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http://irc.umbc.edu/gallery/Fractals/grindex.html Fractal Gallery   
  
http://sashimi.wwa.com:80/mirror/gallerie/fracgall/fg941101.htm   
volume fg941101 (Alan Beck-Virtual Mirror)   
  
http://www.softsource.com/softsource/fractal.html Softsource .  
  
http://www.ncsa.uiuc.edu/SDG/People/rgrant/fav_pics.html   
Favourite Fractals (Ryan Grant)   
  
ftp://csus.edu/pub/alt.fractals.pictures A.F.P. Fractal FTP Archive   
  
http://hydra.cs.utwente.nl/~schol/video.html Eric Schol   
  
http://aleph0.clarku.edu/~djoyce/home.html Mandelbrot and Julia Sets   
(David E. Joyce)   
  
http://aleph0.clarku.edu/~djoyce/newton/newton.html Newton's method .  
  
http://www.vanderbilt.edu/VUCC/Misc/Art1/fractals.html   
Gratuitous Fractals (evans@ctrvax.vanderbilt.edu)   
  
http://www.ccsf.caltech.edu/ismap/image.html Xmorphia   
  
  
Q24b: How do I view fractal pictures from alt.binaries.pictures.fractals?  
A24b: A detailed explanation is given in the "alt.binaries.pictures FAQ"  
(see "pictures-FAQ"). This is posted to the pictures newsgroups and is  
available by ftp: rtfm.mit.edu:/pub/usenet/news.answers/pictures-FAQ  
[18.181.0.24].  
  
In brief, there is a series of things you have to do before viewing these  
posted images. It will depend a little on the system your working with, but  
there is much in common. Some newsreaders have features to automatically  
extract and decode images ready to display ("e" in trn) but if you don't you  
can use the following manual method:  
  
1. Save/append all posted parts sequentially to one file.  
  
2. Edit this file and delete all text segments except what is between the  
BEGIN-CUT and END-CUT portions. This means that BEGIN-CUT and  
END-CUT lines will disappear as well. There will be a section to remove  
for each file segment as well as the final END-CUT line. What is left in the  
file after editing will be bizarre garbage starting with begin 660  
imagename.GIF and then about 6000 lines all starting with the letter "M"  
followed by a final "end" line. This is called a uuencoded file.  
  
3. You must uudecode the uuencoded file. There should be an appropriate  
utility at your site; "uudecode filename" should work under Unix. Ask a  
system person or knowledgeable programming type. It will decode the file and  
produce another file called imagename.GIF. This is the image file.  
  
4. You must use another utility to view these GIF images. It must be  
capable of displaying color graphic images in GIF format. (If you get a JPG  
format file, you may have to convert it to a GIF file with yet another 
utility.)  In the XWindows environment, you may be able to use "xv", 
"xview", or "xloadimage" to view GIF files. If you aren't using X, then 
you'll either have to find a comparable utility for your system or transfer 
your file to some other system. You can use a file transfer utility such 
as Kermit to transfer the binary file to an IBM-PC.  
  
An online resource that may be helpful is:  
  
ftp://ftp.cadence.com/pictures/index.html alt.binaries.pictures utilities  
archive   
  
------------------------------  
  
Subject: Where can I obtain fractal papers?  
  
Q25: Where can I obtain fractal papers?  
A25: There are several Internet sites with fractal papers:  
  
There is an ftp archive site for preprints and programs on nonlinear  
dynamics and related subjects at: lyapunov.ucsd.edu:/pub [132.239.86.10].   
There are also articles on dynamics, including the IMS preprint series,  
available from math.sunysb.edu:/preprints [129.49.31.57].  
  
A collection of short papers on fractal formulas, drawing methods, and  
transforms is available by ftp: ftp.coe.montana.edu:/pub/fractals (this site  
hasn't been working lately).  
  
The WWW site http://inls.ucsd.edu/y/complex.html has  
some fractal papers; they are also available by  
ftp://legendre.ucsd.edu:/pub/Research/Fisher .  
  
The site life.anu.edu.au [150.203.38.74] has a collection of fractal  
programs, papers, information related to complex systems, and gopher and  
World Wide Web connections. The ftp path is:
life.anu.edu.au:/pub/complex_systems .  Look in fractals, tutorial, and 
anu92. The Word Wide Web access is:  
http://life.anu.edu.au/complex_systems/complex.html. The gopher path is:  
Name=BioInformatics gopher at ANU  
Host=life.anu.edu.au  
Type=1  
Port=70  
Path=1/complex_systems/fractals  
  
------------------------------  
  
Subject: How can I join the BITNET fractal discussion?  
  
