{"title":"Using computer algebra methods to determine the chemical dimension of finitely ramified Sierpinski carpets","authors":"A. Franz, C. Schulzky, K. Hoffmann","doi":"10.1145/581316.581318","DOIUrl":null,"url":null,"abstract":"We present a new algorithm for calculating the chemical dimension <i>d</i><inf>1</inf> of finitely ramified Sierpinski carpets. Using an algorithm of Dijkstra, we compute iteratively, using <sc>Mathematica</sc>, the shortest paths through a carpet. The scaling exponent of the lengths of these shortest paths over the linear size of the carpet is <i>d</i><inf>min</inf> the minimum path dimension, which is related to the chemical dimension.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"11 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2002-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIGSAM Bull.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/581316.581318","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
We present a new algorithm for calculating the chemical dimension d1 of finitely ramified Sierpinski carpets. Using an algorithm of Dijkstra, we compute iteratively, using Mathematica, the shortest paths through a carpet. The scaling exponent of the lengths of these shortest paths over the linear size of the carpet is dmin the minimum path dimension, which is related to the chemical dimension.
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