Introduction

Abstract

Fractals everywhere! This is the title of a bestseller, but it is also a reality: Fractals are really everywhere. What a change since the days of Charles Hermite declaring “I turn away with fright and horror of this terrible scourge of continuous functions without derivative”. Historically, the first fractals are the Cantor set, and the Weierstrass function, followed by the famous Brownian motion. In these seminal examples, there were already between the lines the basic properties self-similarity and roughness, we will find throughout this book. But, what does mean this word “fractal”? Or its more or less synonymous “fractional”? There are probably as many definitions as there are people who work on the subject. We follow two tracks in this book.