This lovely little book will take off and fly on its own power, but the author has asked me to write a few words, and one should not say no to a friend. Specific topics in fractal geometry and its applications have already benefited from several excellent surveys of moderate length, and gossip and preliminary drafts tell us that we shall soon see several monographic treatments of broader topics. For the teacher, however, these surveys and monographs are not enough, and an urgent need for more helpful books has been widely recognized. To write such a book is no easy task, but Jens Feder meets the challenge head on. His approach combines the old Viking's willingness to attack many difficulties at the same time, and the modern Norwegian's ability to achieve fine balance between diverging needs. lowe him special gratitude for presenting the main facts about R/ S analysis of long-run dependence; now a wide scientific public will have access to a large group of papers of mine that had until this day remained fairly confidential. Last but not least, we are all grateful to Jens for not having allowed undue personal modesty to deprive us of accounts of his own group's varied and excellent work. He did not attempt to say everything, but what he said is just fine. Benoit B. Mandelbrot Physics Department, IBM Thomas J.

Inhalt

The Fractal Dimension.- The Cluster Fractal Dimension.- Viscous Fingering in Porous Media.- Cantor Sets.- Multifractal Measures.- Percolation.- Fractal Records in Time.- Random Walks and Fractals.- Self-Similarity and Self-Affinity.- Wave-Height Statistics.- The Perimeter-Area Relation.- Fractal Surfaces.- Observations of Fractal Surfaces.