fractal image encoding announcements and questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) i...

72
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. o General questions. o Algorithm (code) questions. o Looking for.... · Miscellaneous material. · Return to the main Fractal Image Encoding pages. Announcements of on-line papers. 1 of 72 7/20/97 11:12 PM Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Upload: others

Post on 09-Oct-2020

4 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Fractal Image EncodingAnnouncements andQuestionsThis dynamic page contains various announcementsand questions related to fractal image encoding.Each section contains a form with whichannouncements and/or questions can be entered intothe document. Please enter only fractal imageencoding material here.

·Announcements of on-line papers. ·Announcements of software. ·Questions about fractal image encoding. o General questions. o Algorithm (code) questions. o Looking for.... ·Miscellaneous material. ·Return to the main Fractal Image Encoding

pages.

Announcements of on-linepapers.

1 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 2: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

·jim ([email protected]) 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? Y

·Anna Bergström ([email protected])writes:

Real3d(Amiga) to DXF or IGES converter

·wayne ponton ([email protected]) writes:

·lee ki tae ([email protected]) writes:

·Eleonore([email protected])writes:

I am a teacher in Minneapolis and I will be teaching fractalsand chaos theory to a small group of students for two weeksthis summer. Does anybody have any suggestions for softwareor curriculum that might be useful. We will have access to Maconly. I would appreciate any input. Eleonore

·Christine Koenig ([email protected])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

2 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 3: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Christine

·Peter W ([email protected]) writes:

Converter IGES to DFX format for PCWin or Dos

·Xiaomin Chen([email protected]) writes:

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

·Kate Bailey-Hellen ([email protected])writes:

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

·Kim ([email protected]) 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 ([email protected]) writes:

3 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 4: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

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

·Alex Galletero ([email protected]) 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 ([email protected])writes:

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

·Kurt Draven (c/o [email protected])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 ([email protected]) writes:

I am studying on new Image Coding Algorithm, maybe the fractaland wavelet will play important role in it. Is anybody can tellme an obvious and direct illustration of the connection betwwenthem?

·Jen ([email protected]) writes:

4 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 5: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

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

·Surojit Chatterjee ([email protected])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 formaking a codebook of the domains.The problem is to find a similarity criteria for the image blocks.Till now I am usingnormalized histograms for this ,any better ideas?...pleasei need it really soon..

·Sundar Dorai-Raj (University of Alabama)([email protected]) writes:

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

·Jackie Dawes ([email protected]) 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 imageas a population of individuals. How can I do this?!

5 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 6: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Jackie Dawes

·Hsueh-Ting Chu ([email protected])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 consoleversions.

·Esquieu-Antoine (Supelec, France)([email protected]) 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 ([email protected]) writes:

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

Robinson Pizzio

·chen jiang tao ([email protected])writes:

Mr fisher:

6 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 7: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

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

·Radhakrishnan K([email protected]) 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 reponseLoveradhakrishnan

·Felix KRause([email protected]) writes:

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

·ANGEL ([email protected]) writes:

¡ HELLO !I AM A MEXICAN STUDENT AND I WANT TO GET INFORMATIONABOUT FRACTAL IMAGE COMPRESSION WITH GENETIC ALGORITMSCOULD YUO PLEASE MAIL ME SOMETHING PAPERS ABOUT THIS?

7 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 8: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

THANKS...

·Al ([email protected]) 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 @ [email protected]

thank's Al

·Evie Gunawan ([email protected]) writes:

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

·Armen Balian ([email protected]) writes:

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

8 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 9: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

·ishan ([email protected])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..

Add an announcement of an on-line paper or result.Feel free to hyperlinks in the announcement. Includeboth your name and email. Name: Email:

Enter Announcement

Announcements of software.

