We construct - and -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 -interpolating fractal surfaces. Finally, -interpolating fractal surfaces are constructed via integration over 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. 201–210DOI 10.4171/ZAA/571