Effects of Initial Symmetry on the Global Symmetry of  One-Dimensional Legal Cellular Automata

Tanaka, Ikuko

doi:10.3390/sym7041768

Cited by 3 publications

(3 citation statements)

References 10 publications

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“…In the literature, CA according to Wolfram's classification, are divided into four classes [85]. The study of symmetry in individual classes was addressed in References [99]. The author investigated the issue of development of pattern formation from the viewpoint of symmetry and he applied a two-dimensional discrete Walsh analysis to a one-dimensional cellular automata model under two types of regular initial conditions.…”

Section: Symmetry Aspectsmentioning

confidence: 99%

Modelling the Impact of Transit Media on Information Spreading in an Urban Space Using Cellular Automata

2019

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Information spreading processes are the key drivers of marketing campaigns. Activity on social media delivers more detailed information compared to viral marketing in traditional media. Monitoring the performance of outdoor campaigns that are carried out using this transportation system is even more complicated because of the lack of data. The approach that is presented in this paper is based on cellular automata and enables the modelling of the information-spreading processes that are initiated by transit advertising within an urban space. The evaluation of classical and graph cellular automata models and a coverage analysis of transit advertising based on tram lines were performed. The results demonstrated how the number of lines affects the performance in terms of coverage within an urban space and the differences between the proposed models. While research is based on an exemplary dataset taken from Szczecin (Poland), the presented framework can be used together with data from the public transport system for modelling advertising resources usage and coverage within the urban space.

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Section: Symmetry Aspectsmentioning

confidence: 99%

Modelling the Impact of Transit Media on Information Spreading in an Urban Space Using Cellular Automata

2019

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“…Various studies exist on symmetry in CA rules based on various methods. Internal symmetries of CA rules based on permutation states [21], β-calculus, and a universal map derived based on β-calculus [22], discrete Walsh analysis [23], and polynomial representation of one dimensional CA [24] symmetropy [25] are the various methods that exist to measure the symmetry of CA rules. If the rule possesses symmetry, it reflects in the output pattern.…”

Section: Introductionmentioning

confidence: 99%

Classification of Two Dimensional Cellular Automata Rules for Symmetric Pattern Generation

Mohandas

Jeganathan

2018

Symmetry

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Cellular automata (CA) are parallel computational models that comprise of a grid of cells. CA is mainly used for modeling complex systems in various fields, where the geometric structure of the lattices is different. In the absence of a CA model to accommodate different types of lattices in CA, an angle-based CA model is proposed to accommodate various lattices. In the proposed model, the neighborhood structure in a two dimensional cellular automata (2D-CA) is viewed as a star graph. The vertices of the proposed graph are determined by a parameter, angle ( θ ) . Based on the angle ( θ ) , the neighborhood of the CA, which is treated as the vertices of the graph, varies. So this model is suitable for the representation of different types of two dimensional lattices such as square lattice, rectangular lattice, hexagonal lattice, etc. in CA. A mathematical model is formulated for representing CA rules which suit for different types of symmetric lattices. The star graph representation helps to find out the internal symmetries exists in CA rules. Classification of CA rules based on the symmetry exists in the rules, which generates symmetric patterns are discussed in this work.

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“…The lattice of the cellular automaton is supplemented with the separate plane containing values of an objective function for all cells. Consequently, during the update of every lattice cell state, the states of k adjacent cells, whose position relative to the central cell is defined by the neighborhood pattern Y, are taken to be σ function arguments [14,17,18].…”

Section: The Cellular Automaton With An Objective Functionmentioning

confidence: 99%

The Algorithm of Continuous Optimization Based on the Modified Cellular Automaton

et al. 2016

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This article is devoted to the application of the cellular automata mathematical apparatus to the problem of continuous optimization. The cellular automaton with an objective function is introduced as a new modification of the classic cellular automaton. The algorithm of continuous optimization, which is based on dynamics of the cellular automaton having the property of geometric symmetry, is obtained. The results of the simulation experiments with the obtained algorithm on standard test functions are provided, and a comparison between the analogs is shown.

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Effects of Initial Symmetry on the Global Symmetry of One-Dimensional Legal Cellular Automata

Cited by 3 publications

References 10 publications

Modelling the Impact of Transit Media on Information Spreading in an Urban Space Using Cellular Automata

Modelling the Impact of Transit Media on Information Spreading in an Urban Space Using Cellular Automata

Classification of Two Dimensional Cellular Automata Rules for Symmetric Pattern Generation

The Algorithm of Continuous Optimization Based on the Modified Cellular Automaton

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