2D Linear CA with Mixing Boundary Conditions and Reversibility

被引：1

作者：

Jumaniyozov, Doston ^{[1
]}

Manuel Casas, Jose ^{[2
,3
]}

Ladra Gonzalez, Manuel ^{[4
,5
]}

Omirov, Bakhrom ^{[6
,7
]}

Redjepov, Shovkat ^{[8
,9
]}

机构：

[1] Uzbek Acad Sci, Inst Math, Univ St, Tashkent 100174, Uzbekistan

[2] Univ Vigo, Pontevedra 36005, Spain

[3] EE Forestal, CITMAga, Pontevedra 36005, Spain

[4] Univ Santiago de Compostela, Praza Obradoiro, Santiago De Compostela 15705, Spain

[5] CITMAga, Santiago De Compostela 15782, Spain

[6] Harbin Inst Technol, Inst Adv Study Math, Harbin 150001, Peoples R China

[7] New Uzbekistan Univ, 54 Mustaqillik Ave, Tashkent 100007, Uzbekistan

[8] Tashkent Univ Informat Technol, Amir Temur St, Tashkent 100200, Uzbekistan

[9] Inst Fundamental & Appl Res, 39 Kari Niyazov St, Tashkent 100000, Uzbekistan

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2023年 / 33卷 / 08期

关键词：

Cellular automata; rule matrix; Garden of Eden; CELLULAR-AUTOMATA;

D O I：

10.1142/S0218127423500943

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider two-dimensional cellular automata (CA) with the von Neumann neighborhood. We study the characterization of 2D linear cellular automata defined by the von Neumann neighborhood with new type of boundary conditions over the field Z(p.) Furthermore, we investigate the rule matrices of 2D von Neumann CA by applying the group of permutations S4. Moreover, the algorithm for computing the rank of rule matrices is given. Finally, necessary and sufficient conditions for the existence of Garden of Eden configurations for considered two-dimensional cellular automata are obtained.

引用

页数：19

共 18 条

[11] VLSI architecture of a cellular automata machine [J].

Khan, AR ;

Choudhury, PP ;

Dihidar, K ;

Mitra, S ;

Sarkar, P .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1997, 33 (05) :79-94

[12]

Muhtaroglu A., 1996, 4 1 CELLULAR AUTOMAT, P62

[13] Garden of Eden states in traffic models [J].

Schadschneider, A ;

Schreckenberg, M .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1998, 31 (11) :L225-L231

[14]

Sethna J. P., 2021, Statistical mechanics: entropy, order parameters and complexity, V14

[15] 2D Cellular Automata with an Image Processing Application [J].

Uguz, S. ;

Sahin, U. ;

Siap, I. ;

Akin, H. .

ACTA PHYSICA POLONICA A, 2014, 125 (02) :435-438

[16]

Von Neumann John, 1966, Theory of self-reproducing automata

[17] STATISTICAL-MECHANICS OF CELLULAR AUTOMATA [J].

WOLFRAM, S .

REVIEWS OF MODERN PHYSICS, 1983, 55 (03) :601-644

[18] On behavior of two-dimensional cellular automata with an exceptional rule [J].

Zhai, Ying ;

Yi, Zhong ;

Deng, Pei-min .

INFORMATION SCIENCES, 2009, 179 (05) :613-622

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