Fractal interpolation functions from \(R^ n\) into \(R^ m\) and their projections
type: Item
instance of: scholarly article
title: Fractal interpolation functions from \(R^ n\) into \(R^ m\) and their projections
zbMATH Open document ID: 0777.41022
DOI: 10.4171/ZAA/549
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1993-10-20T00:00:00Z
review text: Summary: We construct fractal interpolation functions from \(\mathbb{R}^ n\to\mathbb{R}^ m\), and consider the projections of their graphs onto \(\mathbb{R}^ n\times\mathbb{R}\). 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.
Mathematics Subject Classification ID: 41A46
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 37C70
zbMATH DE Number: 428227
zbMATH Keywords: fractal interpolation functions
author: D. P. Hardin
author: Peter Massopust
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/549
OpenAlex ID: W15446707
description: scientific article; zbMATH DE number 428227