Fractals

1. Front Matter

   Pages i-xxv

   PDF

2. Introduction

   • Jens Feder

   Pages 1-5

3. The Fractal Dimension

   • Jens Feder

   Pages 6-30

4. The Cluster Fractal Dimension

   • Jens Feder

   Pages 31-40

5. Viscous Fingering in Porous Media

   • Jens Feder

   Pages 41-61

6. Cantor Sets

   • Jens Feder

   Pages 62-65

7. Multifractal Measures

   • Jens Feder

   Pages 66-103

8. Percolation

   • Jens Feder

   Pages 104-148

9. Fractal Records in Time

   • Jens Feder

   Pages 149-162

10. Random Walks and Fractals

    • Jens Feder

    Pages 163-183

11. Self-Similarity and Self-Affinity

    • Jens Feder

    Pages 184-192

12. Wave-Height Statistics

    • Jens Feder

    Pages 193-199

13. The Perimeter-Area Relation

    • Jens Feder

    Pages 200-211

14. Fractal Surfaces

    • Jens Feder

    Pages 212-228

15. Observations of Fractal Surfaces

    • Jens Feder

    Pages 229-243

16. Back Matter

    Pages 244-283

    PDF

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.

• Cantor
• Mandelbrot
• geometry
• linear optimization
• statistics

`This lovely little book will take off and fly far.'
Benoit Mandelbrot, author of The Fractal Geometry of Nature

• Department of Physics, University of Oslo, Oslo, Norway

  Jens Feder

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