{"title":"模拟随机扩散的四态确定性细胞自动机规则","authors":"Henryk Fukś","doi":"arxiv-2312.11377","DOIUrl":null,"url":null,"abstract":"We show how to construct a deterministic nearest-neighbour cellular automaton\n(CA) with four states which emulates diffusion on a one-dimensional lattice.\nThe pseudo-random numbers needed for directing random walkers in the diffusion\nprocess are generated with the help of rule 30. This CA produces density\nprofiles which agree very well with solutions of the diffusion equation, and we\ndiscuss this agreement for two different boundary and initial conditions. We\nalso show how our construction can be generalized to higher dimensions.","PeriodicalId":501231,"journal":{"name":"arXiv - PHYS - Cellular Automata and Lattice Gases","volume":"34 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Four state deterministic cellular automaton rule emulating random diffusion\",\"authors\":\"Henryk Fukś\",\"doi\":\"arxiv-2312.11377\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show how to construct a deterministic nearest-neighbour cellular automaton\\n(CA) with four states which emulates diffusion on a one-dimensional lattice.\\nThe pseudo-random numbers needed for directing random walkers in the diffusion\\nprocess are generated with the help of rule 30. This CA produces density\\nprofiles which agree very well with solutions of the diffusion equation, and we\\ndiscuss this agreement for two different boundary and initial conditions. We\\nalso show how our construction can be generalized to higher dimensions.\",\"PeriodicalId\":501231,\"journal\":{\"name\":\"arXiv - PHYS - Cellular Automata and Lattice Gases\",\"volume\":\"34 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Cellular Automata and Lattice Gases\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2312.11377\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Cellular Automata and Lattice Gases","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2312.11377","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们展示了如何构建一个具有四个状态的确定性近邻细胞自动机（CA），该自动机模拟了一维晶格上的扩散过程。在规则 30 的帮助下，生成了在扩散过程中引导随机漫步者所需的伪随机数。这种 CA 生成的密度文件与扩散方程的解非常吻合，我们讨论了两种不同边界和初始条件下的吻合情况。我们还展示了如何将我们的构造推广到更高维度。
Four state deterministic cellular automaton rule emulating random diffusion
We show how to construct a deterministic nearest-neighbour cellular automaton
(CA) with four states which emulates diffusion on a one-dimensional lattice.
The pseudo-random numbers needed for directing random walkers in the diffusion
process are generated with the help of rule 30. This CA produces density
profiles which agree very well with solutions of the diffusion equation, and we
discuss this agreement for two different boundary and initial conditions. We
also show how our construction can be generalized to higher dimensions.
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