This article is from the Fractal FAQ, by Ermel Stepp stepp@muvms6.mu.wvnet.edu with numerous contributions by others.

Some references are:

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.

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.

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.

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.

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.

R. Devaney, _A First Course in Chaotic Dynamical Systems, Theory

and Experiment_, Addison Wesley, 1992. A nice undergraduate

introduction to chaos and fractals.

A. K. Dewdney, (1989, February). Mathematical Recreations. _Scientific

American_, pp. 108-111.

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.

K. Falconer, _Fractal Geometry: Mathematical Foundations and

Applications_, Wiley, New York, 1990.

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.

Y. Fisher (Ed), _Fractal Image Compression: Theory and Application_.

Springer Verlag, 1995.

J. Gleick, _Chaos: Making a New Science_, Penguin, New York, 1987.

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.

H. Jurgens, H. O Peitgen, & D. Saupe. (1990, August).

The Language of Fractals. _Scientific American_, pp. 60-67.

H. Jurgens, H. O. Peitgen, H.O., & D. Saupe. (1992). _Chaos and

Fractals: New Frontiers of Science_. New York: Springer-Verlag.

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.

B. Mandelbrot, _The Fractal Geometry of Nature_, W. H. FreeMan,

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.

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.

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.

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.

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.

T. Wegner and M. Peterson, _Fractal Creations_, The Waite Group,

1991. This is the book describing the Fractint program.

http:wwwrefs.html Web references to Julia and Mandelbrot sets

http://alephwww.cern.ch/~zito/chep94sl/sd.html

Dynamical Systems (G. Zito)

http://alephwww.cern.ch/~zito/chep94sl/chep94sl.html

Scanning huge number of events (G. Zito)

http://www.nonlin.tu-muenchen.de/chaos/Dokumente/WiW/wiw.html

The Who Is Who Handbook of Nonlinear Dynamics

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