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Zeitschrift für Analysis und ihre Anwendungen


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Volume 12, Issue 3, 1993, pp. 535–548
DOI: 10.4171/ZAA/549

Published online: 1993-09-30

Fractal Interpolation Functions from $R^n$ into $R^m$ and their Projections

Douglas Hardin[1] and Peter R. Massopust[2]

(1) Vanderbilt University, Nashville, United States
(2) Vanderbilt University, Nashville, USA

We construct fractal interpolation functions from $\mathbb R^n \to \mathbb R^m$, and consider the projections of their graphs onto $\mathbb R^n \times \mathbb R^m$. Since these projections still depend continuously on all the variables we refer to them as hidden variable fractal interpolation surfaces. The hidden variable fractal interpolation surfaces carry additional free parameters and are thus more general than, for instance, the fractal surfaces defined earlier by the authors. These free parameters may prove useful in approximation-theoretic considerations. A formula for the box dimension of a hidden variable fractal interpolation surface is presented.. This dimension parameter could be used to distinguish different textures on natural surfaces.

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

Hardin Douglas, Massopust Peter: Fractal Interpolation Functions from $R^n$ into $R^m$ and their Projections. Z. Anal. Anwend. 12 (1993), 535-548. doi: 10.4171/ZAA/549