Fractal Image Encoding Announcements and Questions

This dynamic page contains various announcements and questions related to fractal image encoding. Each section contains a form with which announcements and/or questions can be entered into the document. Please enter only fractal image encoding material here.

Announcements of on-line papers.
Announcements of software.
Questions about fractal image encoding.
Miscellaneous material.
Return to the main Fractal Image Encoding pages.

Announcements of on-line papers.

jim (chosen@stu.pennvalley.cc.mo.us) writes:

who in cyberspace has considered the  possibility that the inhabitants of this planet being a dynamical systems experiment of some higher intelligence?  Could this intelligence be our future generation? Could this be the source of the philosophical question of free will?  We, (humans),experiment on "lower" beings (mice, rats, ect.,).  Is this an ironic microcosim, or another sublevel in a dimensionally fractal space-time? Ever wonder why you cannot seperate from your innate "animal" insticts?  You are the animal!  Do you realize that you are asleep? Do you realize how easily you are fooled? You are attracted to bright lights and strange sounds.  Ask any advertiser!  It is time to wake from our sleep! Acknowledge the presence of the Grand Order, the Cosmic Code.

Anna Bergström (a94annbe@ikm.his.se) writes:
```
Real3d(Amiga) to DXF or IGES converter
```
wayne ponton (pequod@superlink.net) writes:
lee ki tae (s_lkt@cecc-1.gsnu.ac.kr) writes:

Eleonore (ebalbach@southwester.supertrek.k12.mn.us) writes:

I am a teacher in Minneapolis and I will be teaching fractals
and chaos theory to a small group of students for two weeks
this summer. Does anybody have any suggestions for software
or curriculum that might be useful. We will have access to Mac
only. I would appreciate any input.   Eleonore

Christine Koenig (biwi6s9@vision.ee.ethz.ch) writes:

I'm working on segmentation of SAR images with the add of fractal images and 
I'm looking for good papers about it.
Thanks

Christine

Peter W (info@reklamcenter.se) writes:

Converter IGES to DFX format for PC
Win or Dos

Xiaomin Chen (g_xmchen@mailserv.stu.edu.cn) writes:

I'm looking for material of image compression using fractal!
Who can help me?

Kate Bailey-Hellen (kate@hn.planet.gen.nz) writes:

How do I insert a JPEG image into an email message?

Kim (wwatts@pig.net) writes:

I have a few questions.....
1) I have to do a project on weather radars and fractals, any ideas of how there similiar   different? What could I do to show the two?
2) Any ideas for a fractal project?
3) Is it possible to create your own equation for a fractal?
 
Thanks!

Susumu Morita (s-m@yk.rim.or.jp) writes:

Please send e-mail answers,
Thank you in advance.

Alex Galletero (catala@hostmail.com) writes:

Hi! i'm a computer engeenering student. I need to know if there are any aalgorithm, about fractal compresion i real time.
thanks in advance. Please if anyone know...send me a mail.

Sean Ramplee (smr94@ecs.soton.ac.uk) writes:

I am implementing a fractal image compression algorithm using
R-Trees to search the domain blocks for good pairings.
However, R-Trees are doing my head in.  Does anyone have/know of
a good and simple implementation I could use?

Kurt Draven (c/o kathrich@umf.maine.edu) writes:

  I am working on a thesis paper concerning crop circles and the possibility of their being caused by extraterrestrial intelligence... i am looking for information to support my ideas about the similarity of some of the latest crop circles to fractal designs, and whether or not there is some hidden mathematical or data agenda...

Edward (glfan@ee.cuhk.edu.hk) writes:

I am studying on new Image Coding Algorithm, maybe the fractal
and wavelet will play important role in it. Is anybody can tell
me an obvious and direct illustration of the connection betwwen
them?

Jen (petersjl@acad.etown.edu) writes:

I am writing a paper on fractals in the classroom.
Should fractals be taught as a main math topic?  I would
appreciate any opinions.

Surojit Chatterjee (ppdas@cse.iitkgp.ernet.in) writes:

I am working on Fractal Image Compression with Delaunay triangulation
(adaptively) of the image for finding the domain and range 
blocks.I am using vector quatization for
making a codebook of the domains.The problem is to find a 
similarity criteria for the image blocks.Till now I am using
normalized histograms for this ,any better ideas?...please
i need it really  soon..

Sundar Dorai-Raj (University of Alabama) (sdorai-3@ua1vm.ua.edu) writes:

I am currently working on a project using a peicewise linear
algorithm to generate a fractal. Does anybody know reference 
between the strange attractor of my fractal and the fractional
dimension?  Is the dimesion of the strange attractor the same
as the overall dimension. Hope to hear from someone.

Jackie Dawes (N13037X@tees.ac.uk) writes:

I am working on a thesis involvong fractal image compression coupled with genetic 
genetic algorithms. I need to represent the possible representations of an image
as a population of individuals. How can I do this?!

Jackie Dawes

Hsueh-Ting Chu (mr834342@cs.nthu.edu.tw) writes:

I wrote a fractal coder which can encode a 512x512 image in 1 sec,
and a 256x256 image in 0.1 sec. Is there anyone who is interested in 
my coder? Please send a mail to me. There are Sun sparc ,Linux and Win32 console
versions.

Esquieu-Antoine (Supelec, France) (antoine.esquieu@supelec.fr) writes:

  I have the purpose to make the compression of some sounds
(sound of the sea, traffic jam, ...) and maybe of all sounds
 by fractals. Unfortunatly, I haven't found any information 
about that. Could someone please help me?

Robinson Pizzio (rpizzio@ee.pucrs.br) writes:

I am new in the Fractal field.
Could anybody suggest a good book where I can find a very
good material about fractal, mainly Fractal Image Compression?

Robinson Pizzio

chen jiang tao (szcubeJT@public.szptt.net.cn) writes:

Mr fisher:
 I have read your book one year ago. and did the experience 
by software. The result is not satisfactaly.Do you think compress
ratio can be 100 or more, I doubt. I think I haven't find a  math method
to solve the Fractal problem , Just block coding.

Radhakrishnan K (parol.radhakrishnan@strath.ac.uk) writes:

I want to work on chaotic systems. 
Is it that an image/data set rendering itself to fractal compression 
means it is chaotic?
Is there any restrictions for an image to be decoded by fractals?
Request an early reponse
Love
radhakrishnan

Felix KRause (fkrause@ix.urz.uni-heidelberg.de) writes:

I search for good book where i can find something about
 Image compression or compression itselfe.
please write me! 
Thank you.

