Genden Program and other special contributions. This book was created as a successor to the essays "Fractals: Form, Chance, and Dimension" from 1977 and "Les objets fractals: forme, hasard et dimension" from 1975. Almost all sections were rewritten, and with a few exceptions, significantly expanded, taking into account my earlier works, but especially new developments. I owe special thanks to the Thomas J. Watson Research Center of the International Business Machines Corporation for supporting my research and books. As a group leader, department director, and now research director, IBM Vice President Ralph E. Gomory protected and defended my work when it was still a risk and continues to provide all necessary support. Richard F. Voss made a significant contribution to the 1977 essay and also to this book, particularly through the generation.