Approximation of Measures by Fractal Generation Techniques

In this paper we discuss the constructive approximation aspects of a measure generating technique that was developed in the last decade by fractal geometers. Measures are generated as stationary distributions of Markov chains that are related to function iteration. The general framework provides a robust machine for constructing parametric families of measures and is, thus, very well suited for measure approximation problems. This formalism — called iterated function system theory — has found application in computer image synthesis and image compression. In fact some of the early work was motivated by a desire to create more realistic images for flight simulators. Other areas of potential application include dynamical systems, signal processing - especially chaotic signals, and quadrature theory.