V-variable fractals: Fractals with partial self similarity

Michael F. Barnsley, John E. Hutchinson*, Örjan Stenflo

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    67 Citations (Scopus)

    Abstract

    We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a corresponding class of V-variable fractal sets or measures. These V-variable fractals can also be obtained from the points on the attractor of a single deterministic iterated function system. Existence, uniqueness and approximation results are established under average contractive assumptions. We also obtain extensions of some basic results concerning iterated function systems.

    Original languageEnglish
    Pages (from-to)2051-2088
    Number of pages38
    JournalAdvances in Mathematics
    Volume218
    Issue number6
    DOIs
    Publication statusPublished - 20 Aug 2008

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