Advertisement

Introduction to IMA Fractal Proceedings

  • Michael F. Barnsley
Part of the The IMA Volumes in Mathematics and its Application book series (IMA, volume 132)

Abstract

This volume describes the status of fractal imaging research and looks to future directions. It is to be useful to researchers in the areas of fractal image compression, analysis, and synthesis, iterated function systems, and fractals in education. In particular it includes a vision for the future of these areas.

Keywords

Invariant Measure Fractal Compression Image Compression Iterate Function System Fractal Image 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Davis G.; Why fractal block coders work. In [18], 1992.Google Scholar
  2. [2]
    Sagan H.; Space-Filling Curves. Springer-Verlag: New York, 1991.Google Scholar
  3. [3]
    D. Peak and Frame M.; Chaos Under Control — The Art and Science of Complexity. W.H. Freeman and Company: New York, 1994.Google Scholar
  4. [4]
    Stenflo O.; Ergodic Theorems for Iterated Function Systems Controlled by Stochastic Sequences. Umea University, 1998.Google Scholar
  5. [5]
    Peitgen H.O., Jürgens H., Saupe D.; Chaos and Fractals — New Frontiers in Science. Springer-Verlag: NewYork, 1992.Google Scholar
  6. [6]
    Hutchinson J.; Fractals and self-similarity. Indiana Univ. J. Math. (1981), 30, 713–747.MathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    Mandelbrot B.B.; Fractal Geometry of Nature. W.H. Freeman and Company: New York, 1982.MATHGoogle Scholar
  8. [8]
    Barnsley M.F. and Demko S.G.; Iterated function systems and the global construction of fractals. Proc. Roy. Soc. London Ser. A (1985), 399, 243–275.MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    Barnsley M.F.; Fractals Everywhere. 2d Edition, Academic Press: Boston 1993.MATHGoogle Scholar
  10. [10]
    Doeblin W. and Fortet R.; Sur des chaînes a liasons completes. Bull. Soc. Math. de France (1937), 65, 132–148.MathSciNetGoogle Scholar
  11. [11]
    Kaijser T.; On a new contraction condition for random systems with complete connections. Roumaine Math. Pures Appl. (1981), 26, 1075–1117.MathSciNetMATHGoogle Scholar
  12. [12]
    Elton J.; An ergodic theorem for iterated maps. Ergod. Th. Dynam. Sys. (1987), 7, 481–488.MathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    Stenflo O.; Uniqueness of invariant measures for place-dependent random iteration. This volume, 2001.Google Scholar
  14. [14]
    Lau K.S., Ngai S.M., and Rao H.; Iterated function systems with overlaps and self-similar measures. Preprint, 1999.Google Scholar
  15. [15]
    Maudlin R.D. and Williams S.C.; Random recursive constructions: asymptotic, geometric, and topological properties. Trans. Am. Math. Soc. (1986), 295(1), 325–346.CrossRefGoogle Scholar
  16. [16]
    Vrscay E.; From fractal image compression to fractal-based methods in mathematics. This volume, 2001.Google Scholar
  17. [17]
    Lu N.; Fractal Imaging. Academic Press: Boston, 1997.MATHGoogle Scholar
  18. [18]
    Barnsley M.F. and Hurd L.P.; Fractal Image Compression. A.K. Peters: Boston, 1992.Google Scholar
  19. [19]
    Jacquin A.; Image coding based on a fractal theory of iterated contractive image transformations. IEEE Transactions on Image Processing (1992), 1, 18–30.CrossRefGoogle Scholar
  20. [20]
    Fisher Y. (Ed.); Fractal Image Encoding and Analysis. Springer-Verlag: Berlin, 1998.MATHGoogle Scholar
  21. [21]
    Fisher Y. (Ed.); Fractal Image Compression. Springer-Verlag: New York, 1995.Google Scholar
  22. [22]
    Hamzaoui R. and Saupe D.; Fractal image compression with fast local search. This volume, 2001.Google Scholar
  23. [23]
    Barnsley M. and Sloan A.; A better way to compress images. Byte Magazine, 1988.Google Scholar
  24. [24]
    Ida T. and Sambonsugi Y.; Image segmentation using fractal coding, IEEE Trans. on Circ. Sys. for Video Tech. (1995), 5, 567–570.CrossRefGoogle Scholar
  25. [25]
    Demko S., Khosravi M., and Chen K.; Image descriptors based on fractal transform analysis, SPIE Conference: On Storage and Retrieval for Image and Video Databases VII, 1999, pp. 379–389.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 2002

Authors and Affiliations

  • Michael F. Barnsley
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of MelbourneParkvilleAustralia

Personalised recommendations