ANGEL (RASTACAT@HOTMAIL.COM) writes:

Ą HELLO !
I AM A MEXICAN STUDENT AND I WANT TO GET INFORMATION
ABOUT FRACTAL IMAGE COMPRESSION WITH GENETIC ALGORITMS
COULD YUO PLEASE MAIL ME SOMETHING PAPERS ABOUT THIS?
THANKS...

Al (bridger@primenet.com) writes:

I'm looking for information on common picture formats on PC, 
how they compare and how they relate.
My is to make a chart of Pros and Cons for each formate.

I'm mostly interrested in Gif, Jpg, Tif & bmp

If you can help, or know where to get help 
please Email me @  bridger@primenet.com

thank's Al

Evie Gunawan (beggtem@rad.ned.id) writes:

I am an Indonesia student of informatika.
Do some of you have papers about IFS (iterated function
system)?
Where can I find a good introduction to IFS?

Armen Balian (abalian@ndu.edu.lb) writes:

I have a project to deliver about Split and Merge technique
using RAW image files.  The theory is a peace of cake but the implementation
is real hard, so, if anyone be kind and send me the code for
split and merge technique in C   or PASCAL language.
thank you in advance ...

ishan (ishan@broncho.ct.monash.edu.au) writes:

i am looking for different measures in image compression. Besides 'signal-to-noise ratio', 'root-mean-square', and 'color-ratio' does anyone have come across some other measures?
if yes, please email me..

Announcements of software.

Giovambattista Pulcini (mc0878@mclink.it) writes:

I am an Italian student @ "La Sapienza", Rome.
I would thank you for addressing my friends and me to your postscript
paper. We found much hints and tips in your new book, also.
The result of our work is an encoding/decoding program for 24 bits/pixel
images which is based on IFS compression method, with a two level
quadtree partitioning.
We consider this program as a "tutorial" since it runs under Windows and
shows graphically each step of the encoding, showing dinamically the range
block, the domain block and the isometry selected for mapping on each other
these two.
This sw, called IFSAF, will be soon available at the Valerio Verrando ftp site,\
 
accessible via V.V. WEB home page: 
http://www.webcom.com/~verrando.

fdsdfsdfs (sdfsdfsd) writes:

Susumu Morita (s-m@yk.rim.or.jp) writes:

Please send e-mail answers,
Thank you in advance.

Susumu Morita (s-m@yk.rim.or.jp) writes:

Please send e-mail answers,
Thank you in advance.

Ivan G. Zagaynov (sergey@sean.ab.msk.su) writes:

Hi, I am a student of Moscow Institute of Phisics and Technology
For almost two years I studied myself fractal compression via
internet papers - thanks to Y.Fisher! Recently I wrote a program
that can compress Adobe Premiere Filmstrip color movies at a 
compression ratio 50-500:1 with encoding speed 1-3 sec. per frame
and decoding with over 20 fames per sec. on usual PC with DOS
Movie frame size 320*256*24bit. 1 minute of real time video
takes only 1 floppy disk (about 1.4M with decoder)!!!
Send me E-mail if you are interested. Investors are very welcome...

I must apologize for my poor English - I could've done some mistakes!

q (w) writes:
```
q
q
t
q
```

Hsueh-ting Chu (mr834342@cs.nthu.edu.tw) writes:

I am a Taiwan student.
I received several mails asking me about my coder.
Now I put my coder/decoder into a Windows program, called FICA.
If you are interested in it, You can get it via internet:
http://ipsun1.cs.nthu.edu.tw/~mr834342/fic.html

Angela Krenz (newtonsapple@ktca.org) writes:

What is the Transference of Curves Theory? Please somebody explain....

Questions about fractal image encoding.

General Questions about fractal image encoding.

John Q. Public ( ) writes:

Where can I find a good introduction to fractal image 
compression ?

Answers to this question:

Yuval (yfisher@ucsd.edu) writes:

You can find a good introduction on the fractal image
compression pages at http://inls.ucsd.edu/y/Fractals/
on which you can find the SIGGRAPH 92 course notes.
These notes are written at a very simple level, with
an emphasis on explaining the ideas, not the math, of the
subject. These notes are available with the figures
(977K) or  without the figures(80K).

Jean-loup Gailly (gzip@prep.ai.mit.edu) writes:

The second edition of "The Data Compression Book"
by Mark Nelson & Jean-loup Gailly
( http://web2.airmail.net/markn/tdcb.htm )
has a chapter on fractal image compression including
source code for a simple compression program.

Martin Chadderton (M.Chadderton@edm.hull.ac.uk) writes:

I may have put this in the wrong section but I do not
seem to be having any luck whatsoever with the 
aforementioned web site (web2.airmail.net etc) is this
the right address? Also, would it be possible to send me (via email)
the source code mentioned above?  
Thanks in advance

mariana (mdelfres@tandil.edu.ar) writes:

What happend with the promise of M.Barnsley about the
ratio of 10000:1?

Xiaomin (g_xmchen@mailserv.stu.edu.cn) writes:

I'm looking for material of image compression using fractal!
Who can help me?

Xiaomin (g_xmchen@mailserv.stu.edu.cn) writes:

I'm looking for material of image compression using fractal!
Who can help me?

Susumu Morita (s-m@yk.rim.or.jp) writes:

Please send e-mail answers,
Thank you in advance.

Susumu Morita (s-m@yk.rim.or.jp) writes:

Please send e-mail answers,
Thank you in advance.

Susumu Morita (s-m@yk.rim.or.jp) writes:

Please send e-mail answers,
Thank you in advance.

Michael C Taylor (mctaylor@mta.ca) writes:

For the The Data Compress Book the URL is
 
-Michael

Raghavendra Udupa U. (rudupa@mastech.com) writes:

One can find good material on FIC in the book
"FRACTAL IMAGE COMPRESSION - THEORY AND APPLICATIONS TO DIGITAL IMAGES"
edited by YUVAL FISHER and published by Academic Publishers .

Robinson Pizzio (PUCRS - Brazil) (rpizzio@ee.pucrs.br) writes:

I am complete new in Fractal theory. I am studing Fractal
image compression.
Could any one help? What shoul I study first?
Fractal looks like so difficult? Can any one say that
I am wrong????

