# name
Sistema de funcions iterades i dimensió fractal

# metadata.dc.description[].value
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Núria Fagella Rabionet

# metadata.dc.description.abstract[].value
[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.

# metadata.dc.rights[].value
cc-by-nc-nd (c) Minerva Berenguer Navarro, 2020

# metadata.dc.source[].value
Treballs Finals de Grau (TFG) - Matemàtiques

# metadata.dc.title[].value
Sistema de funcions iterades i dimensió fractal