Countable Iterated Function Systems

Fractal Theory is certainly one of the most dynamical fields in mathematics. The most amazing thing about fractals is the variety of their applications in dynamical systems, physics, quantum mechanics, computer graphics, astronomy, biology, chemistry, medicine, telecommunications, arts and others. Iterated Function Systems (IFSs) are the main generators of fractals. In this book we provide an extension of the well-known Hutchinson-Barnsley theory of finite IFS to Countable IFS (CIFS). After a review of the basic properties of IFSs, we described the features of CIFSs related to the attractor, Hausdorff dimension, self-similarity, Hutchinson measure, fractal interpolation, continuous dependence on parameter. Some generalizations and a modern approach of IFSs and CIFSs are also investigated. This book is written in a rigorous, but accessible, self-contained manner. Several examples are given with the aim to offer a better understanding of the theory. The book is useful for mathematicians, students, researchers, postgraduates, physicians and other specialists which are interested in studying the fractals produced by an iterative process.