Smooth Interpolating Curves and Surfaces Generated by Iterated Function Systems

Abstract

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 hi variate functions thus obtaining $C^1$-interpolating fractal surfaces. Finally, $C^n$-interpolating fractal surfaces are constructed via integration over $C^0$ fractal surfaces.