Sistema de funcions iterades i dimensió fractal

Abstract

[en] Throughout this paper, we will study some of the most relevant characteristics of the geometrical objects that are called fractals, such as the fractal dimension, although we will focus on the ones which are constructed from a iterated function system (IFS), which we are going to define from contraction mappings on the space made up of the compact sets of a complete metric space. The first part of the document consists of an introdution and some of the very-well known geometrical construtions of some fractals. Later we will see some concepts that will allow us to demonstrate the Theorem of the Collage, which claims that fiven a iterated function system, exists a compact set which is fix under the union of those contraction funcitions valued in this set. We will also explain a random iterated algorithm in order to construct a fractal and, finally, we will study the fractal dimension and its applications.