Fractal Space. Introduction and Applications

      Аннотация: Fractal Geometry was developed to understand the geometry of irregular sets which was not possible using methods from classical Euclidean geometry. The setting of a similitude Iterated Function System (IFS) has provided a sufficiently easy environment to produce highly irregular sets which are fractals. In this book, the notion of scaled IFS is defined and its existence conditions are examined. A lower and upper bounds for the Hausdorff dimension of the attractor of a scaled IFS is obtained. We have explained the construction of some super self similar sets. The topology induced by Hausdorff metric on the set of all non empty compact subsets of a complete metric space is explained. The relation between this topology and the convergence of sets is discussed. Partial metric space is the generalization of a metric space with non zero self distance. The completeness of the space under Hausdorff partial metric is proved and the definitions of fractals is extended to this metric space. Some applications of the field of study in the area of ocean sciences are discussed.

Ключевые слова: Fractals, iterated function systems, Topology, Self similar sets, Partial metric space