Characterization of two-dimensional cellular automata over ternary fields

Şiap, İrfan; Akın, Hasan; Şah, Ferhat

doi:10.1016/j.jfranklin.2010.02.002

Cited by 25 publications

(13 citation statements)

References 8 publications

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“…Using the linear rule matrices presented in the work, the presented results give further insight into the algebraic consequences of these 2D hybrid CA and relate to some elegant applications found by the authors in the literature (i.e. [3,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]). …”

Section: Introduction: 2d Cellular Automatamentioning

confidence: 65%

“…It is another goal of this study. It is believed that CA hybrid theory could be applied successfully, especially in image processing area [7][8][9][10][11] and in other science branches in future [12][13][14][15].…”

Section: Discussionmentioning

confidence: 99%

“…Some basic and unified mathematical CA models, considering properties of matrix linear algebra over the binary field Z 2 , that specify the behaviors of 2D linear nearest neighborhood of uniform CA with null or periodic boundary conditions, can be found in the literature [3,4]. Uniform linear CA has been accorded a striking interest in the past decades [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Due to its structure and elegant properties, CA has an opportunity to model many scientific computational problems, to understand many similar model behaviors and sometimes to easily explain * corresponding author; e-mail: karakusecem@harran.edu.tr their nature.…”

Section: Introduction: 2d Cellular Automatamentioning

confidence: 99%

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Characterization of 2D Hybrid Cellular Automata with Periodic Boundary

2017

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We investigate main theoretical aspects of two-dimensional linear-hybrid cellular automata with periodic boundary condition over the Galois field GF(2). We focus on the characterization of two-dimensional hybrid linear cellular automata by way of a special algorithm. Here we set up a relation between reversibility of cellular automata and characterization of two-dimensional hybrid linear cellular automata with a special boundary conditions, i.e. periodic case. The determination of the characterization problem of special type of cellular automaton is studied by means of the matrix algebra theory. It is believed that this type of cellular automata could find many different applications in special case situations, e.g. image processing area, textile design, video processing, DNA research, etc., in the near future.

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Section: Introduction: 2d Cellular Automatamentioning

confidence: 65%

Section: Discussionmentioning

confidence: 99%

Section: Introduction: 2d Cellular Automatamentioning

confidence: 99%

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Characterization of 2D Hybrid Cellular Automata with Periodic Boundary

2017

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“…The auxiliary matrices that play an important role in the representation matrix of a 2-D cellular automaton also considered in several papers ( [10,13,21,22] and [34]) are 29,30]). The next state of all Primary rules (1,3,9,27,81,273,729,2187, 6561) of a ternary 2-D cellular automaton can be represented as follows: Table 1 Null boundary condition in 2-D finite CA 3 Â 3 .…”

Section: Preliminariesmentioning

confidence: 99%

Garden of eden configurations for 2-D cellular automata with rule 2460N

Şiap¹,

Akın²,

Şah³

2010

Information Sciences

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“…An important characterization is the determination of the reversibility of CA [13]. In [14], we have characterized a 2D nite CA by using matrix algebra built on Z 3 . Also, we have analyzed some results about the rule numbers 2460N and 2460P.…”

Section: Introductionmentioning

confidence: 99%