Cédric (cheval_e@epita.fr) writes:

I'm currently doing a work on fractal compression,
and would like to know if there is a link between
fractal compression and artificial intelligence.
Is it possible to use fractalization processes to
find similarities among large databases and to
compress them ???

Mel (Mel@charleston.net) writes:
```
What is a good definition for FRACTAL?
```

hmahoney@sentex.net (hmahoney@sentex.net) writes:

Will fractal compression provide 200:1 or greater compression of a 256
GrayScale Image?
Regards
hmahoney@sentex.net

Answers to this question:

Yuval (yfisher@ucsd.edu) writes:

It depends on the image. Polar bear
in a snow storm ? No problem. But
the typical (what ever that is) image,
no.

Susumu Morita (s-m@yk.rim.or.jp) writes:

Please send e-mail answers,
Thank you in advance.

HOLLY NASTA (ROSA PARKS) writes:

Zhihua Liu (liuzh@ie0.ie.ac.cn) writes:

Hi,
   I am working on synthetic aperture radar(SAR) image compression
and want to use fractal-based coder.
   Has anyone had experience or advice on it?
   Appreciate it very much!
regards.
Zhihua Liu

Answers to this question:

Gary Dickson (garyd@ee.bath.ac.uk) writes:

My experience with SAR images is somewhat limited, but I seem
to remember that they are highly textured in nature. Unfortunately
fractals don't like texture so maybe another type of coder would
be more appropriate.

Gary Dickson (garyd@ee.bath.ac.uk) writes:

My experience with SAR images is somewhat limited, but I seem
to remember that they are highly textured in nature. Unfortunately
fractals don't like texture so maybe another type of coder would
be more appropriate.

Dan Ruderman (dlr@quake.usc.edu) writes:

A few questions...

1. What properites of images from the natural world make 
   them amenable to fractal image compression?

2. What types of images should the procedure fail for?

3. What are the "typical" compression ratios for grayscale
   and color images, and their relation to other techniques?

4. What about "multifractal" image compression?


Many thanks,
Dan Ruderman

Answers to this question:

Yuval (yfisher@ucsd.edu) writes:

These answers are my opinions; your milage may vary:
1) Images compress best when then have large flat
    regions and straight edges.
2) The procedure fails for images that don't have
   self-similarity on different scales, for example
   a pixel-sized checkerboard pattern.
   Highly textured or detailed natural image are 
   difficult for the same reason. 
3) There is no typical compression ratio, since this
   is highly image dependent. Results are comparable
   to other techniques, more or less. However, if you 
   don't compare to the original image but rather you
   just want a good image that is highly compressed,
    fractal image compression can do a good job - better
    than JPEG, for example (which is not optimized for
    high compression ratios anyway).
4) I don't know what multifractal image compression is
    or what be.

Sandeep Sikka (sikka@cse.iitb.ernet.in) writes:

This is regarding Q.1. The compression scheme depends
on the metric used to compare the "likeness" or "goodness" of a transformed domain block and the original range block. The rms metric usually used in all practical fractal image coding schemes is insensitive to image content and edges in particular. So maybe using a good new metric which is sort of adaptive to the content of all image could enlarge the class of images for which fractal coding works very well. Of course the basic point of an image possesing self-similarity across scales still holds. But in the automated algos. we should be able to recognise and capture that very well.

Sandeep Sikka (sikka@cse.iitb.ernet.in) writes:

This is regarding Q.1. The compression scheme depends
on the metric used to compare the "likeness" or "goodness" of a transformed domain block and the original range block. The rms metric usually used in all practical fractal image coding schemes is insensitive to image content and edges in particular. So maybe using a good new metric which is sort of adaptive to the content of all image could enlarge the class of images for which fractal coding works very well. Of course the basic point of an image possesing self-similarity across scales still holds. But in the automated algos. we should be able to recognise and capture that very well.

Carmen Casalderrey (conocer@redestb.es) writes:

This is regarding Q.4: I don´t know what multifractal image is, but in
http://www-syntim.inria.fr/fractales/ 
you can find some references.

G.Sriram (sriram@bronto.iitm.ernet.in) writes:

This is regarding Q.3.Unlike JPEG,there is no standard fractal
image compression algorithm.Depending on the algorithm and its
parameters, ratios of 20:1 can be achieved for typical images with
"moderate" quality of reproduction.

Emmanuel (reusens@lts.de.epfl.ch) writes:

The general theory of IFS says that a collection of contractive of maps
in a metric space (M,d) will give a contractive (hyperbolic) IFS on the 
Haussdorf space with the Hausdorf metric (H,h(d)). This is very clear in the
plane where H is the space of all subsets of points in the plane.


 Now if we want to apply this theory to images, we usually say that
we use a collection of mappings contractive in the metric space of 
images with the distance d such as the supremum metric. Then come the
question : what represents the Hausdorff space H and metric h(d) if (M,d)
represents the space of images?

Answers to this question:

Sandeep Sikka (sikka@cse.iitb.ernet.in) writes:

If I am right we first have to build a mathematical model of what isan image. For eg: Consider just black and white images. They can bemodelled as subsets of R2 i.e the Euclidean plane. The way this worksis pretty clear. X = R2 and d could be say the Euclidean metric.If now we come to gray scale images then we could model them assubsets of R3 but not any, specifically those subsets which representfunctions f:R2 -> R. R2 represents the image base and R the gray scale.Here also we could use the Euclidean metric or the supremum metric. Theformer is preferred because it is better and more meaningful than thelater. After that we construct mappings of the form w(x,y,z) which are
usually affine mappings. The mappings are contractive on the R2 (xy)plane and R (z) axis both. Once we have a collection of such mappingsw all of which are contractive we are sure that the IFS i.e thecollection is also contractive. The point to be noted is that weconstruct the w's such that the collection has a fixed pointwhich is a function and hence an image and not any arbitary subsetof R3 . This is one reason why we take the ranges to be nonoverlapping.(range in the mathematical sense as being the range of w). This is roughlyhow I feel the system works.

Sean (sean@tedser.ucg.ie) writes:

Hi, I'm writing a project on fractal compression and
seen use of affine transformations used just about 
everywhere, but no general transformation,  i.e.
the affine transformation is a parallelogram, whereas
the general transformation would be any four sided shape.
(or a shape with four vertices)

I've did some work on general transformations and got some
nice results, but theres this nagging feeling..  I haven't 
seen general transformations anywhere else other than 
transformations in the complex plane..

Any reason why or is it that I don't read enough?

