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Fantastic Fractals. This program can draw several sorts of fractals
(IFS, L-system, Julia...). Well designed for IFS.
http://library.advanced.org/12740/
Screen savers
Free screen savers : By Philip Baker ()
http://www.pjbsware.demon.co.uk/snsvdsp.htm
JuliaSaver : a W95 screen saver that does real-time fractals, by
Damien M. Jones ()
http://www.icd.com/tsd/juliasaver/
IFS screen saver: a Windows 3 screen saver, by Bill Decker
()
http://www.geocities.com/SoHo/Studios/1450/
Fractint Screen Saver: a Windows 95 - NT screen saver, by Thore
Berntsen ; needs the DOS program Fractint ()
http://home.sol.no/~thbernt/fintsave.htm
Seractal Screen Saver: Windows 3 and Windows 95 time limited versions
(shareware) (
http://www.seraline.com/seractal.htm
the Orb series by 'O' from RuneTEK. For MS-Windows 95/NT only.
http://www.hypermart.net/runetek/
For SunView:
Mandtool: generates Mandelbrot Set
http://fractal.mta.ca/spanky/programs/mandtool/m_tar.z
ftp://spanky.triumf.ca/fractals/programs/mandtool/M_TAR.Z
For Unix/C:
lsys: L-systems as PostScript (in C++)
ftp://ftp.cs.unc.edu/pub/users/leech/lsys.tar.gz
lyapunov: PGM Lyapunov exponent images
ftp://ftp.uu.net/usenet/comp.sources.misc/volume23/lyapunov/
SPD: fractal mountain, tree, recursive tetrahedron
ftp://ftp.povray.org/pub/povray/spd/
Fractal Studio: Mandelbrot set; handles distributed computing
ftp://archive.cs.umbc.edu/pub/peter/fractal-studio
fanal: analysis of fractal dimension for Linux by Jürgen Dollinger
ftp://ftp.uni-stuttgart.de/pub/systems/linux/local/math/fanal-0
1b.tar.gz
XaoS, by Jan Hubicka, fast portable real-time interactive fractal
zoomer. supports X11 (8,15,16,24,31-bit colour, StaticGray,
StaticColor), Curses, Linux/SVGAlib
http://www.paru.cas.cz/~hubicka/XaoS/
For X windows :
xmntns xlmntn: fractal mountains
ftp://ftp.uu.net/usenet/comp.sources.x/volume8/xmntns
xfroot: fractal root window
X11 distribution
xmartin: Martin hopalong root window
X11 distribution
xmandel: Mandelbrot/Julia sets
X11 distribution
lyap: Lyapunov exponent images
ftp://ftp.uu.net/usenet/comp.sources.x/volume17/lyapunov-xlib
spider: Uses Thurston's algorithm, Kobe algorithm, external angles
http://inls.ucsd.edu/y/Complex/spider.tar.Z
xfractal_explorer: fractal drawing program
ftp://ftp.x.org/contrib/applications/xfractal_explorer-v1.0.tar
.gz
Xmountains: A fractal landscape generator
ftp://ftp.epcc.ed.ac.uk/pub/personal/spb/xmountains
xfractint: the Unix version of Fractint : look at XFRACTxxx (xxx being
the version number)
http://spanky.triumf.ca/www/fractint/getting.html
xmfract v1.4: Needs Motif 1.2+, based on FractInt
http://hpftp.cict.fr/hppd/hpux/X11/Misc/xmfract-1.4/
Fast Julia Set and Mandelbrot for X-Windows by Zsolt Zsoldos
http://www.chem.leeds.ac.uk/ICAMS/people/zsolt/mandel.html
XaoS realtime fractal zoomer for X11 or SVGAlibs by Jan Hubicka
http://www.paru.cas.cz/~hubicka/XaoS/
AlmondBread-0.2. Fast algorithm ; simultaneous orbit iteration ;
Fractint-compatible GIF and MAP files ; Tcl/Tk user interface
(Michael R. Ganss )
http://www.cs.tu-berlin.de/~rms/AlmondBread/
Quat - A 3D-Fractal-Generator (Quaternions).
http://wwwcip.rus.uni-stuttgart.de/~phy11733/quat_e.html
XFracky 2.5 by Henrik Wann Jensen based on Tcl/Tk
http://www.gk.dtu.dk/~hwj/
http://sunsite.unc.edu/pub/Linux/X11/apps/math/fractals/
Distributed X systems:
MandelSpawn: Mandelbrot/Julia on a network
ftp://ftp.x.org/R5contrib/mandelspawn-0.07.tar.Z
ftp://ftp.funet.fi/pub/X11/R5contrib/mandelspawn-0.07.tar.Z
gnumandel: Mandelbrot on a network
ftp://ftp.elte.hu/pub/software/unix/gnu/gnumandel.tar.Z
Software for computing fractal dimension:
_Fractal Dimension Calculator_ is a Macintosh program which uses the
box-counting method to compute the fractal dimension of planar
graphical objects.
