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,

1993.

E. Ott, T. Sauer, J.A. Yorke (ed.) "Coping with chaos : analysis of

chaotic data and the exploitation of chaotic systems", New York, J.

Wiley, 1994.

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

pictures.

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

programs.

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

0-471-11857-5.

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

background.

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

nonlinear phenomena".

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

program.

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