Some Historical Precedents of Fractal Functions
Maria Navascues, Univaersity of Zaragoza
Location: Stevenson 1307
In this talk, we wish to pay trivute to the scientists of older generations, who, through their reseatch, lead to the current state of knowledge of the fractal functions. We review the fundamental milestones of the origin and evolution of the self-similar curves that, in some cases, agree with continuous and nowhere differentiable functions, but they are not exhausted by them. Our main interest is to emphasize the lesser known examples, due to a deficient or late publication (Bolzano's map for instance). We will review different ways of defining self-similar curves. We will recall the first functions without tangent, but also some fractal functions having derivative almost everywhere. Most of the models studied may seem quite paradoxical ("monsters" in the words of Poincare) as, for instance, curves with a fractal dimension of two and having a tangent at every point. These instances suggest that the classification and even the definition of fractal functions are far from being established. The strategies of definition of each example compose a toolbox that will provide the audience with a selection of procedures for the construction of its own fractal function.