http://wuarchive.wustl.edu/edu/math/software/mac/fractals/FDC/
http://wuarchive.wustl.edu/packages/architec/Fractals/FDC2D.sea.hqx
http://wuarchive.wustl.edu/packages/architec/Fractals/FDC3D.sea.hqx
_FD3_: estimates capacity, information, and correlation dimension from
a list of points. It computes log cell sizes, counts, log counts, log
of Shannon statistics based on counts, log of correlations based on
counts, two-point estimates of the dimensions at all scales examined,
and over-all least-square estimates of the dimensions.
ftp://inls.ucsd.edu/pub/cal-state-stan
for an enhanced Grassberger-Procaccia algorithm for correlation
dimension.
A MS-DOS version of FP3 is available by request to
gentry@altair.csustan.edu.
Subject: FTP questions
_Q24a_: How does anonymous ftp work?
_A24a_: Anonymous ftp is a method of making files available to anyone
on the Internet. In brief, if you are on a system with ftp (e.g.
Unix), you type "ftp fractal.mta.ca", or whatever system you wish to
access. You are prompted for your name and you reply "anonymous". You
are prompted for your password and you reply with your email address.
You then use "ls" to list the files, "cd" to change directories, "get"
to get files, an "quit" to exit. For example, you could say "cd /pub",
"ls", "get README", and "quit"; this would get you the file "README".
See the man page ftp(1) or ask someone at your site for more
information.
In this FAQ, anonymous ftp addresses are given in the URL form
ftp://name.of.machine/pub/path [138.73.1.18]. The first part is the
protocol, FTP, rather than say "gopher", the second part
"name.of.machine" is the machine you must ftp to. If your machine
cannot determine the host from the name, you can try the numeric
Internet address: "ftp 138.73.1.18". The part after the name:
"/pub/path" is the file or directory to access once you are connected
to the remote machine.
_Q24b_: What if I can't use ftp to access files?
_A24b_: If you don't have access to ftp because you are on a UUCP,
Fidonet, BITNET network there is an e-mail gateway at
ftpmail@decwrl.dec.com that can retrieve the files for you. To get
instructions on how to use the ftp gateway send a message to
ftpmail@decwrl.dec.com with one line containing the word "help".
Warning, these archives can be very large, sometimes several megabytes
(MB) of data which will be sent to your e-mail address. If you have a
disk quota for incoming mail, often 1MB or less, be careful not exceed
it.
Subject: Archived pictures
_Q25a_: Where are fractal pictures archived?
News groups
_A25a_: Fractal images (GIFs, JPGs...) are posted to
alt.binaries.pictures.fractals (also known as abpf); this newsgroup
has replaced alt.fractals.pictures. However, several
alt.binaries.pictures groups being badly reputed,
alt.fractals.pictures seems to have some new activity.
The fractals posted in alt.binaries.pictures.fractals are recorded daily at
http://www.xmission.com/~legalize/fractals/index.html
http://galaxy.uci.agh.edu.pl/pictures//alt.binaries.pictures.fractals/
last.html
http://www.cs.uni-magdeburg.de/pictures/Usenet/fractals/summary/
The following lists are scanty and will evolve soon.
Other archives and university sites (images, tutorials...)
Many Mandelbrot set images are available via
ftp://ftp.ira.uka.de/pub/graphic/fractals
Pictures from 1990 and 1991 are available via anonymous ftp at
ftp://csus.edu/pub/alt.fractals.pictures
Fractal images including some recent alt.binaries.pictures.fractals
images are archived at ftp://spanky.triumf.ca/fractals
This can also be accessed via WWW at http://spanky.triumf.ca/ or
http://fractal.mta.ca/spanky/
From Paris, France one of the largest collections (>= 820MB) is Frank
Roussel's at http://www.cnam.fr/fractals.html
Fractal animations in MPEG and FLI format are in
http://www.cnam.fr/fractals/anim.html
In Bordeaux (France) there is a mirror of this site,
http://graffiti.cribx1.u-bordeaux.fr/MAPBX/roussel/fractals.htm
l
and a Canadian mirror at http://fractal.mta.ca/cnam/
Another collection of fractal images is archived at
ftp://ftp.maths.tcd.ie/pub/images/Computer
Fractal Microscope
http://www.ncsa.uiuc.edu/Edu/Fractal/Fractal_Home.html
"Contours of the Mind"
http://online.anu.edu.au/ITA/ACAT/contours/contours.html
Spanky Fractal Datbase (Noel Giffin)
http://spanky.triumf.ca/www/spanky.html
Yahoo Index of Fractal Art
http://www.yahoo.com/Arts/Visual_Arts/Computer_Generated/Fracta
ls/
Geometry Centre at University of Minnesota
http://www.geom.umn.edu/graphics/pix/General_Interest/Fractals/
Computer Graphics Gallery
http://www.maths.tcd.ie/pub/images/images.html
Many fractal creators have personal web pages showing images, tutorials...
