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Multifractal Decompositions of Digraph Recursive Fractals

1992; Wiley; Volume: s3-65; Issue: 3 Linguagem: Inglês

10.1112/plms/s3-65.3.604

1460-244X

Gerald A. Edgar, R. Daniel Mauldin,

Theoretical and Computational Physics

Proceedings of the London Mathematical SocietyVolume s3-65, Issue 3 p. 604-628 Articles Multifractal Decompositions of Digraph Recursive Fractals G. A. Edgar, G. A. Edgar edgar@mps.ohio-state.edu Department of Mathematics, The Ohio State University, Columbus, Ohio, 43210-1174 U.S.A.Search for more papers by this authorR. Daniel Mauldin, R. Daniel Mauldin MAULDIN@UNTVAX Department of Mathematics, University of North Texas, Denton, Texas, 76203-3886 U.S.A.Search for more papers by this author G. A. Edgar, G. A. Edgar edgar@mps.ohio-state.edu Department of Mathematics, The Ohio State University, Columbus, Ohio, 43210-1174 U.S.A.Search for more papers by this authorR. Daniel Mauldin, R. Daniel Mauldin MAULDIN@UNTVAX Department of Mathematics, University of North Texas, Denton, Texas, 76203-3886 U.S.A.Search for more papers by this author First published: November 1992 https://doi.org/10.1112/plms/s3-65.3.604Citations: 72AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract We prove that the multifractal decomposition behaves as expected for a family of sets K known as digraph recursive fractals, using measures μ of Markov type. For each value of a parameter α between a minimum αmin and maximum αmax, we define ‘multifractal components’ K(α) of K, and show that they are fractals in the sense of Taylor. The dimension f(α) of K(α) is computed from the data of the problem. The typical concave ‘multifractal f(α)’ dimension spectrum curve results. Under appropriate disjointness conditions, the multifractal components K(α) are given by K ( α ) = { x ɛ K : lim ɛ ↓ ( ) log μ ( B ɛ ( x ) ) log diam B ɛ ( x ) = α } that is, K(α) consists of those points where μ has pointwise dimension α. Citing Literature Volumes3-65, Issue3November 1992Pages 604-628 RelatedInformation