Smooth interpolating curves and surfaces generated by iterated function systems
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.
\(C^ 2\)-interpolating fractal functions
scientific article; zbMATH DE number 429266