Flame Index A collection of interesting smoke- and flame-like jpeg
iterated function system images
http://www.cs.cmu.edu/~spot/flame.htm
Some images are also available from:
ftp://hopeless.mess.cs.cmu.edu/spot/film/
Cliff Pickover
http://sprott.physics.wisc.edu/pickover/home.htm
Fractal Gallery (J. C. Sprott) Personal images and a thousand of
fractals collected in abpf
http://sprott.physics.wisc.edu/fractals.htm
Fractal from Ojai (Art Baker)
http://www.bhs.com/ffo/
Skal's 3D-fractal collection (Pascal Massimino)
http://www.eleves.ens.fr:8080/home/massimin/quat/f_gal.ang.html
3d Fractals (Stewart Dickson) via Mathart.com
http://www.wri.com/~mathart/portfolio/SPD_Frac_portfolio.html
Dirk's 3D-Fractal-Homepage
http://wwwcip.rus.uni-stuttgart.de/~phy11733/index_e.html
Softsource
http://www.softsource.com/softsource/fractal.html
Favourite Fractals (Ryan Grant)
http://www.ncsa.uiuc.edu/SDG/People/rgrant/fav_pics.html
Eric Schol
http://snt.student.utwente.nl/~schol/gallery/
Mandelbrot and Julia Sets (David E. Joyce)
http://aleph0.clarku.edu/~djoyce/home.html
Newton's method
http://aleph0.clarku.edu/~djoyce/newton/newton.html
Gratuitous Fractals (evans@ctrvax.vanderbilt.edu)
http://www.vanderbilt.edu/VUCC/Misc/Art1/fractals.html
Xmorphia
http://www.ccsf.caltech.edu/ismap/image.html
Fractal Prairie Page (George Krumins)
http://www.prairienet.org/astro/fractal.html
Fractal Gallery (Paul Derbyshire)
http://chat.carleton.ca/~pderbysh/fractgal.html
David Finton's fractal homepage
http://www.d.umn.edu/~dfinton/fractals/
Algorithmic Image Gallery (Giuseppe Zito)
http://www.ba.infn.it/gallery
Octonion Fractals built using hyper-hyper-complex numbers by Onar Em
http://www.stud.his.no/~onar/Octonion.html
B' Plasma Cloud (animated gif)
http://www.az.com/~rsears/fractp1.html
John Bailey's fractal images ()
http://www.frontiernet.net/~jmb184/interests/fractals/
Fractal Art Parade (Douglas "D" Cootey )
http://www.itsnet.com/~bug/fractals.html
The Fractory (John/Alex )
http://tqd.advanced.org/3288/
FracPPC gallery (Dennis C. De Mars )
http://members.aol.com/ddemars/gallery.html
http://galifrey.triode.net.au/ (Frances Griffin
)
http://galifrey.triode.net.au/
J.P. Louvet's Fractal Album
http://graffiti.cribx1.u-bordeaux.fr/MAPBX/louvet/jpl0a.html )
(Jean-Pierre Louvet French and
English versions)
Carlson's Fractal Gallery
http://sprott.physics.wisc.edu/carlson.htm (Paul Carlson
)
Fractals by Paul Carlson
http://fractal.mta.ca/fractals/carlson/ (an other Paul
Carlson's Gallery)
Daves's Graphics Page
http://www.unpronounceable.com/graphics/ (David J. Grossman
replace the AT with '@'
and DOT with '.' I apologize that I must take this drastic step
to foil the spammers)
Gumbycat's cyberhome
http://www.geocities.com/~gumbycat/index.html (Linda Allison
Delete the dash ("-") in gumbycat to
send e-mail. It's only purpose is to act as a spam deterent!)
