Uma Introdução ao Estudo dos Fractais

Abstract

This work presents an introductory study about fractals that are irregular figures with certain characteristics. Some characters who contributed several discoveries to fractal geometry were Benoit Mandelbrot, George Cantor, Wanclaw Sierpinski, Helge Van Kock, Felix Hausdorff. Initially, a historical overview of Benoit Mandelbrot, considered the father of Fractal Geometry, was explained. The primordial characteristics of a fractal were elucidated, among which are the selfsimilarity, infinite complexity and fractal dimension, and they were classified as deterministic fractals, computer generated fractals or even random fractals. This research emphasizes the fractal dimension, as it aims to conceptualize and exemplify the existence of objects with a decimal dimension and an infinite-length curve. Thus, these discussions were brought and examples were explained using known fractals such as, for example, the Cantor Set, the Koch Curve, the Sierpinski Triangle and the Peano Curve, and later the applicability in medicine to diagnose some diseases was addressed and types of cancer and/or use it in the classroom as a motivation to teach geometric progressions, showing the versatility in teaching fractals.