Answers to this question:

Sandeep Sikka (sikka@cse.iitb.ernet.in) writes:

First point: It is not true that general transformations have not been used. Jacquin used trans of the form (x,y,z) -> (w(x,y),sz o) which is a very restricted affine transformation as you mention. However Monro has used trans. of the form (x,y,z) -> (w(x,y),ax^2   by^2   cx   dx   f). w(x,y) here is the normal 2D affine trans. So, general trans have been investigated. 
Second point: If you use general trans (by which I understand like those which say take a parallelogram to a quadrilateral) then the coefficients of the trans will have to be stored. In current schemes which use the affine transforms this information is implicitly stored by storing the position of the range and domain block. This might lead to less compression. Also is the question of how in a systematic manner would you partition the image so as to use these transforms fruitfully? I had also thought on the same lines initially. But for this and a few more reason didn't purse it. I would be glad to know if you have thought over these and have some answers.

Fabien Carre (e2fabien@etek.chalmers.se) writes:

What are the main advantages & drawbacks of fractals in image
compression compared to other recent techniques like JPEG 
and Wavelets ?

What are the application areas and the future perspectives
of Fractals ?

Answers to this question:

Duraid Madina (duraid@fl.net.au) writes:

Fractals are better than JPEG when extreme
compression ratios are called for, however JPEG
is otherwise better simply because of its
computational ease. Wavelets are better
generally the best form of image compression out
there with compression ratios exceeding those
of fractals (for a given distortion) and their
artifacts look *much* "nicer" than fractal
artifacts, and wavelets share both fractal's
resolution-independence and JPEG's ease of
computation.

Carlo Stazzone (fractal@hermes.dibe.unige.it) writes:

I'm an italian student at "University of Genova:, Genova.
I'm working to develop a dedicated architecture for the
fractal image compression algorithm in "Fractal Image
Compression", M. F. Barnsley and L. P. Hurd, AK Peters, Ltd, 1993.
I'd like to know if there are previous works related to
a dedicated hardware implementation for a fractal image
compression algorithm, and ,eventually, where i can find
material (papers, http or/and ftp sites, books, reports ...)
about them.
Thank you in advance.

Answers to this question:

Bulldog (rcaweb@mbox.vol.it) writes:
```
Contattami
```

Matt Duckham (mjd12@le.ac.uk) writes:

I am a geographer at the University of Leicester and am 
interested in the use of FIC as a surface interpolater.
I have written my own FIC code within a Geographic Information
System and am trying to find a way of calculating the fractal
dimension of the IFS constructed for a given surface.  I have 
seen a few methods for calculating D for an IFS, such as summing
the contraction factors to the power D, but all the methods seem
to hold only for very simple IFS.  Does anyone know of, or 
where to look for, a way of calculating D for the sorts of IFS
used in FIC?
Thanks in anticipation.

Answers to this question:

Marty Davidson (pochariot!mdavidson@photon.att.com) writes:

I am interested in any published information regarding the possibility of using the Partitioned Iterated Function System technique as a speech and music
data compression method. Anyone know of anything?

Much Thanks.

Answers to this question:

Adrian Bolster (A.Bolster@dcs.hull.ac.uk) writes:

Hi, I have this project to do which involves
i) The compression of a heightfield using an IFS
and
ii)The generation of heightfields using IFS
Does anyone out there have any hints, references, pointers,
algorithms, code ANYTHING??

Thanks in advance.

Answers to this question:

Dugal Harris (Harris@underdog.ee.wits.ac.za) writes:

Please could someone tell me where to find a basic 
introduction in coding fractals, I am interested in using
the code to generate fractal music (not images).

Answers to this question:

Aurelio R. Ramos (aurelior@amadeus.upr.clu.edu) writes:

Has fractal compression ever been considered for audio
signals at all? If so, does anybody has any references?
Any personal opinions about this matter?

Answers to this question:

Dave (nearyd@eeng.dcu.ie) writes:

The WWT (windowed wavelet transform) is so much better than any other method available
that there doesn't really seem much point.

Raghavendra Udupa U (rudupa@india.mastech.com) writes:

Can anybody update me on the recent advances in Weighted
Finite Automata based Fractal Image Compression ?
Has WFA FIC technique been applied to video ?

Answers to this question:

Laurie/IBM AUSTRALIA (SHAWL@VNET.IBM.COM) writes:

Curious: Saw TV show example of Budgie's eye being enhanced from low resolution 
image to detailed resolution. Seriously, is it possible to take a black&white picture
frame from,say, a Fred Astair & Ginger Rogers dance sequence, fuzzy image, use same
fractal technique and present a star dazzling crisp image. Commercial applications here?

Answers to this question:

Martin Schaaf (hygore@netcom.com) writes:

No, it won't supply image clarity that was not there to start with.

Jeff Harcourt (Not my computer) writes:

Not quite, Martin! Fractal compression will add detail if the image 
being compressed has self-symmetry (such as the bird's eye), because 
the bird's eye was created from the same mathematics as the fractal 
image. Hence the fractal compressor will find a similar formua to the 
formula from which the object was created.

Surojit Chatterjee (ppdas@cse.iitkgp.ernet.in) writes:

Hi I am a senior year UG student working on fractal compression.
My question is how effective can Neural Network be in vector
quantization of image blocks?

Answers to this question:

Dave (nearyd@eeng.dcu.ie) writes:

This may sound strange, but does anyone have C-code for a PC (16- or 32-bit) on which I 
can put a front-end? My Prof. wants a VB interface on a coder so something
that is fully executable (ie. FracComp) won't do, and I have had MAJOR
headaches trying to compile enc.c and dec.c, mainly due to memory
allocation errors. Does such code exist?

Thanks for the help.

Answers to this question:

Zbynek Jurca (jurcaz@risc.upol.cz) writes:

How can I compare two images? One is original image and 
second is image which was processed by fractal compression.

Thank you in advace.

Answers to this question:

G.Sriram (sriram@bronto.iitm.ernet.in) writes:

Find the RMS difference between the images.This may not
be the best , but is simple and easy to compute.For
more information,read the book - The data compression book -
by Nelson and Gailly.

Questions about fractal image encoding algorithms.

mark whittemore (mark@netheaven.com) writes:

I'd like to see a bit more on these pages regarding
the use of the source codes. What would be really excellent
would be if we could get some opinions from someone
who has done this on the PC platform (Let's face it ...
that's where many of us are). What shareware compiler
can I use ? What sorts of results might I expect in terms
of seconds vs minutes vs hours vs file size.
 
