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Zeitschrift für Analysis und ihre Anwendungen


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Volume 12, Issue 2, 1993, pp. 201–210
DOI: 10.4171/ZAA/571

Published online: 1993-06-30

Smooth Interpolating Curves and Surfaces Generated by Iterated Function Systems

Peter R. Massopust[1]

(1) Vanderbilt University, Nashville, USA

We construct $C^1$- and $C^2$-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 $C^1$-interpolating fractal surfaces. Finally, $C^n$-interpolating fractal surfaces are constructed via integration over $C^0$ fractal surfaces.

Keywords: Iterated function systems, fractal functions and surfaces, attractors, box dimensions

Massopust Peter: Smooth Interpolating Curves and Surfaces Generated by Iterated Function Systems. Z. Anal. Anwend. 12 (1993), 201-210. doi: 10.4171/ZAA/571