{"title":"具有权重的线性分形","authors":"Subhash Kak","doi":"10.1142/s012962642340011x","DOIUrl":null,"url":null,"abstract":"Linear fractals associated with weights are investigated. Such fractals are important from a conservation law perspective that is relevant in a variety of physical systems such as materials science, sand dune fractals, barred galaxies, as well as in temporal processes like in the electroencephalogram (EEG). The weight associated with fractals is an additional feature that may be associated with distributions consistent with the ubiquitous power law and the first digit phenomenon. These distributions form a bridge to processes and applications in natural, biological, and engineering systems and, therefore, open up the possibility of the application of linear weighted fractals to these subjects. Two linear fractal algorithms that are near optimal in the information theoretic sense are described. A mechanism for the emergence of these fractals is proposed: it is the indistinguishability amongst the particles in the evolution and transformation of physical systems. Since the fractal approach is an established method of signal processing and coding, the newly proposed weighted fractals have the potential to lead to new useful algorithms.","PeriodicalId":44742,"journal":{"name":"Parallel Processing Letters","volume":"116 1","pages":"0"},"PeriodicalIF":0.5000,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Linear Fractals with Weights\",\"authors\":\"Subhash Kak\",\"doi\":\"10.1142/s012962642340011x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Linear fractals associated with weights are investigated. Such fractals are important from a conservation law perspective that is relevant in a variety of physical systems such as materials science, sand dune fractals, barred galaxies, as well as in temporal processes like in the electroencephalogram (EEG). The weight associated with fractals is an additional feature that may be associated with distributions consistent with the ubiquitous power law and the first digit phenomenon. These distributions form a bridge to processes and applications in natural, biological, and engineering systems and, therefore, open up the possibility of the application of linear weighted fractals to these subjects. Two linear fractal algorithms that are near optimal in the information theoretic sense are described. A mechanism for the emergence of these fractals is proposed: it is the indistinguishability amongst the particles in the evolution and transformation of physical systems. Since the fractal approach is an established method of signal processing and coding, the newly proposed weighted fractals have the potential to lead to new useful algorithms.\",\"PeriodicalId\":44742,\"journal\":{\"name\":\"Parallel Processing Letters\",\"volume\":\"116 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-10-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Parallel Processing Letters\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s012962642340011x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Parallel Processing Letters","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s012962642340011x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Linear fractals associated with weights are investigated. Such fractals are important from a conservation law perspective that is relevant in a variety of physical systems such as materials science, sand dune fractals, barred galaxies, as well as in temporal processes like in the electroencephalogram (EEG). The weight associated with fractals is an additional feature that may be associated with distributions consistent with the ubiquitous power law and the first digit phenomenon. These distributions form a bridge to processes and applications in natural, biological, and engineering systems and, therefore, open up the possibility of the application of linear weighted fractals to these subjects. Two linear fractal algorithms that are near optimal in the information theoretic sense are described. A mechanism for the emergence of these fractals is proposed: it is the indistinguishability amongst the particles in the evolution and transformation of physical systems. Since the fractal approach is an established method of signal processing and coding, the newly proposed weighted fractals have the potential to lead to new useful algorithms.
期刊介绍:
Parallel Processing Letters (PPL) aims to rapidly disseminate results on a worldwide basis in the field of parallel processing in the form of short papers. It fills the need for an information vehicle which can convey recent achievements and further the exchange of scientific information in the field. This journal has a wide scope and topics covered included: - design and analysis of parallel and distributed algorithms - theory of parallel computation - parallel programming languages - parallel programming environments - parallel architectures and VLSI circuits