Fractal functions and their applications

This paper is a compendium of some results from the theory of fractal functions. The class of fractal functions that are considered are generated via iterated function systems. The Fourier transform and the derivatives, in the strong as well as distributional sense, of this class of fractal functions are investigated. Conditions that guarantee membership in certain Hölder and Sobolev spaces are presented. Finally, in an expository fashion, it is indicated how such fractal functions can be used as finite elements to obtain numerical solutions of partial differential equations.