Q27: What are some general references on fractals and chaos?
A27: Some references are:

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

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.


"Chaos and Graphics" section in the quarterly journal _Computers and
Graphics_.  This contains recent work in fractals from the graphics
perspective, and usually contains several exciting new ideas.

"Mathematical Recreations" section by A. K. Dewdney in _Scientific American_.

Algorithm - The Personal Computer Newsletter.  P.O. Box 29237, Westmount
Postal Outlet, 785 Wonderland Road S., London, Ontario, Canada, N6K 1M6.

Fractal Report.  Reeves Telecommunication Labs. West Towan House, Porthtowan,
TRURO, Cornwall TR4 8AX, U.K.

Amygdala.  P.O. Box 219 San Cristobal, NM  87564-0219.  This is a newsletter
about the Mandelbrot Set and other fractals.  A trial subscription for 6
issues is $15 to: Amygdala Box 219 / San Cristobal, NM 87564.  Contact Rollo
Silver ( for more information.

FRAC'Cetera.  This is a gazetteer of the world of fractals and related areas,
supplied in IBM PC format HD disk.  For more information, contact:  Jon
Horner, Editor, FRAC'Cetera, Le Mont Ardaine, Rue des Ardains, St. Peters,
Guernsey GY7 9EU, Channel Islands, United Kingdom.

Fractals, An interdisciplinary Journal On The Complex Geometry of Nature.
This is a new journal published by World Scientific.  B.B Mandelbrot is the
Honorary Editor and T. Vicsek, M.F. Shlesinger, M.M Matsushita are the
Managing Editors).  The aim of this first international journal on fractals is
to bring together the most recent developments in the research of fractals so
that a fruitful interaction of the various approaches and scientific views on
the complex spatial and temporal behavior could take place.
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