Fractals with Affine Transformations

• Ano de defesa: 2024
• Autor(a) principal: Silva, Barbara Carmona
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Affine transformations; Fractais; Fractals; Iterated function systems; Sistemas iterados de funções; Transformação afim
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/55/55136/tde-21082024-155537/

Fractals are geometric shapes that have the property of self-similarity, that is, parts of the shape have the characteristics of the whole, with slight variations. They are shapes of great beauty, and are found in nature, such as in some plants (branches, leaves, flowers), animals (mollusc shells, feathers), crystals, snowflakes, mountain ranges, rivers, clouds, etc. In this work we study a subset of fractals that can be completely characterized by the self-similarity given by a set of transformations of the plane that keep the figure fixed. The theory that studies such self-similar forms is known as the theory of Iterated Function Systems. Despite the sophistication of the theory, the part with affine transformations is beautiful and accessible to high school students, including computing the dimension of fractals.