Books on fractals

With a little luck, most of these are on reserve at CARLSON.

  1. Encounters with Chaos by Denny Gulick, McGraw- Hill, 1992. The textbook for this course.
  2. Fractals Everywhere by Michael Barnsley, Academic Press Inc., second edition 1993. ISBN 0-12-079061-0. This is an excellent textbook on fractals. This is probably the best book for learning about the mathematics behind iterated function systems. It is also a good source for new fractal types.
  3. Fractals: Endlessly Repeating Geometrical Figures, Hans Lauwerier, Princeton Science Library. 1991. This book has a light touch and a hands on approach. There is a very handy section on complex arithmetic (which is essential for understanding the Mandelbrot set and the classical Julia sets) and a collection of over 40 BASIC programs for producing the fractals shown in the text.
  4. Fractals: An Animated Discussion with Benoit Mandelbrot and Edward Lorenz, the video shown on the first day of class.
  5. A first course in chaotic dynamical systems: theory and experiment by Robert L. Devaney, Addison-Wesley, 1992. ISBN 0-2015-5406-2. Undergraduate level textbook with lots of interesting homework problems.
  6. The Fractal Geometry of the Mandelbrot Set and The Fractal Geometry of the Mandelbrot Set II by Robert L. Devaney, two hypertext papers explaining some basic mathematics behind the Mandelbrot set. This includes an explanation of the periods associated with the bulbs on the Mandelbrot set.
  7. The Fractal Geometry of Nature, Benoit Mandelbrot, New York: W. H. Freeman and Company. ISBN 0-7167-1186-9. 1982. (This book's predecessor, Fractals: Form, Chance and Dimension, 1977, was the first published book on the subject.) In this book Mandelbrot attempts to show that reality is fractal-like. He also has pictures of many different fractals.
  8. Fractal Image Compression, Michael Barnsley and Lyman P. Hurd, AK Peters, Ltd., 1993. ISBN 1-56881-000-8. Detailed discussion of image compression is iterated function systems. Includes several C program listings. Here is a review of this book.
  9. The Beauty of Fractals, H. O. Peitgen and P. H. Richter, New York: Springer-Verlag Inc. 1986. ISBN 0-387-15851-0. A classic with lots of striking pictures and well written discussion of some of the mathematical theory. There is also an appendix giving the coordinates and constants for the color plates and many of the other pictures. The authors were the first to produce really spectacular color pictures of the Mandelbrot and Julia sets, and they made it into a travelling science museum show (``Frontiers of Chaos'') in the mid '80s. The book includes Adrien Douady's excellent article Julia sets and the Mandelbrot set.
  10. The Science of Fractal Images, ed. H. O. Peitgen and P. H. Richter, New York: New York: Springer-Verlag Inc. 1988. ISBN 0- 387- 96608-0. This book contains many color and black and white photographs, high level math, and several pseudocoded algorithms.
  11. Chaos by James Gleick (1987). A bestseller giving an overview of the field from a layman's point of view. It is very readable, but in the latter chapters the author's lack of mathematical background cramps his style. Here is an essay on chaos by him.
  12. Does God Play Dice?: The Mathematics of Chaos, Ian Stewart (1990). A very readable book written by an accomplished popularizer of mathematics.
  13. Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics, Robert L. Devaney, Addison-Wesley. 1990. ISBN 0-201- 23288-X. This is a very readable book. It introduces chaos, fractals, and dynamics using a combination of hands-on computer experimentation and precalculus math. Numerous full-color and black and white images convey the beauty of these mathematical ideas. There is also a video with the same title.
  14. Transition to Chaos: The Orbit Diagram and the Mandelbrot Set, video by Robert L. Devaney.
  15. Fractal Geometry, Ken Falconer.
  16. An Introduction to Chaotic Dynamical Systems, Robert L. Devaney, Second Edition. Addison-Wesley. 1989. ISBN 0-201-13046-7. This book only assumes a knowledge of calculus and introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.
  17. Chaos and Fractals: The Mathematics Behind the Computer Graphics, R. Devaney and L. Keen. This book contains detailed mathematical descriptions of chaos, the Mandelbrot set, etc.
  18. Computers, Pattern, Chaos, and Beauty, C. Pickover. This book contains some interesting explorations of different fractals.
  19. Fractal Creations. This is the book on the FRACTINT program. It has gotten mixed reviews.
  20. Fractals for the Classroom, Peitgen, J\"{urgens, Saupe. This book is aimed at advanced secondary school students (but is appropriate for others too), has lots of examples, explains the math well, and gives BASIC programs.
  21. Fractals, Chaos, and Power Laws, M. Schroeder. This book contains a clearly written explanation of fractal geometry, with lots of puns and word play.
  22. Chaos and Fractals: New Frontiers of Science, H. Peitgen, H. J\"{urgens, D. Saupe. Springer-Verlag. 1992. 984 pages. Thorough, lavishly illustrated and readable introduction to the subject.
  23. COMPLEX DYNAMICAL SYSTEMS: THE MATHEMATICS BEHIND THE MANDELBROT AND JULIA SETS, edited by Robert L. Devaney. Proceedings of the Symposia in Applied Mathematics, Vol. 49, American Mathematical Society, Providence, RI. ISBN 0-8218-0290-9.

Last revised November 9, 1997.

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