JournalszaaVol. 12, No. 2pp. 201–210

Smooth Interpolating Curves and Surfaces Generated by Iterated Function Systems

  • Peter R. Massopust

    Vanderbilt University, Nashville, USA
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Abstract

We construct C1C^1- and C2C^2-interpolating fractal functions using a certain class of iterated function systems. An estimate for the box dimension of the graph of nonsmooth fractal functions generated by this new class is presented. We then generalize this construction to hi variate functions thus obtaining C1C^1-interpolating fractal surfaces. Finally, CnC^n-interpolating fractal surfaces are constructed via integration over C0C^0 fractal surfaces.

Cite this article

Peter R. Massopust, Smooth Interpolating Curves and Surfaces Generated by Iterated Function Systems. Z. Anal. Anwend. 12 (1993), no. 2, pp. 201–210

DOI 10.4171/ZAA/571