Please someone explain to be how I can convert some of my
8 bit greyscale JPEG images to the RAW file which is
required by the fractal program. How about a detailed
description of the Raw file format at a binary level ?
 
I know I'm asking a lot of questions at once, but please
bare with me since this page is relatively new, and none
of my questions appear to be addressed.

Answers to this question:

yuval (yfisher@ucsd.edu) writes:

The enc.c and dec.c code is very vanilla, and it has
compiled without problem using several different C compilers
on several different platforms - all UNIX boxes, though.
PC land is a different world.

In MAC land, there is Photoshop that can convert
to raw format. I don't how to do this
on PCs. The ras2raw.c program can convert SUNRASTER
images to raw format; it is available on this site.

Raw files are row orderd 8 bits per pixel binary data.
Each byte represents the grey level at a pixel.
There is no header information specifying image 
size or depth. This data has to be known or guessed
from the image size (the sample images available
at this site are either 512x512=262144 bytes long
or 256x256=65536 bytes long).

Brendan Ryan (nazpope@freenet.hut.fi) writes:

I have a simple awnser for PC's.. get Linux (Unix
variant) or freeBSD or similar for your PC... 
these are free and come with the gcc compiler(Linux
at least does..) unfortunately, no-one else will get 
linux so try watcom or borland - both are good, watcom
especially (multiple platform support) Oh, I know
they're not shareware.. it's good, PAY FOR IT! As for 
conversion, try SEA, a popular viewer which does
multiple formats and conversion, is one of the best
i've seen..
	Rest been answered,
			   Nazlfrag Pope..:Ź)

Chris Melchior (cmelchio@runet.edu) writes:

From yuval's answer, the Raw format sounds to me like
the Windows bitmap without the header. Lots of software
will convert image formats to Windows Bitmap, then it's
usually easy to see where the header ends and write some simple
code to chop it off.

Dennis Lim (c107@ee-alta.bham.ac.uk) writes:

The altenative to getting linux for PC is to get
the DJGPP compiler which is a GNU port of the unix
compiler. It is free. I don't know if it can run 
Unix code straight off but I am told that whatever
conversions required are easy.

Anjan Kr. Dasgupta (adgcal@giascl01.vsnl.net.in) writes:

One Windows based environment that can handle images in many formats including the 
ones mentioned above is MATLAB under windows .

Susumu Morita (s-m@yk.rim.or.jp) writes:

Please send e-mail answers,
Thank you in advance.

Andreas Kassler (kassler@informatik.uni-ulm.de) writes:

One very nice solution doing fractal compression 
on a windows PC (Win95) is the program fracomp,
which you can find on my fractal-page at
http://www-vs.informatik.uni-ulm.de/Mitarbeiter/Kassler/fractals.htm
It can handle almost all kind of image formats
used in the PC world and generates the fractal
code. It also produces some analysis on the code.
Feel free to check it out.

Martin Schaaf (hygore@netcom.com) writes:

Where can I download the enc.c and dec.c code?

Ben Schouten (bens@cwi.nl) writes:

Ben Schouten (bens@cwi.nl) writes:

I myself use Fractal Imager from Iterated.com, which is quite good and fast.
For testing we work with a program "fract" from
The technical University Delft (The Netherlands).
Lot's parameters to change the algoritme. It is slow 
but on top it gives you beautifull pictures of the range and 
domainblocks that are selected in the algoritme.
http://dutiosd.twi.tudelft.nl/~valery

Julie Phipps (juliep@corel.ca) writes:

If you want a couple of great image conversion programs, try IMAGE ALCHEMY or DEBABELIZER PRO. Both of which I am certain can convert your JPEGs into RAWs with no problem. The process can also be run in batches allowing you to convert hundreds of images in no time.

Take a look at these programs if you work with images regularly.

Tor Andre Myrvoll (tormy@stud.unit.no) writes:

One problem with the traditional way of scaling and translating blocks
is that the frequency contents of the original and the resampled block
will differ. This makes the cofing of e.g. coarse textures (tiled roofs,
striped suits) difficult.
Has there been published any papers that addresses this problem? I also
wonder if theres any research regarding the use of nonlinear transforms
different from the usual affine ones?
 
Yours Sincerely
Tor Andre Myrvoll

Answers to this question:

Sandeep Sikka (sikka@cse.iitb.ernet.in) writes:

This about Non-linear transforms. If you are looking for PIFS in which the 
maps are non-linear in the z-directions such as polynomials of order 2 or 
3 then people have experimented it. Look at work by Monro et. all which 
somewhat attempts this. Also you can look at the reference "E. Groeller. 
Modelling and rendering of nonlinear IFS", Computer and Graphics 18(5), 
1994, pp 739-748. He gives a new way of specifying non-linear transforms 
via distortions on regular grids (2D and 3D). He leaves the way in which 
they should be applied to this particular problem of FIC open. I have seen 
more stuff but can't remember of hand.

Saeed Asgari (asgari@cae.wisc.edu) writes:

This answer is in regard to the question about the use of Nonaffine 
Transformations for FIC...I have introduced a new wavelet-based fractal 
transform (WBFT) on the space of all images (F=L^2(I^2)) which is nonaffine
and is a generalization of Monro's polynomial fractal transforms...
I showed the potential results without using an exhaustive search
for domain block candidates both on 1D and 2D images...
I have found the conditions for (strict) contractivity of 
the operator under the rms metric and showed that
parameters associated to the transformations which
form the wavelet-based fractal code can be solved
via any interior point method of optimization 
such as LMI toolbox of MATLAB which is in fact
the toolbox I used to write all the codes...That's
why the coder/decoder are slow at this point...
For a reference to the aformentioned claims, if anybody is interested,
I can email a copy of my thesis which is in postscript format and 
the papers, two of, which are still pending for publication...

Martin Chadderton (M.Chadderton@edm.hull.ac.uk) writes:

Hi. I am trying to compile the enc.c and dec.c programs found here 
but without much luck. I keep getting compiler errors,
I am using both cc and gcc on a UNIX platform but I still get
compiler errors with both these programs. Does anybody have any
idea about what I could be doing wrong?