·Giovambattista Pulcini ([email protected])writes:

I am an Italian student @ "La Sapienza", Rome.I would thank you for addressing my friends and me to your postscriptpaper. We found much hints and tips in your new book, also.The result of our work is an encoding/decoding program for 24 bits/pixelimages which is based on IFS compression method, with a two level

9 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 10: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

quadtree partitioning.We consider this program as a "tutorial" since it runs under Windows andshows graphically each step of the encoding, showing dinamically the rangeblock, the domain block and the isometry selected for mapping on each otherthese 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 ([email protected]) writes:

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

·Susumu Morita ([email protected]) writes:

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

·Ivan G. Zagaynov ([email protected])writes:

Hi, I am a student of Moscow Institute of Phisics and TechnologyFor almost two years I studied myself fractal compression viainternet papers - thanks to Y.Fisher! Recently I wrote a programthat can compress Adobe Premiere Filmstrip color movies at a compression ratio 50-500:1 with encoding speed 1-3 sec. per frame

10 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 11: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

and decoding with over 20 fames per sec. on usual PC with DOSMovie frame size 320*256*24bit. 1 minute of real time videotakes 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:

qqtq

·Hsueh-ting Chu ([email protected])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 ([email protected])writes:

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

Add an announcement of new software. Feel free tohyperlinks in the announcement. Include both your

11 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 12: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

name and email. Name: Email:

Enter Announcement

Questions about fractal imageencoding.

General Questions aboutfractal image encoding.

·John Q. Public ( ) writes:

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

Answers to this question: o Yuval ([email protected]) writes:

You can find a good introduction on the fractal image

12 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 13: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

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, withan emphasis on explaining the ideas, not the math, of thesubject. These notes are available (977K) or without the figures(80K).

o Jean-loup Gailly ([email protected])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 includingsource code for a simple compression program.

o Martin Chadderton([email protected]) writes:

I may have put this in the wrong section but I do notseem to be having any luck whatsoever with the aforementioned web site (web2.airmail.net etc) is thisthe right address? Also, would it be possible to send me (via email)the source code mentioned above? Thanks in advance

o mariana ([email protected]) writes:

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

13 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 14: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

o Xiaomin ([email protected])writes:

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

o Xiaomin ([email protected])writes:

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

o Susumu Morita ([email protected]) writes:

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

o Susumu Morita ([email protected]) writes:

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

o Susumu Morita ([email protected]) writes:

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

o Michael C Taylor ([email protected])writes:

14 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 15: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

For the The Data Compress Book the URL is -Michael

o Raghavendra Udupa U.([email protected]) 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 .

o Robinson Pizzio (PUCRS - Brazil)([email protected]) writes:

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

o Cédric ([email protected]) writes:

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

15 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 16: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

o Mel ([email protected]) writes:

What is a good definition for FRACTAL?

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·[email protected]([email protected]) writes:

Will fractal compression provide 200:1 or greater compression of a 256GrayScale [email protected]

Answers to this question: o Yuval ([email protected]) writes:

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

16 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 17: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

o Susumu Morita ([email protected]) writes:

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

o HOLLY NASTA (ROSA PARKS) writes:

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Zhihua Liu ([email protected]) writes:

Hi, I am working on synthetic aperture radar(SAR) image compressionand 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: o Gary Dickson ([email protected])

writes:

17 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 18: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

My experience with SAR images is somewhat limited, but I seemto remember that they are highly textured in nature. Unfortunatelyfractals don't like texture so maybe another type of coder wouldbe more appropriate.

o Gary Dickson ([email protected])writes:

My experience with SAR images is somewhat limited, but I seemto remember that they are highly textured in nature. Unfortunatelyfractals don't like texture so maybe another type of coder wouldbe more appropriate.

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Dan Ruderman ([email protected]) 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?

18 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 19: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

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: o Yuval ([email protected]) 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

19 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 20: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

or what be.

o Sandeep Sikka ([email protected])writes:

This is regarding Q.1. The compression scheme dependson 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 hol

o Sandeep Sikka ([email protected])writes:

This is regarding Q.1. The compression scheme dependson 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 hol

o Carmen Casalderrey ([email protected])writes:

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

o G.Sriram ([email protected])writes:

This is regarding Q.3.Unlike JPEG,there is no standard fractalimage compression algorithm.Depending on the algorithm and itsparameters, ratios of 20:1 can be achieved for typical images with

20 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 21: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

"moderate" quality of reproduction.

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Emmanuel ([email protected]) writes:

The general theory of IFS says that a collection of contractive of mapsin 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 theplane 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 thatwe use a collection of mappings contractive in the metric space of images with the distance d such as the supremum metric. Then come thequestion : what represents the Hausdorff space H and metric h(d) if (M,d)represents the space of images?

