FRACTAL, page 30 of 36, hit 002'364

Q28a:

What are some general references on fractals, chaos, and complexity?

A28a:

Some references are:

M. Barnsley, Fractals Everywhere, Academic Press Inc., 1988, 1993. 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, The Desktop Fractal Design System Versions 1 and 2. 1992,

1988. Academic Press. Available from Iterated Systems.

M. Barnsley and P H Lyman, Fractal Image Compression. 1993. AK Peters

Limited. Available from Iterated Systems.

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.

L. Gardini (ed), Chaotic Dynamics in Two-Dimensional Noninvertive Maps.

World Scientific 1996, ISBN: 9810216475

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.

I. Hargittai and C. Pickover. Spiral Symmetry 1992 World Scientific

Publishing, River Edge, New Jersey 07661. ISBN 981-02-0615-1. Topics: Spirals

in nature, art, and mathematics. Fractal spirals, plant spirals, artist's

spirals, the spiral in myth and literature... Loads of images.

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.

B. Mandelbrot, Les objets fractals, Flammarion, Paris. ISBN 2-08-211188-1.

The French Mandelbrot's book, where the word fractal has been used for the

first time.

J.L. McCauley, Chaos, dynamics, and fractals : an algorithmic approach to

deterministic chaos, Cambridge University Press, 1993.

E. R. Mac Cormac (ed), M. Stamenov (ed), Fractals of Brain, Fractals of

Mind : In Search of a Symmetry Bond (Advances in Consciousness Research, No

7), John Benjamins, ISBN: 1556191871, Subjects include: Neural networks

(Neurobiology), Mathematical models, Fractals, and Consciousness

G.V. Middleton, (ed), 1991: Nonlinear Dynamics, Chaos and Fractals (w/

application to geological systems) Geol. Assoc. Canada, Short Course Notes

Vol. 9, 235 p. This volume contains a disk with some examples (also as pascal

source code) ($25 CDN)

T.F. Nonnenmacher, G.A Losa, E.R Weibel (ed.) Fractals in Biology and

Medicine Birkhaeuser Verlag

L. Nottale, Fractal Space-Time and Microphysics, Towards a Theory of Scale

Relativity, World Scientific (1993).

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 on 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.

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.

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.

Q28b:

What are some relevant journals?

A28b:

Some relevant journals are:

"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 I. Stewart in Scientific American.

Fractal Report. Reeves Telecommunication Labs. West Towan House,

Porthtowan, TRURO, Cornwall TR4 8AX, U.K. WWW:

http://ourworld.compuserve.com/homepages/JohndeR/fractalr.htm Email:

John@longevb.demon.co.uk (John de Rivaz)

FRAC'Cetera. This is a gazetteer of the world of fractals and related

areas, supplied on IBM PC format HD disk. FRACT'Cetera is the home of FRUG -

the Fractint User Group. For more information, contact: Jon Horner, Editor,

FRAC'Cetera Le Mont Ardaine, Rue des Ardains, St. Peters Guernsey GY7 9EU

Channel Islands, United Kingdom. Email: 100112.1700@compuserve.com

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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Q28c:

What are some other Internet references?

A28c:

Some other Internet references:

Web references to nonlinear dynamics

Dynamical Systems (G. Zito)

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

Scanning huge number of events (G. Zito)

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

The Who Is Who Handbook of Nonlinear Dynamics

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