Global fractal transformations and global addressing

Abstract

The attractor is a central object of an iterated function system (IFS), and fractal transformations are the natural maps from the attractor of one IFS to the attractor of another. This paper presents a global point of view, showing how to extend the domain of a fractal transformation from an attractor with non-empty interior to the ambient space. Intimately related is the extension of addressing from such an attractor to the set of points of the ambient space. Properties of such global fractal transformations are obtained, and tilings are constructed based on global addresses.