Q26: How can I join the BITNET fractal discussion?  
A26: There is a fractal discussion on BITNET that uses an automated mail  
server that sends mail to a distribution list. (On some systems, the contents  
of FRAC-L appear in the Usenet newsgroup bit.listserv.frac-l.) To join the  
mailing list, send a message to listserv@gitvm1.gatech.edu or  
listserv@GITVM1 with the following line of text:  
SUBSCRIBE FRAC-L John Doe  
(where John Doe is replaced by your name)  
To unsubscribe, send the message:  
UNSUBSCRIBE FRAC-L or SIGNOFF FRAC-L (GLOBAL)  
  
Messages posted to frac-l are archived along with several files. The index  
of the archive may be obtained by sending email to:  
listserv@GITVM1.BITNET or listserv@GITVM1.GATECH.EDU  
with the sole line of text in the body: INDEX FRAC-L  
  
Files identified in the index (filelist) may then be retrieved by sending  
another message to the listserv with the line of text: GET filename  
(where filename is replaced by the exact name of a file given in the index).  
  
If there is any difficulty contact the listowner: Ermel Stepp  
(stepp@marshall.edu.  
  
------------------------------  
  
Subject: Complexity  
  
Q27: What is complexity?  
A27: Emerging paradigms of thought encompassing fractals, chaos,  
nonlinear science, dynamic systems, self-organization, artificial life, 
neural networks, and similar systems comprise the science of complexity. 
Several helpful online resources on complexity are:  
  
http://www.marshall.edu/~stepp/vri/irc/irc.html  
Institute for Research on Complexity  
  
The site life.anu.edu.au [150.203.38.74] has a collection of fractal  
programs, papers, information related to complex systems, and gopher and  
World Wide Web connections.  
  
 The ftp path is life.anu.edu.au:/pub/complex_systems ; (look in  
 fractals, tutorial, and anu92).  
  
 The gopher path is:  
 gopher://life.anu.edu.au:70/1/complex_systems/fractals  
  
 The Word Wide Web access is  
 http://life.anu.edu.au/complex_systems/complex.html.  
  
http://www.seas.upenn.edu/~ale/cplxsys.html Complex Systems  
(UPENN)  
  
http://jaguar.cssr.uiuc.edu/CCSRHome.html Complex Systems Research  
(UIUC)  
  
http://life.anu.edu.au/ci/ci,html Complexity International Journal or  
ftp://life.anu.edu.au/pub/complex_systems/ci  
  
ftp://xyz.lanl.gov/nlin-sys Nonlinear Science Preprints  
  
Nonlinear Science Preprints via emaiL:  
To subscribe to public bulletin board to receive announcements of the  
availability of preprints from Los Alamos National Laboratory, send email  
to nlin-sys@xyz.lanl.gov containing the sole line of text:  
subscribe your-real-name  
  
------------------------------  
  
Subject: References  
  
Q28a: What are some general references on fractals, chaos, and  
complexity?  
A28a: 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   
  
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.  
  
_FRAC'Cetera_. This is a gazetteer of the world of fractals and related 
areas, supplied on IBM PC format HD disk. FRACTCetera 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.  
  
------------------------------  
  
 Subject: Notices  
  
Q29: Are there any special notices?  
  
NOTICE (from Michael Peters):  
  
HOP - Fractals in Motion  
  
opens the door to a completely new world of fractals!  
  
Based on almost 30 new Hopalong type formulas and loads of incredible  
special effects, it produces an unlimited variety of images/animations  
quite unlike anything you have seen before.  
  
HOP features Fractint-like parameter files, GIF read/write,  
MAP palette editor, a screensaver for DOS, Windows, and OS/2, and more.  
Math coprocessor (386 and above) and SuperVGA required  
  
"HOP was originally based on HOPALONG, the Barry Martin creation which  
was popularized by A.K. Dewdney in one of his Scientific American  
articles. The HOP authors have taken Martin's idea well beyond his  
original concept, and developed it to such a degree that you need to keep  
reminding yourself of its modest beginnings. This program illustrates  
compellingly how a fundamentally simple idea can be extended, through the  
use of various graphics techniques, into something far removed from its  
humble origins. Don't let the simple name fool you - this is serious,  
robust, user friendly, IMAGINATIVE software !"  
(Jon Horner, editor, FRAC'cetera)  
  
$30 shareware  
Written by Michael Peters and Randy Scott  
  
HOP is usually contained in a self-extracting HOPZIP.EXE file.  
Places to download HOPZIP.EXE from:  
  
Compuserve GRAPHDEV forum, lib 4  
The Well under ibmpc/graphics  
slopoke.mlb.semi.harris.com  
ftp.uni-heidelberg.de (under /pub/msdos/graphics)  
spanky.triumf.ca [128.189.128.27] (under pub.fractals.programs.ibmpc)  
  
HOP WWW page: http://rever.nmsu.edu/~ras/hop  
  
HOP mailing list: write to hop-request@acca.nmsu.edu  
  
To subscribe to the HOP mailing list, simply send a message with the  
word "subscribe" in the Subject: field. For information, send a message  
with the word "INFO" in the Subject: field.  
  
