Theory and applications of fractal tops

Abstract

We consider an iterated function system (IFS) of one-to-one contractive maps on a compact metric space. We define the top of an IFS; define an associated symbolic dynamical system; present and explain a fast algorithm for computing the top; describe an example in one dimension with a rich history going back to work of A. Rényi [Representations for Real Numbers and Their Ergodic Properties, Acta Math. Acad. Sci. Hung., 8 (1957), pp. 477-493]; and we show how tops may be used to help to model and render synthetic pictures in applications in computer graphics. © 2005 Springer-Verlag London Limited.