This volume describes the status of fractal imaging research and looks to future directions. It will be useful to researchers in the areas of fractal image compression, analysis, and synthesis, iterated function systems, and fractals in education. In particular it includes a vision for the future of these areas. It aims to provide an efficient means by which researchers can look back over the last decade at what has been achieved, and look forward towards second-generation fractal imaging. The articles in themselves are not meant to be detailed reviews or expositions, but to serve as signposts to the state of the art in their areas. What is important is what they mention and what tools and ideas are seen now to be relevant to the future. The contributors, a number of whom have been involved since the start, are active in fractal imaging, and provide a well-informed viewpoint on both the status and the future. Most were invited participants at a meeting on Fractals in Multimedia held at the IMA in January 2001. Some goals of the mini-symposium, shared with this volume, were to demonstrate that the fractal viewpoint leads to a broad collection of useful mathematical tools, common themes, new ways of looking at and thinking about existing algorithms and applications in multimedia, and to consider future developments. This book should be useful to commercial and university researchers in the rapidly evolving field of digital imaging, specifically, chief information officers, professors, software engineers, and graduate students in the mathematical sciences. While much of the content is quite technical, it contains pointers to the state-of-the-art and the future in fractal imaging.

This book is based on notes for the course Fractals: lntroduction, Basics and Perspectives given by MichaelF. Barnsley, RobertL. Devaney, Heinz-Otto Peit gen, Dietmar Saupe and Richard F. Voss. The course was chaired by Heinz-Otto Peitgen and was part of the SIGGRAPH '87 (Anaheim, California) course pro gram. Though the five chapters of this book have emerged from those courses we have tried to make this book a coherent and uniformly styled presentation as much as possible. It is the first book which discusses fractals solely from the point of view of computer graphics. Though fundamental concepts and algo rithms are not introduced and discussed in mathematical rigor we have made a serious attempt to justify and motivate wherever it appeared to be desirable. Ba sic algorithms are typically presented in pseudo-code or a description so close to code that a reader who is familiar with elementary computer graphics should find no problem to get started. Mandelbrot's fractal geometry provides both a description and a mathemat ical model for many of the seemingly complex forms and patterns in nature and the sciences. Fractals have blossomed enormously in the past few years and have helped reconnect pure mathematics research with both natural sciences and computing. Computer graphics has played an essential role both in its de velopment and rapidly growing popularity. Conversely, fractal geometry now plays an important role in the rendering, modelling and animation of natural phenomena and fantastic shapes in computer graphics."

This IMA Volume in Mathematics and its Applications FRACTALS IN MULTIMEDIA is a result of a very successful three-day minisymposium on the same title. The event was an integral part of the IMA annual program on Mathemat ics in Multimedia, 2000-2001. We would like to thank Michael F. Barnsley (Department of Mathematics and Statistics, University of Melbourne), Di etmar Saupe (Institut fUr Informatik, UniversiUit Leipzig), and Edward R. Vrscay (Department of Applied Mathematics, University of Waterloo) for their excellent work as organizers of the meeting and for editing the proceedings. We take this opportunity to thank the National Science Foundation for their support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume grew out of a meeting on Fractals in Multimedia held at the IMA in January 2001. The meeting was an exciting and intense one, focused on fractal image compression, analysis, and synthesis, iterated function systems and fractals in education. The central concerns of the meeting were to establish within these areas where we are now and to develop a vision for the future."

Das Buch, ursprunglich 1993 in englischer Sprache erschienen, ist das Standardwerk zu einem der wichtigsten Kompressionsverfahren fur Bilddateien, geschrieben von den Erfindern Michael Barnsley und Lyman Hurd. Es spannt den Bogen von den mathematischen Grundlagen, von der Modellierung von "Realweltbildern" bis hin zur Realisierung in einer hoeheren Programmiersprache, gewinnt vor dem Hintergrund neuer Multimedia- und Speicheranforderungen hohe Aktualitat. UEbersetzt wurde das Werk sowohl von einem Mathematiker wie einem Informatiker. Das Werk erscheint in der neuen Reihe des Verlages Vieweg: Multimedia-Engineering.