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Organizers:
Michael F. Barnsley
Edward Vrscay
Department of Applied Mathematics
University of Waterloo
ervrscay@links.uwaterloo.ca
Dietmar Saupe
Institut fur Informatik
Universitaet Leipzig
saupe@informatik.unileipzig.de
The development of multimedia has often showcased its achievements, in resolution and computing power, by displaying fractal pictures. These pictures of strange attractors and Julia sets have been emblematic of the beauty and depth of mathematics. This minisymposium will demonstrate, however, that fractals are more than pretty pictures; the underlying mathematics leads to a broad collection of useful mathematical tools, common themes, new ways of looking at and thinking about existing algorithms, and practical applications. The focus will be on the main ideas of fractal mathematics as applied to multimedia, and science, and how they may develop in the future.
Fractal mathematics has developed out of the observation that in the real world and in the scientific measurement of it, there can occur patterns that repeat at different scales. This mathematics consists of some basic tools and theorems, such as IFS theory and Hutchinson's theorem; it is centered in real analysis, geometry, measure theory, dynamical systems, and stochastic processes. Its application to multimedia lies principally in the attempt to bridge the divide between the discrete world of digital representation and the natural continuum world in which we seem to live. It has served as inspiration for algorithms that try to recreate sounds, pictures, motion video, and textures, and to organize databases, in computer environments.
Topics addressed at the minisymposium will include multimedia video algorithms, lossless fractal compression, resolution enhancement, fractal transform image compression, fractal image recognition, segmentation, spacefilling curves, fractal graphics, and fractals in education. The meeting will involve mathematicians, computer scientists, engineers and industrial researchers who are interested in the application of fractal methods. The philosophical basis for the symposium is the set of those intuitions and insights that a fractal perspective brings, and the mathematics that sustains those realizations. It is intended that the various speakers will say what their intuitions are, how they look mathematically, and how they are applied in his or her topic. The conference would try to identify areas where the fractal viewpoint has potential to increase understanding and lead to new algorithms.
WEDNESDAY,
JANUARY 17 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 


8:30am  Coffee and Registration 
Reception Room EE/CS 3176 

9:10 am  Willard Miller, Fred Dulles, and Michael F. Barnsley  Introduction  
Fractals in Education and on the Internet  
9:30 am  Vicki
G. Fegers and Mary Beth
Johnson School Board of Broward County (FL) 
Talk pdf  
10:30 am  Break  Reception Room EE/CS 3176  
11:00 am12:00 pm  Michael
Frame Union College 
A WebBased Fractal Geometry Course for NonScience Students  
Fractal Image Compression  
1:30 pm  Dietmar
Saupe Universitaet Leipzig 
The State of the Art in Pure Fractal Compression  
2:30 pm  Break  Reception Room EE/CS 3176  
2:45 pm  Raouf
Hamzaoui Universitat Leipzig 
Fast Local Search for Fractal
Image Compression
Material from Talk Slides pdf 

3:45 pm  Break  Reception Room EE/CS 3176  
4:00 pm  Edward
Vrscay University of Waterloo 
From Fractal Image Compression to Fractalbased Methods in Mathematics  
5:00 pm  IMA
Tea A variety of appetizers and beverages will be served. 
IMA East, 400 Lind Hall  
THURSDAY,
JANUARY 18 All talks are in Lind Hall 409 unless otherwise noted. 

8:45 am  Coffee  Reception Room, Lind Hall 400  
9:00 am  Michael F. Barnsley University of Melbourne 
Lossless Fractal Compression Using IFS  
10:0011:00 am  John
Elton Georgia Institute of Technology 
IFS with PlaceDependent Probabilities  
11:00 am  Break  Reception Room, Lind Hall 400  
11:00 am12:30 pm  Doug
Hardin Vanderbilt Univerity 
From Fractal Interpolation Functions to Wavelets: The HD Problem for Refinable Functions  


2:00 pm  JeanLuc
Dugelay Institut EURECOM 
Fractals in Multimedia Imaging: From Compression to Image Indexing to Watermarking  
3:00 pm  Break  Reception Room, Lind Hall 400  
3:30 pm  Ning
Lu Advanced Digital Imaging Laboratories, Inc. 
Fractal Techniques in Image Segmentation  
4:305:30 pm  Jacques
LevyVehel INRIA, Rocquencourt 
TBA  
FRIDAY,
JANUARY 19 All talks are in Lind Hall 409 unless otherwise noted. 



