This article is from the sci.fractals FAQ, by Michael C. Taylor and Jean-Pierre Louvet with numerous contributions by others.

Fractal compression is quite controversial, with some people

claiming it doesn't work well, and others claiming it works

wonderfully. The basic idea behind fractal image compression is to

express the image as an iterated function system (IFS). The image can

then be displayed quickly and zooming will generate infinite levels of

(synthetic) fractal detail. The problem is how to efficiently generate

the IFS from the image. Barnsley, who invented fractal image

compression, has a patent on fractal compression techniques

(4,941,193). Barnsley's company, Iterated Systems Inc

(http://www.iterated.com/), has a line of products including a Windows

viewer, compressor, magnifier program, and hardware assist board.

Fractal compression is covered in detail in the comp.compression FAQ

file (See "compression-FAQ").

ftp://rtfm.mit.edu/pub/usenet/ .

One of the best online references for Fractal Compress is Yuval

Fisher's Fractal Image Encoding page

(http://inls.ucsd.edu/y/Fractals/) at the Institute for Nonlinear

Science, University for California, San Diego. It includes references

to papers, other WWW sites, software, and books about Fractal

Compression.

Three major research projects include:

Waterloo Montreal Verona Fractal Research Initiative

http://links.uwaterloo.ca/

Groupe FRACTALES

http://www-syntim.inria.fr/fractales/

Bath Scalable Video Software Mk 2

http://dmsun4.bath.ac.uk/bsv-mk2/

Several books describing fractal image compression are:

1. M. Barnsley, "Fractals Everywhere", Academic Press Inc., 1988.

ISBN 0-12-079062-9. This is an excellent text book on fractals.

This is probably the best book for learning about the math

underpinning fractals. It is also a good source for new fractal

types.

2. M. Barnsley and L. Anson, "The Fractal Transform", Jones and

Bartlett, April, 1993. ISBN 0-86720-218-1. Without assuming a

great deal of technical knowledge, the authors explain the

workings of the Fractal Transform(TM).

3. M. Barnsley and L. Hurd, "Fractal Image Compression", Jones and

Bartlett. ISBN 0-86720-457-5. This book explores the science of

the fractal transform in depth. The authors begin with a

foundation in information theory and present the technical

background for fractal image compression. In so doing, they

explain the detailed workings of the fractal transform. Algorithms

are illustrated using source code in C.

4. Y. Fisher (Ed), "Fractal Image Compression: Theory and

Application". Springer Verlag, 1995.

5. Y. Fisher (Ed), "Fractal Image Encoding and Analysis: A NATO ASI

Series Book", Springer Verlag, New York, 1996 contains the

proceedings of the Fractal Image Encoding and Analysis Advanced

Study Institute held in Trondheim, Norway July 8-17, 1995. The

book is currently being produced.

Some introductary articles about fractal compression:

1. The October 1993 issue of Byte discussed fractal compression. You

can ftp sample code:

ftp://ftp.uu.net/published/byte/93oct/fractal.exe .

2. A Better Way to Compress Images," M.F. Barnsley and A.D. Sloan,

BYTE, pp. 215-223, January 1988.

3. "Fractal Image Compression," M.F. Barnsley, Notices of the

American Mathematical Society, pp. 657-662, June 1996.

(http://www.ams.org/publications/notices/199606/barnsley.html)

4. A. E. Jacquin, Image Coding Based on a Fractal Theory of Iterated

Contractive Image Transformation, "IEEE Transactions on Image

Processing", January 1992.

5. A "Hitchhiker's Guide to Fractal Compression" For Beginners by

E.R. Vrscay

ftp://links.uwaterloo.ca/pub/Fractals/Papers/Waterloo/vr95.ps.gz

Andreas Kassler wrote a Fractal Image Compression with WINDOWS package

for a Fractal Compression thesis. It is available at

http://www-vs.informatik.uni-ulm.de/Mitarbeiter/Kassler/papers.htm

Other references:

Fractal Compression Bibliography

http://www.dip.ee.uct.ac.za/imageproc/compression/fractal/fract

al.bib.html

Fractal Video Compression

http://inls.ucsd.edu/y/Fractals/Video/fracvideo.html

Many fractal image compression papers are available from

ftp://ftp.informatik.uni-freiburg.de/documents/papers/fractal

A review of the literature is in Guide.ps.gz.

ftp://ftp.informatik.uni-freiburg.de/documents/papers/fractal/R

EADME

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