Sylvie Gallet Gallery
http://spanky.triumf.ca/www/fractint/SYLVIE/GALLET.HTML
Sylvie Gallet's Fractal Gallery New pages
http://ourworld.compuserve.com/homepages/Sylvie_Gallet/homepage
.htm (Sylvie Gallet )
Howard Herscovitch's Home Page
http://home.echo-on.net/~hnhersco/
Fractalus Home. Fractals by Damien M. Jones
http://www.geocities.com/SoHo/Lofts/2605/ (Damien M. Jones
)
Fractopia Home page. Bill Rossi
http://members.aol.com/billatny/fractopi.htm (Bill Rossi
)
Doug's Gallery. Doug Owen
http://www.zenweb.com/rayn/doug/ (Doug Owen
)
TWG's Gallery. Terry W. Gintz
http://www.zenweb.com/rayn/twg/ (Terry W. Gintz
)
Fractal Gallery
http://members.aol.com/MKing77043/index.htm (Mark King
)
Julian's fractal page
http://members.aol.com/julianpa/index.htm (Julian Adamaitis
)
Don Archer's fractal art
http://www.ingress.com/~arch/ (Don Archer )
The 4D Julibrot Homepage
http://www.shop.de/priv/hp/3133/fr_4d.htm (Benno Schmid
)
The Fractal of the Day
http://home.att.net/~Paul.N.Lee/FotD/FotD.html Each day Jim Muth
() post a new fractal !
The Beauty of Chaos
http://i30www.ira.uka.de/~ukrueger/fractals/ A journey in the
Mandelbrot set (Uwe Krüger )
The Brian E. Jones Computer Art Gallery
http://ourworld.compuserve.com/homepages/Brian_E_Jones/ (Brian E.
Jones )
Phractal Phantasies
http://www.globalserve.net/~jval/intro.htm (Margaret
and Jack Valero)
Glimpses of a fugitive Universe
http://www.artvark.com/artvark/ (Rollo Silver )
Earl's Computer Art Gallery
http://computerart.org/
Jacco's Homepage (Jaap Burger )
http://wwwserv.caiw.nl/~jaccobu/index.htm
MOCA: the Museum Of Computer Art The fractal art of Sylvie Gallet, and
several other artists (Bob Dodson, MOCA curator ;
Don Archer, MOCA director)
http://www.dorsai.org/~moca/
Les St Clair's Fractal Home Page (Les St Clair
)
http://ourworld.compuserve.com/homepages/Les_StClair/
Numerous links to fractal galleries and other fractal subjects can be found
at
Spanky fractal database
http://spanky.triumf.ca/www/welcome1.html
Fractal Images / Immagini frattali su Internet
http://www.ba.infn.it/www/fractal.html
Chaffey High School's Fractal Image Gallery Links
http://www.chaffey.org/fractals/galleries.html
Fantastic Fractals. Reference Desk
http://library.advanced.org/12740/cgi-bin/linking.cgi?browser=m
sie&language=enu
The Infinite Fractal Loop
The Infinite Fractal Loop was initiated by Douglas Cootey ; it is now
managed by Damien M. Jones. It is a link between a number of personal
fractal galleries. The home page of the subscribers display the logo
of the Infinite Fractal Loop. By clicking on selected areas of this
logo the server of the loop will call an other site of this loop and
from this new page, you can go to an other gallery... There are nearly
40 members in the loop.
You can have more information and subscribe at
http://www.emi.net/~dmj/ifl/
_Q25b_: How do I view fractal pictures from
alt.binaries.pictures.fractals?
_A25b_: 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:
ftp://rtfm.mit.edu:/pub/usenet/news.answers/pictures-faq/.
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 you are
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.
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 or JPEG 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.
Automated method
Most of the news readers for Windows or Macintosh, as well as web
browsers such as Netscape or MSIE will automate the decoding for you.
This may not be true of all web browsers.
Subject: Where can I obtain papers about fractals?
_Q26_: Where can I obtain papers about fractals?
_A26_: 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: ftp://inls.ucsd.edu/pub.
There are also articles on dynamics, including the IMS preprint
series, available from ftp://math.sunysb.edu/preprints.
The WWW site http://inls.ucsd.edu/y/Complex/ has some fractal papers.
The site life.csu.edu.au has a collection of fractal programs, papers,
information related to complex systems, and gopher and World Wide Web
connections.
The ftp path is:
ftp://life.csu.edu.au/pub/complex/ (Look in fractals and chaos)
via WWW:
http://life.csu.edu.au/complex/
R. Vojak has some papers and preprints available from his home page at
Université Paris IX Dauphine.
R. Vojak's home page
http://www.ceremade.dauphine.fr/~vojak/
Subject: How can I join fractal mailing lists?
_Q27_: How can I join fractal mailing lists?
_A27_: There are now 4 mailing lists devoted to fractals.
