超混合迷宫分形

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2018-02-15 DOI:10.4171/jfg/88

L. Cristea, G. Leobacher

{"title":"超混合迷宫分形","authors":"L. Cristea, G. Leobacher","doi":"10.4171/jfg/88","DOIUrl":null,"url":null,"abstract":"Labyrinth fractals are dendrites in the unit square. They were introduced and studied in the last decade first in the self-similar case [Cristea & Steinsky (2009,2011)], then in the mixed case [Cristea & Steinsky (2017), Cristea & Leobacher (2017)]. Supermixed fractals constitute a significant generalisation of mixed labyrinth fractals: each step of the iterative construction is done according to not just one labyrinth pattern, but possibly to several different patterns. In this paper we introduce and study supermixed labyrinth fractals and the corresponding prefractals, called supermixed labyrinth sets, with focus on the aspects that were previously studied for the self-similar and mixed case: topological properties and properties of the arcs between points in the fractal. The facts and formulae found here extend results proven in the above mentioned cases. One of the main results is a sufficient condition for infinite length of arcs in mixed labyrinth fractals.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2018-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Supermixed labyrinth fractals\",\"authors\":\"L. Cristea, G. Leobacher\",\"doi\":\"10.4171/jfg/88\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Labyrinth fractals are dendrites in the unit square. They were introduced and studied in the last decade first in the self-similar case [Cristea & Steinsky (2009,2011)], then in the mixed case [Cristea & Steinsky (2017), Cristea & Leobacher (2017)]. Supermixed fractals constitute a significant generalisation of mixed labyrinth fractals: each step of the iterative construction is done according to not just one labyrinth pattern, but possibly to several different patterns. In this paper we introduce and study supermixed labyrinth fractals and the corresponding prefractals, called supermixed labyrinth sets, with focus on the aspects that were previously studied for the self-similar and mixed case: topological properties and properties of the arcs between points in the fractal. The facts and formulae found here extend results proven in the above mentioned cases. One of the main results is a sufficient condition for infinite length of arcs in mixed labyrinth fractals.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2018-02-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/jfg/88\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/jfg/88","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 3

摘要

迷宫分形是单位正方形中的枝晶。它们在过去十年中被引入和研究，首先是在自相似情况下[Cristea&Steinsky（20092011）]，然后是在混合情况下[C里斯tea&Steinsky（2017），Cristea&Leobacher（2017）]。超混合分形构成了混合迷宫分形的一个重要概括：迭代构造的每一步不仅根据一个迷宫模式进行，而且可能根据几个不同的模式进行。在本文中，我们介绍和研究了超混合迷宫分形和相应的预分形，称为超混合迷宫集，重点研究了先前针对自相似和混合情况研究的方面：拓扑性质和分形中点之间弧的性质。这里发现的事实和公式扩展了在上述情况下证明的结果。主要结果之一是混合迷宫分形中弧长无穷大的一个充分条件。

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

Supermixed labyrinth fractals

Labyrinth fractals are dendrites in the unit square. They were introduced and studied in the last decade first in the self-similar case [Cristea & Steinsky (2009,2011)], then in the mixed case [Cristea & Steinsky (2017), Cristea & Leobacher (2017)]. Supermixed fractals constitute a significant generalisation of mixed labyrinth fractals: each step of the iterative construction is done according to not just one labyrinth pattern, but possibly to several different patterns. In this paper we introduce and study supermixed labyrinth fractals and the corresponding prefractals, called supermixed labyrinth sets, with focus on the aspects that were previously studied for the self-similar and mixed case: topological properties and properties of the arcs between points in the fractal. The facts and formulae found here extend results proven in the above mentioned cases. One of the main results is a sufficient condition for infinite length of arcs in mixed labyrinth fractals.

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.