External References

What are some general references on fractals and chaos?

1. M. Barnsley, Fractals Everywhere, Academic Press Inc., 1988. ISBN 0-12-079062-9. This is an excellent text book on fractals. This is probably the best book for learning about the math underpinning fractals. It is also a good source for new fractal types.

2. M. Barnsley and L. Anson, The Fractal Transform, Jones and Bartlett, April, 1993. ISBN 0-86720-218-1. This book is a sequel to Fractals Everywhere. Without assuming a great deal of technical knowledge, the authors explain the workings of the Fractal Transform (tm). The Fractal Transform is the compression tool for storing high-quality images in a minimal amount of space on a computer. Barnsley uses examples and algorithms to explain how to transform a stored pixel image into its fractal representation.

3. R. Devaney and L. Keen, eds., Chaos and Fractals: The Mathematics Behind the Computer Graphics, American Mathematical Society, Providence, RI, 1989. This book contains detailed mathematical descriptions of chaos, the Mandelbrot set, etc.

4. R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley, 1989. ISBN 0-201-13046-7. This book introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas. It goes into great detail on the exact structure of the logistic equation and other 1-D maps. The book is fairly mathematical using calculus and topology.

5. R. L. Devaney, Chaos, Fractals, and Dynamics, 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.

6. R. Devaney, A First Course in Chaotic Dynamical Systems, Theory and Experiment, Addison Wesley, 1992. A nice undergraduate introduction to chaos

and fractals.

7. G. A. Edgar, Measure Topology and Fractal Geometry, Springer- Verlag Inc., 1990. ISBN 0-387-97272-2. This book provides the math necessary for the study of fractal geometry. It includes the background material on metric topology and measure theory and also covers topological and fractal dimension, including the Hausdorff dimension.

8. K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, Wiley, New York, 1990.

9. J. Feder, Fractals, Plenum Press, New York, 1988. This book is recommended as an introduction. It introduces fractals from geometrical ideas, covers a wide variety of topics, and covers things such as time series and R/S analysis that aren't usually considered.

10. J. Gleick, Chaos: Making a New Science, Penguin, New York, 1987.

11. B. Hao, ed., Chaos, World Scientific, Singapore, 1984. This is an excellent collection of papers on chaos containing some of the most significant reports on chaos such as ``Deterministic Nonperiodic Flow'' by E.N.Lorenz.

12. S. Levy, Artificial life : the quest for a new creation, Pantheon Books, New York, 1992. This book takes off where Gleick left off. It looks at many of the same people and what they are doing post-Gleick.

13. B. Mandelbrot, The Fractal Geometry of Nature, W. H. FreeMan and Co., New York. ISBN 0-7167-1186-9. In this book Mandelbrot attempts to show that reality is fractal-like. He also has pictures of many different fractals.

14. H. O. Peitgen and P. H. Richter, The Beauty of Fractals, Springer- Verlag Inc., New York, 1986. ISBN 0-387-15851-0. This book has lots of nice pictures. There is also an appendix giving the coordinates and constants for the color plates and many of the other pictures.

15. H. Peitgen and D. Saupe, eds., The Science of Fractal Images, Springer-Verlag Inc., New York, 1988. ISBN 0-387-96608-0. This book contains many color and black and white photographs, high level math, and several pseudocoded algorithms.

16. H. Peitgen, H. Juergens and D. Saupe, Fractals for the Classroom, Springer-Verlag, New York, 1992. These two volumes are aimed at advanced secondary school students (but are appropriate for others too), have lots of examples, explain the math well, and give BASIC programs.

17. H. Peitgen, H. Juergens and D. Saupe, Chaos and Fractals: New Frontiers of Science, Springer-Verlag, New York, 1992.

18. C. Pickover, Computers, Pattern, Chaos, and Beauty: Graphics from an Unseen World, St. Martin's Press, New York, 1990. This book contains a bunch of interesting explorations of different fractals.

19. J. Pritchard, The Chaos Cookbook: A Practical Programming Guide, Butterworth-Heinemann, Oxford, 1992. ISBN 0-7506-0304-6. It contains type-in-and-go listings in BASIC and Pascal. It also eases you into some of the mathematics of fractals and chaos in the context of graphical experimentation. So it's more than just a type-and-see-pictures book, but rather a lab tutorial, especially good for those with a weak or rusty (or even non-existent) calculus background.

20. P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants, Springer-Verlag, NY, 1990. ISBN 0-387-97297-8. A very good book on L-systems, which can be used to model plants in a very realistic fashion. The book contains many pictures.

21. M. Schroeder, Fractals, Chaos, and Power Laws: Minutes from an Infinite Paradise, W. H. Freeman, New York, 1991. This book contains a clearly written explanation of fractal geometry with lots of puns and word play.

22. J. Sprott, Strange Attractors: Creating Patterns in Chaos, M&T Books (subsidary of Henry Holt and Co.), New York. " ISBN 1-55851-298-5. This book describes a new method for generating beautiful fractal patterns by iterating simple maps and ordinary differential equations. It contains over 350 examples of such patterns, each producing a corresponding piece of fractal music. It also describes methods for visualizing objects in three and higher dimensions and explains how to produce 3-D stereoscopic images using the included red/blue glasses. The accompanying 3.5" IBM-PC disk contain source code in BASIC, C, C++, Visual BASIC for Windows, and QuickBASIC for Macintosh as well as a ready-to-run IBM-PC executable version of the program. Available for $39.95 + $3.00 shipping from M&T Books (1-800-628-9658).

23. D. Stein, ed., Proceedings of the Santa Fe Institute's Complex Systems Summer School, Addison-Wesley, Redwood City, CA, 1988. See especially the first article by David Campbell: ``Introduction to nonlinear phenomena''.

24. R. Stevens, Fractal Programming in C, M&T Publishing, 1989 ISBN 1-55851-038-9. This is a good book for a beginner who wants to write a fractal program. Half the book is on fractal curves like the Hilbert curve and the von Koch snow flake. The other half covers the Mandelbrot, Julia, Newton, and IFS fractals.

25. I. Stewart, Does God Play Dice?: the Mathematics of Chaos, B. Blackwell, New York, 1989.

26. T. Wegner and M. Peterson, Fractal Creations, The Waite Group, 1991. This is the book describing the Fractint program.