This book is a collection of early papers by Benoit B. Mandelbrot on the topic, combined with additional papers written by the author on the occasion of this book. The aim of the collection is not only to describe the historical context and background of the theory of fractals but also to give a self contained presentation of the topic. Twenty-five papers are divided into five parts of the book. Each of the first four parts starts with introductory paper(s) written in 2003, followed by the collection of the original papers form early 1980s. The fifth part is then devoted to the background and history of the field from the point of view of the 21st century. In such a way, we gradually learn about quadratic Julia and Mandelbrot sets, non quadratic rational dynamics, iterated functional systems and Kleinian groups, multifractal invariant measures and many other phenomena connected to fractals and chaos. The reader will surely appreciate the huge amount of pictures and illustrations, including the first “famous” picture of Mandelbrot set (a “turtle set”), obtained by the author in early 1980s. The book will be valued by both mathematicians and physicists interested in the field. It is written in the clear and straightforward way, pointing out to lots of applications. A non mathematician will appreciate the minimal number of formulas used throughout the book. On the other hand, also the mathematicians’ eye will be pleased by the exactness of the presentation.

Reviewer:

mrok