Answers to this question: o Sandeep Sikka ([email protected])

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 Eu

21 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 22: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

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 bei

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Sean ([email protected]) writes:

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

I've did some work on general transformations and got somenice 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: o Sandeep Sikka ([email protected])

writes:

22 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 23: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

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 th

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Fabien Carre ([email protected])writes:

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

What are the application areas and the future perspectivesof Fractals ?

Answers to this question: o Duraid Madina ([email protected]) writes:

Fractals are better than JPEG when extremecompression ratios are called for, however JPEGis otherwise better simply because of itscomputational ease. Wavelets are better

23 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 24: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

generally the best form of image compression outthere with compression ratios exceeding thoseof fractals (for a given distortion) and theirartifacts look *much* "nicer" than fractalartifacts, and wavelets share both fractal'sresolution-independence and JPEG's ease ofcomputation.

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Carlo Stazzone ([email protected])writes:

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

24 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 25: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Answers to this question: o Bulldog ([email protected]) writes:

Contattami

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Matt Duckham ([email protected]) 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 InformationSystem and am trying to find a way of calculating the fractaldimension of the IFS constructed for a given surface. I have seen a few methods for calculating D for an IFS, such as summingthe contraction factors to the power D, but all the methods seemto hold only for very simple IFS. Does anyone know of, or where to look for, a way of calculating D for the sorts of IFSused in FIC?Thanks in anticipation.

Answers to this question:

25 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 26: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Marty Davidson([email protected])writes:

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

Much Thanks.

Answers to this question:

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

26 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 27: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

·Adrian Bolster ([email protected])writes:

Hi, I have this project to do which involvesi) The compression of a heightfield using an IFSandii)The generation of heightfields using IFSDoes anyone out there have any hints, references, pointers,algorithms, code ANYTHING??

Thanks in advance.

Answers to this question:

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Dugal Harris ([email protected])writes:

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

27 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 28: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Answers to this question:

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Aurelio R. Ramos([email protected]) writes:

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

Answers to this question: o Dave ([email protected]) writes:

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

Add an answer. Include both your name andemail. Name: Email:

28 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 29: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Enter Answer

·Raghavendra Udupa U([email protected]) writes:

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

Answers to this question:

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Laurie/IBM AUSTRALIA([email protected]) 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 pictureframe from,say, a Fred Astair & Ginger Rogers dance sequence, fuzzy image, use same

29 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 30: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

fractal technique and present a star dazzling crisp image. Commercial applications here?

Answers to this question: o Martin Schaaf ([email protected])

writes:

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

o 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.

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Surojit Chatterjee ([email protected])writes:

Hi I am a senior year UG student working on fractal compression.

30 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 31: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

My question is how effective can Neural Network be in vectorquantization of image blocks?

Answers to this question:

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Dave ([email protected]) 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 somethingthat is fully executable (ie. FracComp) won't do, and I have had MAJORheadaches trying to compile enc.c and dec.c, mainly due to memoryallocation errors. Does such code exist?

Thanks for the help.

Answers to this question:

Add an answer. Include both your name andemail.

31 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 32: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Name: Email:

Enter Answer

·Zbynek Jurca ([email protected]) 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: o G.Sriram ([email protected])

writes:

Find the RMS difference between the images.This may notbe the best , but is simple and easy to compute.Formore information,read the book - The data compression book -by Nelson and Gailly.

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

32 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 33: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Enter your general questions about fractal imagecompression below. Include both your name andemail. Name: Email:

Post Question

Questions about fractal imageencoding algorithms.

·mark whittemore ([email protected])writes:

I'd like to see a bit more on these pages regardingthe use of the source codes. What would be really excellentwould be if we could get some opinions from someonewho has done this on the PC platform (Let's face it ...

33 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 34: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

that's where many of us are). What shareware compilercan I use ? What sorts of results might I expect in termsof seconds vs minutes vs hours vs file size. Please someone explain to be how I can convert some of my8 bit greyscale JPEG images to the RAW file which isrequired by the fractal program. How about a detaileddescription of the Raw file format at a binary level ? I know I'm asking a lot of questions at once, but pleasebare with me since this page is relatively new, and noneof my questions appear to be addressed.

