Bilinear fractal interpolation and box dimension

Michael F. Barnsley, Peter R. Massopust*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    80 Citations (Scopus)

    Abstract

    In the context of general iterated function systems (IFSs), we introduce bilinear fractal interpolants as the fixed points of certain Read-Bajraktarević operators. By exhibiting a generalized "taxi-cab" metric, we show that the graph of a bilinear fractal interpolant is the attractor of an underlying contractive bilinear IFS. We present an explicit formula for the box-counting dimension of the graph of a bilinear fractal interpolant in the case of equally spaced data points.

    Original languageEnglish
    Pages (from-to)362-378
    Number of pages17
    JournalJournal of Approximation Theory
    Volume192
    DOIs
    Publication statusPublished - 1 Apr 2015

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