TCC - Licenciatura em Matemática (Sede)
URI permanente para esta coleçãohttps://arandu.ufrpe.br/handle/123456789/466
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Resultados da Pesquisa
Item Introdução à compressão fractal de imagens através de sistemas de funções iteradas(2023-05-12) Silva, Maria Fernanda Pires da; Silva, Tarciana Maria Santos da; http://lattes.cnpq.br/1650180237175460; http://lattes.cnpq.br/4722608617162314The study object of this work is the fractal image compression method through systems of iterated functions. This technique consists of describing, through affine transformations, fractals that have a special characteristic: self-similarity. To understand this method of compression, we make a brief explanation about fractal geometry, start a study on linear transformations and define affine transformations in the plane. Then, we focus on the concepts of Metric Spaces necessary for understanding Banach’s Fixed Point Theorem, which is the key for the application of systems of iterated functions in the construction of self-similar fractals. We present the Hausdorff distance, as it is used in the compression of real images that have little or no similarity and, finally, we show the application in practice by building two very important fractals: the Sierpinski Triangle and the Sierpinski Carpet.Item Construções de fractais com o GeoGebra e dimensão fractal(2021-12-21) Souto, Rafael Almeida; Tanaka, Thiago Yukio; Didier, Maria Ângela Caldas; http://lattes.cnpq.br/9721552594807972; http://lattes.cnpq.br/3394446426392577; http://lattes.cnpq.br/5859671240920200In this work, we will present the elements and concepts related to Fractal Geometry such as its definition, classification into types, properties, and some measurable characteristics such as area, perimeter, and dimension measurements. At first, we will focus on the characterization of the most classic fractals of the theory, such as the Sierpinski triangle, the Koch curve, the Cantor set, among others. We will show how to build these objects using the mathematical tool of geometric transformations and their matrix translations and the implementation of these concepts through GeoGebra dynamic geometry software, which allows us to build the vast majority of fractals that will be mentioned during the work. Finally, we will also present a study on the concept of fractal dimension, whose applications are vast in various areas such as Economics, Medicine, Biology, among others. More precisely, we will present two methods of obtaining a fractal dimension, the first using the Hausdorff-Besicovitch method and a second way using the box-counting method. We believe that this monograph can be used as the first guiding material for studies and research in the field of Fractal Geometry, mainly due to the richness of details, especially for those who are unaware or know little about the theory. In addition, by bringing construction methods with GeoGebra, we believe that the material also serves as a guide to guide the use of theory in the classroom for students of the Licentiate Degree in Mathematics, future teachers. Finally, for those who already have a basic knowledge of fractals, the dimension study serves as a basis for guiding the application of this object.