We study three-dimensional rotation-symmetric cellular automata with the von Neumann neighborhood that conserve the sum of states. We show that any non-trivial such automaton requires at least seven states, which agrees with intuition based on the known results for the one and two-dimensional cases. We also give a full characterization of these cellular automata with a seven-element state set and the result is quite surprising.

Barbara Wolnik

Mrozek Nikodem

Adam Dzedzej

Bernard De Baets

Journal of cellular automata

THE JOURNAL OF CELLULAR AUTOMATA 发表了高质量的论文，这些论文在理论上研究了元胞自动机或用作数学、物理、化学、生物、社会和工程系统的计算模型。下面的列表中给出了一些例子，这只是一个小例子本杂志探索的感兴趣领域的样本：结构形成、热传导、自我复制、语言识别、进化游戏、图像处理、密码学、随机数生成、计算普遍性、交通动力学、神经网络、替代离散物理模型，人口动态等。欢迎全长原创论文，简短的交流，评论和教程文章。

The Journal of Cellular Automata publishes high-quality papers that theoretically study cellular automata or use them as computational models for mathematical, physical, chemical, biological, social, and engineering systems. Below is a sample of some areas of interest explored by the journal: structure formation, heat conduction, self-replication, language recognition, evolutionary games, image processing, cryptography, random number generation, computational universality, traffic dynamics, neural networks, alternative discrete physical models, and population dynamics. Original full-length papers, brief communications, reviews, and tutorial articles are welcome.

《Journal of Cellular Automata》发表高质量的论文，主要研究元胞自动机的理论，或将其作为数学、物理、化学、生物、社会和工程系统的计算模型。以下是本期刊探索的一些感兴趣领域的示例：结构形成、热传导、自我复制、语言识别、进化博弈、图像处理、密码学、随机数生成、计算普遍性、交通动力学、神经网络、替代离散物理模型以及人口动态等。欢迎提交原创的长篇论文、简短交流、评论和教程文章。

Category	Quartile
计算机科学	4
计算机科学, 计算机理论方法	4
计算机科学, 数学跨学科应用	4

Three-dimensional rotation-symmetric number-conserving cellular automata

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Journal Info

Category	Quartile
MATHEMATICS, INTERDISCIPLINARY APPLICATIONS	4