Answers to this question: o yuval ([email protected]) writes:

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

In MAC land, there is Photoshop that can convertto raw format. I don't how to do thison PCs. The ras2raw.c program can convert SUNRASTERimages 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

34 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 35: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

size or depth. This data has to be known or guessedfrom the image size (the sample images availableat this site are either 512x512=262144 bytes longor 256x256=65536 bytes long).

o Brendan Ryan ([email protected])writes:

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

o Chris Melchior ([email protected])writes:

From yuval's answer, the Raw format sounds to me likethe Windows bitmap without the header. Lots of softwarewill convert image formats to Windows Bitmap, then it'susually easy to see where the header ends and write some simplecode to chop it off.

35 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 36: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

o Dennis Lim ([email protected])writes:

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

o Anjan Kr. Dasgupta([email protected]) writes:

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

o Susumu Morita ([email protected]) writes:

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

o Andreas Kassler([email protected]) 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 athttp://www-vs.informatik.uni-ulm.de/Mitarbeiter/Kassler/fractals.htmIt can handle almost all kind of image formatsused in the PC world and generates the fractal

36 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 37: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

code. It also produces some analysis on the code.Feel free to check it out.

o Martin Schaaf ([email protected])writes:

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

o Ben Schouten ([email protected]) writes:

o Ben Schouten ([email protected]) writes:

I myself use Fractal Imager from Iterated.com, which is quite good and fast.For testing we work with a program "fract" fromThe 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

o Julie Phipps ([email protected]) 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.

Add an answer. Include both your name andemail. Name: Email:

37 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 38: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Enter Answer

·Tor Andre Myrvoll ([email protected])writes:

One problem with the traditional way of scaling and translating blocksis that the frequency contents of the original and the resampled blockwill 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 alsowonder if theres any research regarding the use of nonlinear transformsdifferent from the usual affine ones? Yours SincerelyTor Andre Myrvoll

Answers to this question: o Sandeep Sikka ([email protected])

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

38 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 39: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

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.

o Saeed Asgari ([email protected])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 nonaffineand is a generalization of Monro's polynomial fractal transforms...I showed the potential results without using an exhaustive searchfor 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 thatparameters associated to the transformations whichform the wavelet-based fractal code can be solvedvia any interior point method of optimization such as LMI toolbox of MATLAB which is in factthe toolbox I used to write all the codes...That'swhy 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...

Add an answer. Include both your name andemail. Name: Email:

39 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 40: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Enter Answer

·Martin Chadderton([email protected]) 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 getcompiler errors with both these programs. Does anybody have anyidea about what I could be doing wrong?

Answers to this question: o Bjoern Bunte ([email protected]) writes:

At the moment, I`ve got the same problem. I tried to compile the codewith 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 codeas a help.Thank you...

Add an answer. Include both your name andemail. Name: Email:

40 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 41: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Enter Answer

·mary o'neill ([email protected]) 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 andemail. Name: Email:

Enter Answer

·Brendan Ryan ([email protected])writes:

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

41 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 42: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Answers to this question: o chul woo park

([email protected]) writes:

o Maxim Zotov ([email protected])writes:

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

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Micahel Baun ([email protected]) 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:

Add an answer. Include both your name andemail.

42 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 43: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Name: Email:

Enter Answer

·Altug Koker ([email protected]) writes:

I am dealing mostly the hardware implementation offractal-based image compression. Do you know any pointersabout the subject?

Answers to this question: o Sandeep Sikka ([email protected])

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.

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Centonze Angelo

43 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 44: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

([email protected]) 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: o Dave ([email protected]) writes:

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

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Fan Lixin ([email protected]) writes:

I am M.Sc. student at the National University of Singapore.I would like to know more detail about the Hexagonal Partitioningwhich was mentioned in the Appendix C.16 in the "Fractal imagecompression: Theory and application".Especially, I want to know if there is an effective way for

44 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 45: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

implementation of hept-tree.Thanks in advance.

-Lixin

Answers to this question:

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·G.Satheesh ([email protected]) 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:

45 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 46: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·G.Sriram ([email protected]) 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 withgood quality,but a comp.ratio of around 3:1!Is the 't' option problema bug?Why such a low ratio for good quality reproduction?

Answers to this question:

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

46 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 47: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

·Edouard Mercier ([email protected])writes:

I'd like to make up my mind about the fractal compressiondevice, but I haven't found yet any precise notes on thedevice itself. That is the reason why I dare asking for somehelp 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 someinformation on the device or if someone told me where tofind precise informations on the net. Thank you.

