HYDROLOGICAL PROCESSES BOOK REVIEW Hydrol. Process. 16, 3097 – 3098 (2002) Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/hyp.5059 A Mathematical River Walk Fractal River Basins: Chance and Self-Organization Ignacio Rodr´ ıguez-Iturbe and Andrea Rinaldo (Eds.) Cambridge University Press, Cambridge, UK, 547pp US$120 ISBN-0-521-47398-5 (hardback) Published 1997; US$50 ISBN 0-521-00405-5 (paperback) Published 2001 Reviewer: Glenn E. Moglen Department of Civil and Environmental Engineering, University of Maryland, College Park, MD 20742, USA Correspondence to: Glenn E. Moglen, University of Maryland, Civil & Environmental Engineering, 1173 Martin Hall, USA. E-mail: moglen@eng.umd.edu Cover, reprinted with the permission of Cambridge University Press. Fractal River Basins: Chance and Self-Organization by Ignacio Rodr´ ıguez-Iturbe and Andrea Rinaldo is a compilation and revisitation of the published journal writings of these two central authors and many of their colleagues over the last 10–15 years. The authors have worked extensively in the analysis of natural drainage networks and simulation of drainage networks using a set of governing, process-based, equations maintaining a minimization of energy as water flows across the landscape. This book brings together their ideas in one location and allows the reader interested in this area to review an impressive amount of work quickly and easily. But be warned, the text requires considerable mathematical sophistication from the reader and one would do well to have access to or previous experience with the ‘new math’ texts on fractals and chaos theory, such as the one edited by Pietgen and Saupe (1988). Additionally, a strong grounding in theoretical geomorphology would serve the reader well. That said, were I to encounter a newly beginning graduate student with interests in this area, I would heartily recommend this book for the foundation of knowledge and inspiration it provides. Below I describe the central themes that the reader will find. A summary of the basic content of this book is merited. The initial chapter, entitled a Leopoldesque, ‘A View of River Basins’ provides an excellent review of many fundamental geomorphic measures and drainage network simulation models. Much of the value for a newcomer to this area is contained in this single chapter. Chapters 2 and 3 begin the presentation of the work of Rodr´ ıguez-Iturbe and Rinaldo on fractals, multifractals, and power-law relationships. These chapters generally examine the planar structure of drainage networks: lengths, drainage areas, and the width function. Entropy and drainage network energy, which is the heart of the book’s theme, is more greatly elaborated in Chapter 4. A central contribution of these authors is the use of the concept of minimum energy expenditure to produce what the authors have coined ‘optimal channel networks’ (OCNs). In this chapter the authors present a range of compelling pictures of simulated networks and network statistics that make a convincing case that OCNs produce drainage structures similar to those observed in nature. Following on this theory, Chapters 5 and 6 invoke the concept of self-organized criticality to broaden the range of models presented by the authors and to produce two- and three-dimensionally realistic drainage networks and landscapes. Finally, in Chapter 7 of this book, the authors examine the linkage between geomorphic structure Copyright  2002 John Wiley & Sons, Ltd. 3097