利用计算机代数方法确定有限分枝席尔宾斯基地毯的化学维数

SIGSAM Bull. Pub Date : 2002-06-02 DOI:10.1145/581316.581318

A. Franz, C. Schulzky, K. Hoffmann

{"title":"利用计算机代数方法确定有限分枝席尔宾斯基地毯的化学维数","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 d<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 d<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":"{\"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 d<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 d<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}","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

摘要

提出了一种计算有限分枝Sierpinski地毯化学维数d1的新算法。使用Dijkstra算法，我们使用Mathematica迭代地计算通过地毯的最短路径。这些最短路径长度在地毯线性尺寸上的缩放指数等于最小路径尺寸，这与化学尺寸有关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Using computer algebra methods to determine the chemical dimension of finitely ramified Sierpinski carpets

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

SIGSAM Bull.

自引率

0.00%

发文量