Answers to this question:

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

Enter your questions about fractal image encodingalgorithms below. Include both your name and email. Name: Email:

47 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 48: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Post Question

Looking for fractal imageencoding resources.

·Marketing Multimedia ([email protected])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, butwe want to know, if it possible if there are some group that isdeveloping something concerning that. Thank You Roberto

Answers to this question: o jesus sosa ([email protected])

writes:

48 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 49: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

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

o Susumu Morita ([email protected]) writes:

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

o Ivan G. Zagaynov([email protected]) writes:

Look at announ. of software for details and sendme your coord. to contact - I think I almost havewhat you really need

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Scott Webber ([email protected]) writes:

Hi. I am interested in getting fractal compressionsoftware for an IBM compatable PC. Could you tell me whereI can find some software that compressed and decompresses

49 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 50: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

any standard file format like BMP,PCX,TGA or if possible,GIF. Also I heard that fractal technology could be used toscale Pictures without loss of image quality. Do you knowanything about that. Thanks, I appreciate your help,Scott Webber

Answers to this question: o Latapy Matthieu

([email protected])writes:

Hello

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

About Zooming on Fractal compressed images, youmust understand that the methods creates detailsjust like (or better than) the classics zoomingmethods do. That is, to a certain degree of

50 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 51: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

zoom, the loss of quality will be hided bythe fractal scheme. However, you can't expect ascheme that would create true details from an image that does not conatin them...

Expecting my English's not too bad,Matthieu.

o Sandeep Sikka ([email protected])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.

o Kyle Kline ([email protected])writes:

This is in regards to your question about encoding software...Iterated Systems (http://www.iterated.com) has a very goodprogram (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 usageonly, 30-day trial period. It is a very good, easy to useprogram. Give it a shot! It's worth it! (The PC version requires Windows95 or the newest release of Win32s.)Try it!!

o TMD ([email protected]) writes:

Use a netbrowser to find it!

51 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 52: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

o Snickers ([email protected]) writes:

May the farce be with you!

o Dennis Aubrey([email protected]) writes:

Altamira Group in California has a fractal compressionproduct for Photoshop called Genuine Fractals. Theirweb site is www.altamira-group.com.

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Ken Call ([email protected]) writes:

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

Answers to this question: o jon tubmen ([email protected]) writes:

To Ken Call

52 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 53: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

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.

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Armin Roehrl ([email protected]) writes:

Hi,

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

Thanks a lot,Armin

53 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 54: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Answers to this question: o Mentrup Lars

([email protected]) 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?

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Torsten Fink([email protected]) writes:

Hi,is anybody working on IFS-implementations on SIMD-architectures? We are thinking about animplementation for the MasPar MP-2.

Answers to this question:

54 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 55: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Andre Mok ([email protected]) writes:

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

A.

Answers to this question: o Erik Nilsen ([email protected])

writes:

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

55 of 72 7/20/97 11:12 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 56: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

o Dennis Aubrey([email protected]) writes:

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

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·William ([email protected]) writes:

At one time I saw software in a catalog that includedcompression and the ability to zoom in on an image, notfractal images, but regular raster images with no lossof resolution. Any idea where I can find such?

Answers to this question: o Bob ([email protected]) writes:

Hello. Try http://www.catalog.com

Add an answer. Include both your name and

56 of 72 7/20/97 11:13 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 57: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

email. Name: Email:

Enter Answer

·Becky (101543,[email protected])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 andemail. Name: Email:

Enter Answer

·EMT AB ([email protected]) 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

57 of 72 7/20/97 11:13 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 58: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

to me ASAP!

Answers to this question:

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Marty Davidson ([email protected])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 appreciateany and all help.Thanks in advance,Marty

Answers to this question:

Add an answer. Include both your name andemail. Name: Email:

58 of 72 7/20/97 11:13 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 59: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Enter Answer

·Jan M. Rasmussen ([email protected])writes:

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

Answers to this question:

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Fernando Machado ([email protected])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?

59 of 72 7/20/97 11:13 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 60: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Thanks in advance,Fernando

Answers to this question:

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·G.Satheesh ([email protected]) 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:

Add an answer. Include both your name andemail. Name: Email:

60 of 72 7/20/97 11:13 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 61: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Enter Answer

·G.Sriram ([email protected]) writes:

Suppose I have a 256-level grayscale image,which I divide into64x64 pixel blocks(ranges?).To achieve commonly claimed compressionratio 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 goodquality 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:

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Pedro Anton ([email protected]) writes:

Could you tell me about papers on image normalization (in

61 of 72 7/20/97 11:13 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 62: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

order to be compared during the search process of imagecompressing)Thanks.