Answers to this question:

Bjoern Bunte (bbunte@usa.net) writes:

At the moment, I`ve got the same problem. I tried to compile the code
with MS Visual C   5.0, Borland C   4.52 (both running Win95)
and gcc on a Spark an Linux. All without any success.
Now I`ve started to re-write the code.
If there is anybody out there, who has done the same before,
it would be very nice if you could send me your code
as a help.
Thank you...

mary o'neill (oneill@mala.bc.ca) writes:
```
I am looking for fpu init (shareware) for a mac. Any ideas?
Thanx
```
Answers to this question:
Add an answer. Include both your name and email.
Name: Email:

Brendan Ryan (nazpope@freenet.hut.fi) writes:

Is there any good C archives of fractal compression software
around?? I've just gotten enc/dec and was looking for some
more, esp. video related...
might just have to write my own..:Ź)
	Regards,
		Nazlfrag Pope

Answers to this question:

chul woo park (cwpark@cesb.tongnae.ac.kr) writes:

Maxim Zotov (maxim@inter-soft.com.ru) writes:

Look at ftp://ftp.mei.co.jp/free/Graphics/Compression/fractal/Limbo/
You can find there cool paper and C sources of fractal compression
of single images and sequences of images.

Micahel Baun (baun@valleynet.com) writes:

Since fractal compression methods utilize at their core the notion of self similarity - can the fractal representation of an image be used to manipulate an image at a more fundamental level then other image transformation algorithmns? (Are there usefull transformations of the following variety  --- fractal compression/transformation/decompression?)

Answers to this question:

Altug Koker (akoker@eng.buffalo.edu) writes:

I am dealing mostly the hardware implementation of
fractal-based image compression. Do you know any pointers
about the subject?

Answers to this question:

Sandeep Sikka (sikka@cse.iitb.ernet.in) writes:

Barnsley I believe has a few patents related to hardware implementation of FIC algorithms. You can try at the patent office. There are pointers to it on these pages itself.
- on the root page. To start of you could look at these patents. Since the technique is very much similar to VQ you could also look at h/w imp. of VQ if such are around. Let me know if you find any literature references to this.

Centonze Angelo (acentonz@adriatica.peoples.it) writes:

I am an Italian student in  the University of Bari.
I would like to know more detail about fractal coding using HV partitioning instead of Quadtree, and if exist  software regarding this tecnique.
Thanks very much.

Angelo Centonze

Answers to this question:

Dave (nearyd@eeng.dcu.ie) writes:

There is a good paper on this in Yuval Fisher's book...no software though.

Fan Lixin (fanlixin@iscs.nus.sg) writes:

I am M.Sc. student at the National University of Singapore.
I would like to know more detail about the Hexagonal Partitioning
which was mentioned in the Appendix C.16 in the "Fractal image
compression: Theory and application".
Especially, I want to know if there is an effective way for 
implementation of hept-tree.
Thanks in advance.

-Lixin

Answers to this question:

G.Satheesh (ens_trn2@hss.hns.com) writes:

With reference to the article "Fractal Image Compression" by
 Y.Fisher which appeared in the SIGGRAPH'92 notes,
I don't understand how it takes 7 bits to determine o(i) 
and 5 bits for determining s(i). I would be most grateful if
 I can get an answer for it at the earliest.

		Thanking You,
		Satheesh	.

Answers to this question:

G.Sriram (sriram@bronto.iitm.ernet.in) writes:

I recently downloaded enc/dec software and compiled it on a 
linux machine.But for different values of option 't',I am 
getting the same encoded image(20,12 and 4 were the values 
I tried)!If the option is not given,I got compression with
good quality,but a comp.ratio of around 3:1!Is the 't' option problem
a bug?Why such a low ratio for good quality reproduction?

Answers to this question:

Edouard Mercier (merciere@mines.u-nancy.fr) writes:

I'd like to make up my mind about the fractal compression
device, but I haven't found yet any precise notes on the
device itself. That is the reason why I dare asking for some
help so that a can really make an expose on this new method.
Moreover, I don't want to buy any book : too dear for me !
I would be very grateful if someone could send me some
information on the device or if someone told me where to
find precise informations on the net. Thank you.

Answers to this question:

Looking for fractal image encoding resources.

Marketing Multimedia (mmminfo@mmm.inet.it) writes:

We are interested in a fractal image compress viewer for netscape.
We know that MCI bought the right for FIF images on the NET, but
we want to know, if it possible if there are some group that is
developing something concerning that.
 
Thank You
 
Roberto

Answers to this question:

jesus sosa (jesus@dec5500.sgia.imp.mx) writes:

iterated function systems, the Barnsley company
has released a plug in for netscape, wich is a fif
viewer and you can donwload from:
  http://www.iterated.com/

Susumu Morita (s-m@yk.rim.or.jp) writes:

Please send e-mail answers,
Thank you in advance.

Ivan G. Zagaynov (sergey@sean.ab.msk.su) writes:

Look at announ. of software for details and send
me your coord. to contact - I think I almost have
what you really need

Scott Webber (webber@norden1.com) writes:

    Hi.  I am interested in getting fractal compression
software for an IBM compatable PC.  Could you tell me where
I can find some software that compressed and decompresses
any standard file format like BMP,PCX,TGA or if possible,
GIF.  Also I heard that fractal technology could be used to
scale Pictures without loss of image quality.  Do you know
anything about that.
 
Thanks, I appreciate your help,
Scott Webber

Answers to this question:

Latapy Matthieu (latapy@amertume.ufr-info-p7.ibp.fr) writes:

Hello

The best place for getting fractal compression
programs is certainly Yuval's Fractal Image
Compression page.
However, the public-domain programs are not yet 
developped enough to allow you a complete use in
a PC environnement. For my part, I don't know any
powerful drawing software that includes fractal
compression of usual formats files.
However, they'll certainely appear in the next
mounths... Just wait for us.

About Zooming on Fractal compressed images, you
must understand that the methods creates details
just like (or better than) the classics zooming
methods do. That is, to a certain degree of
zoom, the loss of quality will be hided by
the fractal scheme. However, you can't expect a
scheme that would create true details from an 
image that does not conatin them...

Expecting my English's not too bad,
Matthieu.

Sandeep Sikka (sikka@cse.iitb.ernet.in) writes:

This is about the decoding: Basically the fractal code obtained from a given image is resolution independant. So it can be decoded to any resolution. Decoding at a higher resolution than input image is called "creating artificial detail". How close is this "artificial detail" to "real detail"? I am not aware of any systematic study which has been conducted to study this.
However I remember looking at the color picture of a lizard in Hurd's book. There it does seem very very real like.

