Fractals and Quasi-Affine Transformations

Abstract

In the continuum , contracting affine transformations have a unique fixed point. It is well known that this property is not preserved by dicretization and that the dynamics of discretized functions are very complicated. Discrete geometry allows us to start a theory for these dynamics and to illustrate some of their features by pictures. These pictures, rendered by a simple algorithm, reveal a very large spectrum of fractal structures, from the simplest to the intricatest.