Fractals in Multimedia

1. Front Matter

   Pages i-x

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2. Introduction to IMA Fractal Proceedings

   • Michael F. Barnsley

   Pages 1-12

3. Uniqueness of Invariant Measures for Place-Dependent Random Iterations of Functions

   • Örjan Stenflo

   Pages 13-32

4. Iterated Function Systems for Lossless Data Compression

   • Michael F. Barnsley

   Pages 33-63

5. From Fractal Image Compression to Fractal-Based Methods in Mathematics

   • Edward R. Vrscay

   Pages 65-106

6. Fractal Image Compression with Fast Local Search

   • Raouf Hamzaoui, Dietmar Saupe

   Pages 107-120

7. Wavelets are Piecewise Fractal Interpolation Functions

   • Douglas P. Hardin

   Pages 121-135

8. Self-Affine Vector Measures and Vector Calculus on Fractals

   • F. Mendivil, E. R. Vrscay

   Pages 137-155

9. Using the Picard Contraction Mapping to Solve Inverse Problems in Ordinary Differential Equations

   • H. E. Kunze, E. R. Vrscay

   Pages 157-174

10. Fractal Modulation and Other Applications from a Theory of the Statistics of Dimension

    • J. M. Blackledge, S. Mikhailov, M. J. Turner

    Pages 175-195

11. Signal Enhancement Based on Hölder Regularity Analysis

    • J. Lévy Véhel

    Pages 197-209

12. Iterated Data Mining Techniques on Embedded Vector Modeling

    • Ning Lu

    Pages 211-231

13. A Web-Based Fractal Geometry Course for Non-Science Students

    • Michael Frame

    Pages 233-257

14. Back Matter

    Pages 259-269

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This IMA Volume in Mathematics and its Applications FRACTALS IN MULTIMEDIA is a result of a very successful three-day minisymposium on the same title. The event was an integral part of the IMA annual program on Mathemat­ ics in Multimedia, 2000-2001. We would like to thank Michael F. Barnsley (Department of Mathematics and Statistics, University of Melbourne), Di­ etmar Saupe (Institut fUr Informatik, UniversiUit Leipzig), and Edward R. Vrscay (Department of Applied Mathematics, University of Waterloo) for their excellent work as organizers of the meeting and for editing the proceedings. We take this opportunity to thank the National Science Foundation for their support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume grew out of a meeting on Fractals in Multimedia held at the IMA in January 2001. The meeting was an exciting and intense one, focused on fractal image compression, analysis, and synthesis, iterated function systems and fractals in education. The central concerns of the meeting were to establish within these areas where we are now and to develop a vision for the future.

• Area
• Digital Imaging
• Interpolation
• Measure
• Volume
• algorithms
• data compression
• modeling
• multimedia
• statistics

• Department of Mathematics and Statistics, University of Melbourne, Parkville, Australia

  Michael F. Barnsley

• Institut für Informatik, Universität Leipzig, Leipzig, Germany

  Dietmar Saupe

• Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Canada

  Edward R. Vrscay

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