Iterated Function Systems for Lossless Data Compression

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


Iterated Function Systems with place-dependent probabilities are considered. Fascinating geometrical invariants, that apply even when there is no unique invariant measure, are presented. Furthermore, it is shown that the invariant measure of a stationary stochastic process, when it contains no atoms and is fully supported, can sometimes be associated with an IFS with probabilities, and with an associated dynamical system. This leads to the idea of an ergodic transform of a string of symbols, with respect to a given string; this is introduced and shown to be useful; it provides a unifying geometrical approach to the description of data compression algorithms such as Huffman, arithmetic, and the Burrows-Wheeler transform.


Invariant Measure Iterate Function System Compression Function Stationary Stochastic Process Intuitive Picture 
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.


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Copyright information

© Springer-Verlag New York, Inc. 2002

Authors and Affiliations

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

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