Fractal Geometry. Self similarity and separation properties

      Аннотация: Fractal geometry, introduced by Benoit Mandelbrot in1975, is a branch of geometry that is capable of providing a mathematical outlook to the complex and unpredictable structures present in both real-world and mathematics. Unlike the other branches of geometry, fractals extend a mathematical approach to such objects, apprehending the infinitely many details they carry. Fractals enable one to examine the roughness, irregularity and chaotic nature of such structures through simple yet intrinsic analytical and topological tools. Since it provides a mathematical framework to capture the tiniest details inherent in phenomena, Fractal theory is a rapidly evolving research area that has a wide verity of applications in fields such as cancer diagnosis, astronomy, weather prediction, image processing, mathematical modeling, cosmology, etc. This book attempts to provide an overlook of the basic concepts in Fractal geometry, such as the self-similar property of fractal objects and their separation properties in higher dimensional spaces. We strongly believe that this book will help students, researchers, and faculties all around the globe to undergo research in the field of fractal theory.

Ключевые слова: Fractal, self similarity, iterated function sysytem