8:45 am  Coffee  Reception Room, Lind Hall 400  
9:00 am  Ken
Musgrave FractalWorlds.com 
Windows on a Parallel Universe: Exploring Fractal Planets  
10:00 am  Break  Reception Room, Lind Hall 400  
10:3011:30 am  Lyman
P. Hurd Iterated Systems, Inc. 
A Lagrangian Cost Model for a Fractal Transform Compressor Talk pdf 

11:30 am12: 30 pm  Martin
J. Turner De Montfort University 
On the Statistics of Dimension:
Multifractalsand Fractal Modulation
Related Papers: imapapjmb.pdf (949KB) imapapjmb.ps (32.6MB) imapapjmb.ps.gz (1.4MB) papifs.pdf (4MB) papifs.ps (26KB) papifs.ps.gz (5.7MB) 

12:30 pm  IMA Lunchtime Movie  "Is God a Number?"  
Fractal Image Compression II : The Future  
2:00  3:30 pm 
Panel Discussion on Fractal Image Compression


3:00 pm  Break  Reception Room, Lind Hall 400  
4:00 pm  Franklin
Mendivil Acadia University 
Fractal VectorMeasures on Fractals Talk pdf postscript 

5:005:30 pm  Herb
Kunze University of Guelph 
Using the Picard Contraction Mapping to Solve Problems in ODEs Talk pdf 
Name  Department  Affiliation 

Simon Alexander  Applied Mathematics  University of Waterloo 
Michael Barnsley  Mathematics & Statistics  University of Melbourne 
Eugene Belogay  Honors College, FAU  5353 Parkside Dr. 
Santiago Betelu  Institute for Mathematics and its Applications  
Jamylle Carter  Institute for Mathematics and its Applications  
Barry Cipra  
Steven Demko  Iterated Systems, Inc.  
JeanLuc Dugelay  Multimedia Communications  Institut EURECOM 
Fred Dulles  Institute for Mathematics & its Applications  
John Elton  Mathematics  Georgia Institute of Technology 
Selim Esedoglu  Institute for Mathematics and its Applications  
Vicki Fegers  Program Development and Alignment  School Board of Broward County, FL 
Michael Frame  Mathematics  Union College 
Robert Gulliver  Mathematics  University of Minnesota 
Raouf Hamzaoui  Inst. fur Informatik  Universitat Leipzig 
Bin Han  Institute for Mathematics and its Applications  
Doug Hardin  Mathematics  Vanderbilt University 
Lyman Hurd  MediaBin  Iterated Systems, Inc. 
Mary Beth Johnson  Program Development and Alignment  School Board of Broward County, Florida 
Herb E. Kunze  Math & Stats  University of Guelph 
Instructor Kevin Lee  Mathematic/Computer Science  Normandale Community College 
Jaques LevyVehel  INRIA, Rocquencourt  
Ning Lu  Advanced Digital Imaging Laboratories, Inc.  
Franklin Mendivil  Math  Acadia University 
Willard Miller  Institute for Mathematics & its Applications  
Ken Musgrave  FractalWorlds.com  
Jianliang Qian  Institute for Mathematics and its Applications  
Dietmar Saupe  Institut fur informatik  Universitaet Leipzig 
Cheri Shakiban  University of St. Thomas  
Martin J. Turner  Institute of Simulation Sciences  De Montfort University 
Edward Vrscay  Applied Mathematics  University of Waterloo 
Ruifeng Xie  Iterated Systems, Inc. 