Number-conserving cellular automata with a von Neumann neighborhood of range one

被引：12

作者：

Wolnik, Barbara ^{[1
]}

Dzedzej, Adam ^{[1
]}

Baetens, Jan M. ^{[2
]}

De Baets, Bernard ^{[2
]}

机构：

[1] Univ Gdansk, Fac Math Phys & Informat, Inst Math, PL-80308 Gdansk, Poland

[2] Univ Ghent, KERMIT, Dept Math Modelling Stat & Bioinformat, Coupure Links 653, B-9000 Ghent, Belgium

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2017年 / 50卷 / 43期

关键词：

cellular automata; number-conservation; von Neumann neighborhood; UNIVERSALITY;

D O I：

10.1088/1751-8121/aa89cf

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We present necessary and sufficient conditions for a cellular automaton with a von Neumann neighborhood of range one to be number-conserving. The conditions are formulated for any dimension and for any set of states containing zero. The use of the geometric structure of the von Neumann neighborhood allows for computationally tractable conditions even in higher dimensions.

引用

页数：19

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