One thing that I forgot to mention about HOP is that it is contained in   
the December issue of Jon Horner's FRAC'cetera magazine, and that   
FRAC'cetera subscribers can register HOP for $20 instead of $30.  
  
NOTICE from J. C. (Clint) Sprott (SPROTT@juno.physics.wisc.edu):  
  
The program, Chaos Data Analyzer, which I authored is a research and 
teaching tool containing 14 tests for detecting hidden determinism in a  
seemingly random time series of up to 16,382 points provided by the user in  
an ASCII data file. Sample data files are included for model chaotic  
systems. When chaos is found, calculations such as the probability  
distribution, power spectrum, Lyapunov exponent, and various measures of  
the fractal dimension enable you to determine properties of the system  
Underlying the behavior. The program can be used to make nonlinear  
predictions based on a novel technique involving singular value  
decomposition. The program is menu-driven, very easy to use, and even  
Contains an automatic mode in which all the tests are performed in succession  
and the results are provided on a one-page summary.  
  
Chaos Data Analyzer requires an IBM PC or compatible with at least 512K  
of memory. A math coprocessor is recommended (but not required) to  
Speed some of the calculations. The program is available on 5.25 or 3.5"  
disk and includes a 62-page User's Manual. Chaos Data Analyzer is peer-  
reviewed software published by Physics Academic Software, a cooperative  
Project of the American Institute of Physics, the American Physical Society,  
And the American Association of Physics Teachers.  
  
Chaos Data Analyzer and other related programs are available from The  
Academic Software Library, North Carolina State University, Box 8202,  
Raleigh, NC 27695-8202, Tel: (800) 955-TASL or (919) 515-7447 or  
Fax: (919) 515-2682. The price is $99.95. Add $3.50 for shipping in U.S.  
or $12.50 for foreign airmail. All TASL programs come with a 30-day,  
money-back guarantee.  
  
NOTICE from Noel Giffin (noel@erich.triumf.ca):  
  
Welcome to the Spanky Fractal Database   
  
This is a collection of fractal's and fractal related material for free  
distribution on the net. Most of the software was gathered from various  
ftp sites on the internet and it is generally freeware or shareware. Please  
abide by the guidelines set down in the individual packages. I would also  
like to make a disclaimer here. This page points to an enormous amount  
of information and no single person has the time to thoroughly check it  
all. I have tested software when I had the resources, and read through  
papers when I had the time, but other than certifying that it is related to  
fractals I can't assume any other responsibility.   
  
Enjoy and discover.   
  
	The correct URL for this site is:  
  
	http://spanky.triumf.ca/  
  
------------------------------  
  
Subject: Acknowledgements  
  
Q30: Who has contributed to the Fractal FAQ?  
A30:  
  
Participants in the Usenet group sci.fractals and the listserv forum frac-l  
have provided most of the content of Fractal FAQ. For their help with this  
FAQ, special thanks go to:  
  
Alex Antunes, Steve Bondeson, Erik Boman, Jacques Carette, John Corbit,  
Abhijit Deshmukh, Tony Dixon, Robert Drake, Detlev Droege, Gerald  
Edgar, Gordon Erlebacher, Yuval Fisher, Duncan Foster, David Fowler,  
Murray Frank, Jean-loup Gailly, Noel Giffin, Earl Glynn, Jon Horner, Lamont  
Granquist, Luis Hernandez- Ure:a, Jay Hill, Arto Hoikkala, Carl Hommel,  
Robert Hood, Oleg Ivanov, Simon Juden, J. Kai-Mikael, Leon Katz, Matt  
Kennel, Tal Kubo, Jon Leech, Brian Meloon, Tom Menten, Guy Metcalfe,  
Eugene Miya, Lori Moore, Robert Munafo, Miriam Nadel, Ron Nelson,  
Tom Parker, Dale Parson, Matt Perry, Cliff Pickover, Francois Pitt, Kevin  
Ring, Michael Rolenz, Tom Scavo, Jeffrey Shallit, Rollo Silver, J. C. Sprott,  
Ken Shirriff, Gerolf Starke, Bruce Stewart, Dwight Stolte, Tommy Vaske,  
Tim Wegner, Andrea Whitlock, Erick Wong, Wayne Young, and others.  
  
Special thanks to Matthew J. Bernhardt (mjb@acsu.buffalo.edu) for  
collecting many of the chaos definitions.  
  
------------------------------  
  
Subject: Copyright  
  
Q31: Copyright?  
A31: Copyright (c) 1995 Ermel Stepp; 1994, 1993 Ken Shirriff  
  
The Fractal FAQ was created by Ken Shirriff and edited by him through  
September 26, 1994. The current editor of the Fractal FAQ is Ermel Stepp.  
Standing permission is given for non-profit reproduction and distribution of  
this issue of the Fractal FAQ as a complete document. Contact the editor for  
further information:  
  
Dr. Ermel Stepp  
Editor, Fractal FAQ  
Marshall University  
Huntington, WV 25755-2440  
(stepp@marshall.edu).  
  

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