Kyle Kline (kkline@quantumlink.net) writes:

This is in regards to your question about encoding software...
Iterated Systems (http://www.iterated.com) has a very good
program (Fractal Imager) that will convert an image in almost any format
(supported are: TGA, BMP, GIF, PCX, RAS, TIF, PCD, & JPG)
to their FIF format.  It can be downloaded for trial usage
only, 30-day trial period.  It is a very good, easy to use
program.  Give it a shot!  It's worth it!  (The PC version 
requires Windows95 or the newest release of Win32s.)
Try it!!

TMD (DMA@AntwerpCity.be) writes:
```
Use a netbrowser to find it!
```
Snickers (DMA@AntwerpCity.BE) writes:
```
May the farce be with you!
```

Dennis Aubrey (70541.3621@compuserve.com) writes:

Altamira Group in California has a fractal compression
product for Photoshop called Genuine Fractals.  Their
web site is www.altamira-group.com.

Ken Call (gbush@upr1.upr.clu.edu) writes:

	Where could I find Machintosh programs that compress and decompress either pictures or video.

Answers to this question:

jon tubmen (jon@indelible.com) writes:

To Ken Call

Hi Ken,

The only decoder I know is the one 
available from http://www.iterated.com/


cheers,             jon

PS. Please mail me direct if you come across more Mac resources.

Armin Roehrl (m94asr@ecs.ox.ac.uk) writes:

Hi,

Does anyone know if there's any code
for K. Culik II's (see Fisher's book, Chapter 13) compression of images,
using WFA available anywhere?

Thanks a lot,
Armin

Answers to this question:

Mentrup Lars (scmentru@fmi.uni-passau.de) writes:

Sorry no answer to your question. (Does anyone know if there's any code
     for K. Culik II's (see Fisher's book, Chapter 13) compression of images,
     using WFA available anywhere?) But another question, do you have an own home page?

Torsten Fink (tnfink@cip.informatik.uni-erlangen.de) writes:
```
Hi,
is anybody working on IFS-implementations on 
SIMD-architectures? We are thinking about an
implementation for the MasPar MP-2.
	
```
Answers to this question:
Add an answer. Include both your name and email.
Name: Email:

Andre Mok (andrem@ddc.aus.net) writes:

Hi
I am trying to find commercialy produced fractal image compression 
software. In particular medical image compression and still image
compression.  All repsonses appreciated.

A.

Answers to this question:

Erik Nilsen (enilsen@engr.latech.edu) writes:

I think you will find www.iterated.com a very
helpful site. Also, I would suggest you visit the 
Waterloo Fractal Compression Page (use a search 
engine to find it).
                      good luck and enjoy,
                                           erik

Dennis Aubrey (70541.3621@compuserve.com) writes:

Altamira Group in California has a Photoshop application 
called Genuine Fractals for PC.  The web site is
www.altamira-group.com.

William (wjk@phuture.is.net) writes:

At one time I saw software in a catalog that included
compression and the ability to zoom in on an image, not
fractal images, but regular raster images with no loss
of resolution. Any idea where I can find such?

Answers to this question:

Bob (bob@gillies.win.net) writes:
```
Hello. Try http://www.catalog.com
```

Becky (101543,3445@compuserve.com) writes:
```
I am interested in using Fractal compressed images in an 
Access database. Which compression software should I use?
```
Answers to this question:
Add an answer. Include both your name and email.
Name: Email:

EMT AB (lasseb@emt.se) writes:

I have heard the rumor that there is a fractal compression component 
available for Borland's Delphi. Borland doesn't seem to know,
so I wonder where I can find this? Please e-mail all answers
to me ASAP!

Answers to this question:

Marty Davidson (md.md@worldnet.att.net) writes:

Anyone know of any resources I may get a hold of in the 
area of using PIFS as a speech/music compression method?  
How about as a voice recognition method?  I would appreciate
any and all help.
Thanks in advance,
Marty

Answers to this question:

Jan M. Rasmussen (c958548@student.dtu.dk) writes:

I am searching for material on triangular partitioning when
encoding images. Does anyone have books or online documen-
tation (or whatever!) on the subject?

Answers to this question:

Fernando Machado (machado@alma.uc.pt) writes:

I want to make a comparison between diferent methods of 
image compression.
Does anybody know were I can find a good set of test images?
Thanks in advance,
Fernando

Answers to this question:

G.Satheesh (ens_trn2@hss.hns.com) writes:

With reference to the article on "Fractal Image Compression" which appeared in the SIGGRAPH'92 course notes by Y.Fisher.
I would like to know how it takes just 8 bits in the x and y direction to determine the position of D(i), 7 bits for o(i) , 5 bits for s(i).
I would be most grateful if anyone can give an explanation for this question.
	Thanking you,
	Satheesh..

Answers to this question:

G.Sriram (sriram@bronto.iitm.ernet.in) writes:

Suppose I have a 256-level grayscale image,which I divide into
64x64 pixel blocks(ranges?).To achieve commonly claimed compression
ratio of 50:1, each of these blocks is represented as 1.28 bytes 
of information!How will this suffice for good quality reproduction?
Even the example codes of Barnsley,Fisher etc. do not give good
quality of reproduction at more than 15:1 ratio of compression.
Please Help me with everything you know about this.( I am a student)

Answers to this question:

Pedro Anton (panton@ctv.es) writes:

Could you tell me about papers on image normalization (in 
order to be compared during the search process of image
compressing)
Thanks.

Answers to this question:

Estuardo Licona-Nunez (jel15@cornell.edu) writes:

I am looking for the following paper:
R.D. Boss and E.W. Jacobs. Studies of iterated transform
image compression, and its application to color and DTED.
Technical Report 1468, Naval Ocean Systems Center, San
Diego CA, 1991.  
I have already looked in the ftp site mentioned in Yuval
Fisher's web page and it isn't there.  If anyone knows of
a way to get a copy or how to contact R.D. Boss or E. W.
Jacobs please let me know.

Answers to this question:

Suelika J. Chial (gt2098a@prism.gatech.edu) writes:

Hi.

I am an undergraduate student at Georgia Tech and I am working
on a project on fractal interpolation of images.  Where can I
find papers or related websites on fractal interpolation?

Thanks!

Answers to this question:

Marcin Chady (M.Chady-ACS96@cs.bham.ac.uk) writes:
```
Is it possible to get the spec for the FIF image format?
(God this page is a mess!)
```
Answers to this question:
Add an answer. Include both your name and email.
Name: Email:

Miscellaneous material.

