Fractal patterns arising in chaotic dynamical systems

Abstract

Fractals are everywhere. This is no accident, because even the simplest mathematical expressions, when interpreted as dynamical systems, yield fractals. The goal of this chapter is to make this statement precise. We will describe some of the elements of the field of mathematics known as dynamical systems and show how fractals arise quite naturally in this context. We will also present some of the algorithms by which some of these fractal patterns may be generated.