This article is from the sci.fractals FAQ, by Michael C. Taylor and Jean-Pierre Louvet with numerous contributions by others.
E. Ott, "Chaos in dynamical systems", Cambridge University Press,
E. Ott, T. Sauer, J.A. Yorke (ed.) "Coping with chaos : analysis of
chaotic data and the exploitation of chaotic systems", New York, J.
D. Peak and M. Frame, "Chaos Under Control: The Art and Science of
Complexity", W.H. Freeman and Company, New York 1994, ISBN
0-7167-2429-4 "The book is written at the perfect level to help a
beginner gain a solid understanding of both basic and subtler appects
of chaos and dynamical systems." - a review from the back cover
H. O. Peitgen and P. H. Richter, "The Beauty of Fractals",
Springer-Verlag, 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
H. Peitgen and D. Saupe, eds., "The Science of Fractal Images",
Springer-Verlag, 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.
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
H. Peitgen, H. Juergens and D. Saupe, "Chaos and Fractals: New
Frontiers of Science", Springer-Verlag, New York, 1992.
E. Peters, "Fractal Market Analysis - Applying Chaos Theory to
Investment & Economics", John Wiley & Sons, 1994, ISBN 0-471-58524-6.
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.
C. Pickover, "Keys to Infinity", (1995) John Wiley: NY. ISBN
C. Pickover, (1995) "Chaos in Wonderland: Visual Adventures in a
Fractal World." St. Martin's Press: New York. ISBN 0-312-10743-9.
(Devoted to the Lyapunov exponent.)
C. Pickover, "Computers and the Imagination" (Subtitled: Visual
Adventures from Beyond the Edge) (1993) St. Martin's Press: New York.
C. Pickover. "The Pattern Book: Fractals, Art, and Nature" (1995)
World Scientific. ISBN 981-02-1426-X Some of the patterns are
ultramodern, while others are centuries old. Many of the patterns are
drawn from the universe of mathematics.
C. Pickover, "Visualizing Biological Information" (1995) World
Scientific: Singapore, New Jersey, London, Hong Kong.
on the use of computer graphics, fractals, and musical techniques to
find patterns in DNA and amino acid sequences.
C. Pickover, "Fractal Horizons: The Future Use of Fractals." (1996)
St. Martin's Press, New York.
Speculates on advances in the 21st Century. Six broad sections:
Fractals in Education, Fractals in Art, Fractal Models and Metaphors,
Fractals in Music and Sound, Fractals in Medicine, and Fractals and
Mathematics. Topics include: challenges of using fractals in the
classroom, new ways of generating art and music, the use of fractals
in clothing fashions of the future, fractal holograms, fractals in
medicine, fractals in boardrooms of the future, fractals in chess.
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 nonexistent) calculus
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.
Edward R. Scheinerman, "Invitation to Dynamical Systems",
Prentice-Hall, 1996, ISBN 0-13-185000-8, xvii + 373 pages
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.
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).
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
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.
I. Stewart, "Does God Play Dice?: the Mathematics of Chaos", B.
Blackwell, New York, 1989.
Y. Takahashi, "Algorithms, Fractals, and Dynamics", Plenum Pub Corp,
(May) 1996, ISBN: 0306451271 Subjects: Differentiable dynamical syste,
Congresses, Fractals, Algorithms, Differentiable Dynamical Systems,
Algorithms (Computer Programming)
T. Wegner and B. Tyler, "Fractal Creations", 2nd ed. The Waite Group,
1993. ISBN 1-878739-34-4 This is the book describing the Fractint