{"title":"Multiplication cubes and multiplication automata","authors":"JOHAN KOPRA","doi":"10.1017/etds.2024.44","DOIUrl":null,"url":null,"abstract":"We extend previously known two-dimensional multiplication tiling systems that simulate multiplication by two natural numbers <jats:italic>p</jats:italic> and <jats:italic>q</jats:italic> in base <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000440_inline1.png\"/> <jats:tex-math> $pq$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> to higher dimensional multiplication tessellation systems. We develop the theory of these systems and link different multiplication tessellation systems with each other via macrotile operations that glue cubes in one tessellation system into larger cubes of another tessellation system. The macrotile operations yield topological conjugacies and factor maps between cellular automata performing multiplication by positive numbers in various bases.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":"9 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ergodic Theory and Dynamical Systems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/etds.2024.44","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We extend previously known two-dimensional multiplication tiling systems that simulate multiplication by two natural numbers p and q in base $pq$ to higher dimensional multiplication tessellation systems. We develop the theory of these systems and link different multiplication tessellation systems with each other via macrotile operations that glue cubes in one tessellation system into larger cubes of another tessellation system. The macrotile operations yield topological conjugacies and factor maps between cellular automata performing multiplication by positive numbers in various bases.
期刊介绍：
Ergodic Theory and Dynamical Systems focuses on a rich variety of research areas which, although diverse, employ as common themes global dynamical methods. The journal provides a focus for this important and flourishing area of mathematics and brings together many major contributions in the field. The journal acts as a forum for central problems of dynamical systems and of interactions of dynamical systems with areas such as differential geometry, number theory, operator algebras, celestial and statistical mechanics, and biology.
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