FRACTAL GEOMETRY: MATHEMATICAL PROPERTIES AND THEIR APPLICATIONS IN THE NATURAL WORLD

Abstract

Fractal geometry is a branch of mathematics that studies complex shapes and structures characterized by self-similarity at various scales. This concept, developed by Benoît B. Mandelbrot, has been widely applied to understand natural phenomena and create technological innovations. Fractal geometry allows for the precise description of natural patterns, such as the branching of blood vessels, the distribution of rivers, and plant growth. Moreover, fractals have been used in areas such as computer graphics, image compression, and the simulation of natural patterns. The main objective of this study was to analyze the mathematical properties of fractal geometry and explore its applications in the natural world, investigating how these properties can be observed in biological, geological, and technological phenomena. The specific objectives were to investigate the properties of fractals, their applications in biology and geology, and their contributions to the development of technologies in computing and art. The justification for this study lies in the growing importance of fractal geometry in various fields of knowledge, particularly in biology, geology, computing, and art, providing innovative solutions for modeling natural systems and developing efficient technologies. The methodology adopted was a bibliographical research, based on the analysis of scientific articles, books, and other relevant publications on the subject. This approach allowed for a comprehensive review of the state of the art regarding fractal geometry and its applications. In conclusion, this study highlighted the significant contribution of fractals to the understanding of natural phenomena and technological advancement, particularly in the fields of computing and design. Fractal geometry offers an efficient way to describe and optimize complex systems, making it an essential tool for the natural and technological sciences.