Smooth interpolating curves and surfaces generated by iterated function systems (Q687217)
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scientific article; zbMATH DE number 429266
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Smooth interpolating curves and surfaces generated by iterated function systems |
scientific article; zbMATH DE number 429266 |
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Smooth interpolating curves and surfaces generated by iterated function systems (English)
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2 December 1993
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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.
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\(C^ 1\)-interpolating surfaces
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\(C^ 2\)-interpolating fractal functions
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iterated function systems
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