Answers to this question:

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Estuardo Licona-Nunez ([email protected])writes:

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

Answers to this question:

62 of 72 7/20/97 11:13 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 63: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

·Suelika J. Chial ([email protected])writes:

Hi.

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

Thanks!

Answers to this question:

Add an answer. Include both your name andemail. Name: Email:

Enter Answer

63 of 72 7/20/97 11:13 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 64: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

·Marcin Chady([email protected]) 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 andemail. Name: Email:

Enter Answer

Enter your queries about fractal image encodingresources below. Include both your name and email. Name: Email:

64 of 72 7/20/97 11:13 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 65: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Post Question

Miscellaneous material.

Miscellaneous Postings:

·Michael C Taylor ([email protected])writes:

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

·Becky (101543,[email protected])writes:

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

·Becky (101543,[email protected])writes:

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

65 of 72 7/20/97 11:13 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 66: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

·Becky (101543,[email protected])writes:

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

·Carmen Casalderrey ([email protected])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 ([email protected]) writes:

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

·Don Berliner ([email protected]) 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 toFractal compression and have been told that there is a hardwaresolution 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.([email protected]) writes:

66 of 72 7/20/97 11:13 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 67: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

I and Vinayaka Pandit have developed a more efficient decoding algorithm for Weighted Finite Automata ( WFA ) introduced byKarel Culik and Jarrco Kari. This work was done as apart of our undergraduate project on WFA based Fractla Image Compression. Those interested can contact me [email protected] . Our algorithm requires significantly less memory and is faster than Culik_Kari algorithm .

·Raghavendra Udupa U.([email protected]) writes:

Vinayaka D. Pandit can be contacted at [email protected] .

·Mindaugas Satas([email protected]) writes:

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

·Ivan G. Zagaynov ([email protected])writes:

Hi, I am a student of Moscow Institute of Physics and Tech.During last two years i've studied fractal compression myselfvia internet papers. Finally I wrote myself program thattakes Adobe Premiere Filmstrips and compresses them with

67 of 72 7/20/97 11:13 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 68: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

50-500:1 compression ratio with only 1-3 sec. per frame on PCDecoding is possible with 20 frames/sec for color movieswith size 320*256*24bit. If someone is really interested,please send me E-mail, and I will give it for exchange...

·Yao Zhao ([email protected]) 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 SchemeCombining 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.

68 of 72 7/20/97 11:13 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 69: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

·Dr. Itzhak Messing([email protected]) 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 statehow can one hide below the grid without attracting attention in a publicarea?

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

If this type of technology is used for surveillance by the statehow can one hide below the grid without attracting attention in a publicarea?

·Pierre Greborio ([email protected])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 fewquestion:

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

69 of 72 7/20/97 11:13 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 70: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

2) where may I find information about multifractal theory ?

Thank you in advance.

Pierre

·G.Sriram ([email protected]) writes:

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

Thanking you all in advance,G.Sriram

·Diana Dubel ([email protected]) 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 theinternet.

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

·ANGEL ([email protected]) writes:

¡ HELLO !

70 of 72 7/20/97 11:13 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 71: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

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

·Marcos R. Garcia ([email protected])writes:

Quieres dar (give) u obtener (ask)?

·Marcos R. Garcia ([email protected])writes:

Quieres dar (to give) u pedir (to ask for)?

Enter whatever below. Include both your name andemail. Name: Email:

Enter Stuff

Return to the main Fractal Image Encoding pages.

Yuval Fisher Institute for Nonlinear Science

71 of 72 7/20/97 11:13 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html

Page 72: Fractal Image Encoding Announcements and Questionscourses.cs.vt.edu/~cs4624/pdf/fractal.pdf · 1) I have to do a project on weather radars and fractals, any ideas of how there similiar

Univeristy of California, San Diego December 15, 1995

72 of 72 7/20/97 11:13 PM

Fractal Image Encoding Announcements and Questions http://inls.ucsd.edu/y/Fractals/frac-an.html