a computational task. In this paper nonuniform CAs are studied, where each cell may contain a different rule, in contrast to the original, uniform model. We describe experiments in which nonuniform CAs are evolved to perform the computational task using a local, coevolutionary algorithm. For radius r = 3 we attain peak performance values of 0:92 comparable to those obtained for uniform CAs (0:93 \Gamma 0:95). This is notable considering the huge search spaces involved, much larger than the uniform case. Smaller radius CAs (previously unstudied in this context) attain performance values of 0:93 \Gamma 0:94. For r = 1 this is considerably higher than the maximal possible uniform CA performance of 0:83, suggesting that nonuniformity reduces con...