Smooth interpolating curves and surfaces generated by iterated function systems
type: Item
instance of: scholarly article
title: Smooth interpolating curves and surfaces generated by iterated function systems
zbMATH Open document ID: 0777.41024
DOI: 10.4171/ZAA/571
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1993-12-02T00:00:00Z
review text: Summary: 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 bivariate functions thus obtaining \(C^ 1\)-interpolating fractal surfaces. Finally, \(C^ n\)-interpolating fractal surfaces are constructed via integration over \(C^ 0\) fractal surfaces.
Mathematics Subject Classification ID: 41A46
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 37C70
zbMATH DE Number: 429266
zbMATH Keywords: \(C^ 1\)-interpolating surfaces
zbMATH Keywords: \(C^ 2\)-interpolating fractal functions
zbMATH Keywords: iterated function systems
author: Peter Massopust
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 429266