Miscellaneous Postings:

Michael C Taylor (mctylr@mailserv.mta.ca) writes:

I am looking for the URL for the UIUC Complexity group.
The one in the Fractal FAQ is out of date.

Becky (101543,3445@compuserve.com) writes:

I am interested in using Fractal compressed images in an Access database. Which compression software should I use.

Becky (101543,3445@compuserve.com) writes:

I am interested in using Fractal compressed images in an Access database. Which compression software should I use?

Becky (101543,3445@compuserve.com) writes:

I am interested in using Fractal compressed images in an 
Access database. Which compression software should I use?

Carmen Casalderrey (conocer@redestb.es) writes:

I'm a spanish student working on my Final Project about Fractal Image Compression.
I'd like to know if there are any references about Fractal Image Segmentation.

                               Thanks in advance.

Susumu Morita (s-m@yk.rim.or.jp) writes:

Please send e-mail answers,
Thank you in advance.

Don Berliner (exec@usmailbox.com) writes:

I'm trying to compress many images of pages of magazines 
to be placed on a CD-ROM and distributed. I've been led to
Fractal compression and have been told that there is a hardware
solution in a production environment.
Question: Is this a good use for fractal compression?
2nd Question: Where might I find such a board?

Raghavendra Udupa U. (rudupa@india.mastech.com) writes:

I and Vinayaka Pandit have developed a more efficient decoding algorithm 
for Weighted Finite Automata ( WFA ) introduced by
Karel Culik and Jarrco Kari. This work was done as a
part of our undergraduate project on WFA based Fractla Image 
Compression. Those interested can contact me at
rudupa@india.mastech.com . 
       Our algorithm requires significantly less memory 
and is faster than Culik_Kari algorithm .

Raghavendra Udupa U. (rudupa@india.mastech.com) writes:

Vinayaka D. Pandit can be contacted at vinayak@wipinfo.soft.net .

Mindaugas Satas (satas@santaka.sc-uni.ktu.lt) writes:

Hi, I am a student of Lithuanian University of Technology.
I am interesting in image compression methods and I need information
about this one. I am waiting messages from students, who do or have done
undergraduate works of image compression.

Ivan G. Zagaynov (sergey@sean.ab.msk.su) writes:

Hi, I am a student of Moscow Institute of Physics and Tech.
During last two years i've studied fractal compression myself
via internet papers. Finally I wrote myself program that
takes Adobe Premiere Filmstrips and compresses them with
50-500:1 compression ratio with only 1-3 sec. per frame on PC
Decoding is possible with 20 frames/sec for color movies
with size 320*256*24bit. If someone is really interested,
please send me E-mail, and I will give it for exchange...

Yao Zhao (yzhao@center.njtu.edu.cn) writes:

   I am a image compression researcher majoring in fractal 
image coding. I received my Ph.D degree in May this year.
I have published a lot of articles about fractal image 
coding, here are some of them:
1. Yao Zhao, Baozong Yuan, A Hybrid Image compression Scheme
Combining Block-based Fractal Coding and DCT, Signal Processing:
Image Communication,8(1996),pp.73-78.
2. Yao Zhao, Baozong Yuan, A New Fractal Theory of Iterated 
Transformation Theory for Image Coding, Advances in Modelling 
& Analysis, B, Vol. 35, No.3. 1995.
3. Yao Zhao, Baozong Yuan, A New Affine Transformation: Its 
Theory and Application to Image Coding, IEEE Trans on CSVT(revised).
4. Yao Zhao, Baozong Yuan, Sequence Image Coding Compression
 Using Fractal Technique, ICSPAT-95.
5. Yao Zhao, Baozong Yuan, Still Color Image Coding Using 
Local Iterated Function Systems(LIFS), ICSP-96.
    If you are interested in my papers, do not to hesitate 
to contact me, I will mail them to you.
    By the way, after my graduation, I still want to proceed 
my study,but I have no project to support me now, If you 
have any project and need a co-worker, please contact me, 
you will find a qualified young worker.
Regards.

Dr. Itzhak Messing (imessing@dekel.technion.ac.il) writes:

Dear Dr. Yao,
	I wiil apprreciate if you can send me reprints of your
	publications.
	My address: Electrical Engineering Dept.
		Technion, Haifa 32000 Israel

Ted Blackwood ((sorry don't have one)) writes:

If this type of technology is used for surveillance by the state
how can one hide below the grid without attracting attention in a public
area?

Ted Blackwood ((sorry don't have one)) writes:

If this type of technology is used for surveillance by the state
how can one hide below the grid without attracting attention in a public
area?

Pierre Greborio (gsoft@compuserve.com) writes:

I'm a belgian and I'm studing at University of Pavia (ITALY).
I'm working on a thesis involing multifractal image compression and I've few
question:

1) there's somebody that works already at this project ?

2) where may I find information about multifractal theory ?

Thank you in advance.

Pierre

G.Sriram (sriram@bronto.iitm.ernet.in) writes:

I'm a first year M.Tech student in CS Dept of Indian Institute
of Technology,Madras,India.I plan to do my project in Fractal
image compression.Dr.Yao,could you please mail me your papers?
I also welcome other related materials,especially those that
demystify the maths behind fractal image compression.

Thanking you all in advance,
G.Sriram

Diana Dubel (dldubel@earthlink.net) writes:

This is a request for information.
I have a Macintosh Performa 631CD.  This is not a "Power Mac".
  I would like to find out what fractal software is
 available to download off the
internet.

I was a math major at San Jose State University in 1976,
and I am very interested in math and art.  Thankyou

ANGEL (RASTACAT@HOTMAIL.COM) writes:

Ą HELLO !
I AM STUDENT OF IPN-MEXICO AND I WANT TO GIVE INFORMATION
ABOUT FRACTAL IMAGE COMPRESSION WITH GENETIC ALGORITHMS.
COULD YOU PLEASE MAIL ME YOUR PAPERS AND NOTES ABOUT THIS?

Marcos R. Garcia (addsmgt@finred.com.mx) writes:
```
Quieres dar (give) u obtener (ask)?
```
Marcos R. Garcia (addsmgt@finred.com.mx) writes:
```
Quieres dar (to give) u pedir (to ask for)?
```

Return to the main Fractal Image Encoding pages.

Yuval Fisher
Institute for Nonlinear Science
Univeristy of California, San Diego
December 15, 1995