FRAC-L
Fractal-Art
Fractint
Fractal Programmers
The FRAC-L mailing list
FRAC-L is a mailing list "Forum on Fractals, Chaos, and Complexity".
The purpose of frac-l is to be a globally networked forum for
discourse and collaboration on fractals, chaos, and complexity in
multiple disciplines, professions, and arts.
To subscribe to frac-l an email message to
listproc@archives.math.utk.edu containing the sole line of text:
SUBSCRIBE FRAC-L [email address optional]
To unsubscribe from frac-l, send LISTPROC (_NOT frac-l_) the message:
UNSUBSCRIBE FRAC-L
Messages may be posted to frac-l by sending email to:
frac-l@archives.math.utk.edu
Ermel Stepp founded this list; the current listowner is Larry Husch
and you should contact him (husch@math.utk.edu) if there are any
difficulties.
The Frac-L archives (http://archives.math.utk.edu/hypermail/frac-l/)
go back to Fri 09 Jun 1995.
The Fractal-Art Discussion List
This mailing list is open to all individuals and organizations
interested in all aspects of Fractal Art. This would include fractal
and digital artists, fractal software developers, gallery owners,
museum curators, art marketers and brokers, printers, art collectors,
and simply anybody who just plain likes to look at fractal images.
This should include just about everybody!
Administrator: Jon Noring noring@netcom.com
To subscribe Fractal-Art send an email message to majordomo@aros.net
containing the sole line of text:
subscribe fractal-art
Messages may be posted to the fractal-art mailing list by sending
email to: fractal-art@aros.net
An innovative member of Fractal-Art has created the Unofficial Links
from Fractal-Art Email Digest
(http://www.ee.calpoly.edu/~jcline/fractalart-links.htm) which
collects all the URLs posted to the Fractal-Art mailing list and makes
them into a web page. Created by Jonathan Cline.
The Fractint mailing list
This mailing list is for the discussion of fractals, fractal art,
fractal algorithms, fractal software, and fractal programming.
Specific discussion related to the freeware MS-DOS program Fractint
and it's ports to other platforms is welcome, but discussion need not
be Fractint related. Technical discussion is welcome, but so are
beginner's questions, so don't be shy. This is a good place to share
Fractint tips, tricks, and techniques, or to wax poetic about other
fractal software.
To subscribe you can send a mail to majordomo@xmission.com with the
following command in the body of your email message:
subscribe fractint
Messages may be posted to the fractint mailing list by sending email
to: Fractint@xmission.com
You can contact the fractint list administrator, Tim Wegner, by
sending e-mail to: twegner@phoenix.com
The Fractal Programmers mailing list
Subcription/unsubscription/info requests should always be sent to the
-request address of the mailinglist. This would be:
. To subscribe to the
mailinglist, simply send a message with the word "subscribe" in the
_Subject:_ field to .
As in: To: fracprogrammers-list-request@terindell.com
Subject: subscribe
To unsubscribe from the mailinglist, simply send a message with the
word "unsubscribe" in the _Subject:_ field to
.
Subject: Complexity
_Q28_: What is complexity?
_A28_: 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:
Institute for Research on Complexity
http://webpages.marshall.edu/~stepp/vri/irc/irc.html
The site life.csu.edu.au has a collection of fractal programs, papers,
information related to complex systems, and gopher and World Wide Web
connections.
LIFE via WWW
http://life.csu.edu.au/complex/
Center for Complex Systems Research (UIUC)
http://www.ccsr.uiuc.edu/
Complexity International Journal
http://www.csu.edu.au/ci/ci.html
Nonlinear Science Preprints
http://xxx.lanl.gov/archive/nlin-sys
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@xxx.lanl.gov containing the sole line of text:
subscribe your-real-name
The Complexity and Management Mailing List. For more information see
the web archive at http://HOME.EASE.LSOFT.COM/archives/complex-m.html
or their lexicon of terms at http://lissack.com/lexicon/lexicon.html.
To subscribe:
http://home.ease.lsoft.com/scripts/wa.exe?SUBED1=complex-m or send a
message to list@lissack.com with the message "subscribe complex-m" in
the _body_.
To send a message to the list, send them to COMPLEX@lissack.com or to
COMPLEX-M@HOME.EASE.LSOFT.COM.
Subject: References
_Q29a_: What are some general references on fractals, chaos, and
complexity?
_A29a_: 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. Jürgens, H. O Peitgen, & D. Saupe. 1990 August, The Language of
Fractals. _Scientific American_, pp. 60-67.
H. Jürgens, 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. MacCormac (ed), M. Stamenov (ed), _Fractals of Brain, Fractals
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