Fractal transformations of harmonic functions

Michael F. Barnsley*, Uta Freiberg

*Corresponding author for this work

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    2 Citations (Scopus)

    Abstract

    The theory of fractal homeomorphisms is applied to transform a Sierpinski triangle into what we call a Kigami triangle. The latter is such that the corresponding harmonic functions and the corresponding Laplacian Δ take a relatively simple form. This provides an alternative approach to recent results of Teplyaev. Using a second fractal homeomorphism we prove that the outer boundary of the Kigami triangle possesses a continuous first derivative at every point. This paper shows that IFS theory and the chaos game algorithm provide important tools for analysis on fractals.

    Original languageEnglish
    Title of host publicationComplexity and Nonlinear Dynamics
    DOIs
    Publication statusPublished - 2007
    EventComplexity and Nonlinear Dynamics - Adelaide, Australia
    Duration: 12 Dec 200613 Dec 2006

    Publication series

    NameProceedings of SPIE - The International Society for Optical Engineering
    Volume6417
    ISSN (Print)0277-786X

    Conference

    ConferenceComplexity and Nonlinear Dynamics
    Country/TerritoryAustralia
    CityAdelaide
    Period12/12/0613/12/06

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