Condición del Conjunto Abierto para hallar la dimensión de Haussdorff en fractales
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Date
2024
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Universidad Nacional de Trujillo
Abstract
El presente trabajo de investigación proporciono los fundamentos teóricos
maten áticos necesarios para determinar la dimensión de Hausdorff de un conjunto generado a partir de un Sistema de Funciones Iteradas (SFI), siendo esta dimensión el único valor critico real no negativo calculado a través del Teorema Fundamental del Conjunto Abierto que, en concordancia a la definición de Benoit Maldebrot y conocido su dimensión topológica (inductiva), permite identificar si el conjunto es un fractal. También, se presenta un algoritmo que permite comprimir imágenes usando la autosimilaridad y/o autosemejanza de los fractales
Abstract The present research work provided the mathematical theoretical foundations necessary to determine the Hausdorff dimension of a set, generated of a Iterated Functions System (IFS), being this dimension the only non-negative real critical value calculated through the Fundamental Theorem of the Open Set that, according to Benoit Maldebrot’s definition and knowing its topological (inductive) dimension, allows to identify if the set is a fractal. Also, an algorithm that allows to compress images using self-similarity and/or self-similarity of fractals is presented
Abstract The present research work provided the mathematical theoretical foundations necessary to determine the Hausdorff dimension of a set, generated of a Iterated Functions System (IFS), being this dimension the only non-negative real critical value calculated through the Fundamental Theorem of the Open Set that, according to Benoit Maldebrot’s definition and knowing its topological (inductive) dimension, allows to identify if the set is a fractal. Also, an algorithm that allows to compress images using self-similarity and/or self-similarity of fractals is presented
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Dimensión de Hausdorff, dimensión topológica, conjunto fractal