Network View of Binary Cellular Automata

Kayama, Yoshihiko

doi:10.1007/978-3-642-33350-7_23

Cited by 4 publications

(3 citation statements)

References 13 publications

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“…Kayama and Imamura (2011) have shown the network representation of Game of Life, where the characteristics is like one of Wolfram's class IV rules. In Kayama (2012), the network derived from ECAs and five neighbor totalistic CA rules are further reviewed. However, the studies in this area are still at a very early stage.…”

Section: Automata Networkmentioning

confidence: 99%

A survey of cellular automata: types, dynamics, non-uniformity and applications

et al. 2018

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Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of several researchers over various backgrounds and fields for modelling different physical, natural as well as reallife phenomena. Classically, CAs are uniform. However, non-uniformity has also been introduced in update pattern, lattice structure, neighborhood dependency and local rule. In this survey, we tour to the various types of CAs introduced till date, the different characterization tools, the global behaviors of CAs, like universality, reversibility, dynamics etc. Special attention is given to non-uniformity in CAs and especially to non-uniform elementary CAs, which have been very useful in solving several real-life problems.

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Section: Automata Networkmentioning

confidence: 99%

A survey of cellular automata: types, dynamics, non-uniformity and applications

et al. 2018

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“…The goal of this process is to produce large stable structures by evolving rules and parameters of the building blocks. Kayama has investigated a network representation of binary cellular automata rules [12]. The goal was to focus on the effective relationships between cells rather than the states themselves.…”

Section: Introductionmentioning

confidence: 99%

Evolution of cellular automata with conditionally matching rules

Bidlo

Vašíček

2013

2013 IEEE Congress on Evolutionary Computation

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This paper introduces a method of representing transition functions for the purposes of evolutionary design of cellular automata. The proposed approach is based on conditions specified in the transition rules that have to be satisfied in order to determine the next state of a cell according to a specific rule. The goal of this approach is to reduce the number of elements needed to represent a transition function while preserving the possibility to specify traditional transition rules known from the conventional table-based representation. In order to demonstrate abilities of the proposed approach, the replication problem and pattern transformation problem in cellular automata will be investigated. It will be shown that the evolution is able to design transition functions for non-trivial behavior of two-dimensional cellular automata that perfectly fulfil the specified requirements.

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“…Methodology of complex networks has been used as an important tool to investigate the dynamics of some discrete systems and even chaotic cryptanalysis [Liou & Chen, 2012;Kayama, 2012;Sanchez & Rodriguez, 2015;Wang et al, 2016;Xie et al, 2017]. The general framework of the analyses can be summarized as four stages: selection of nodes; establishment of linkage between any pair of nodes; definition of some characteristic parameters of the obtained network; comparison with other recognized (convincing) metrics.…”

Section: Introductionmentioning

confidence: 99%

On the Network Analysis of the State Space of Discrete Dynamical Systems

Lü

et al. 2017

Int. J. Bifurcation Chaos

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This paper discusses the letter entitled "Network analysis of the state space of discrete dynamical systems" by A. Shreim et al. [Physical Review Letters, 98, 198701 (2007)]. We found that some theoretical analyses are wrong and the proposed indicators based on two parameters of the state-mapping network cannot discriminate the dynamical complexity of the discrete dynamical systems composed of a 1-D Cellular Automata.

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Network View of Binary Cellular Automata

Cited by 4 publications

References 13 publications

A survey of cellular automata: types, dynamics, non-uniformity and applications

A survey of cellular automata: types, dynamics, non-uniformity and applications

Evolution of cellular automata with conditionally matching rules

On the Network Analysis of the State Space of Discrete Dynamical Systems

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