Polar IFS + Individual Genetic Programming = Efficient IFS Inverse Problem Solving

Abstract : The inverse problem for Iterated Functions Systems (finding an IFS whose attractor is a target 2D shape) with non-affine IFS is a very complex task. Successful approaches have been made using Genetic Programming, but there is still room for improvement in both the IFS and the GP parts. The main difficulty with non-linear IFS is the efficient handling of contractance constraints. This paper introduces Polar IFS, a specific representation of IFS functions that shrinks the search space to mostly contractive functions. Moreover, the Polar representation gives direct access to the fixed points of the functions, whereas the fixed point of general non-linear IFS can only be numerically estimated. On the evolutionary side, the "individual" approach is similar to the Michigan approach of Classifier Systems: each individual of the population embodies a single function rather than the whole IFS. A solution to the inverse problem is then built from a set of individuals. Both improvements show a drastic cut-down on CPU-time: good results are obtained with small populations in few generations.
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Contributor : Marc Schoenauer <>
Submitted on : Tuesday, November 29, 2005 - 5:06:34 PM
Last modification on : Friday, May 25, 2018 - 12:02:05 PM
Long-term archiving on: Friday, April 2, 2010 - 11:15:58 PM


  • HAL Id : inria-00000877, version 1



Pierre Collet, Evelyne Lutton, Frédéric Raynal, Marc Schoenauer. Polar IFS + Individual Genetic Programming = Efficient IFS Inverse Problem Solving. [Research Report] 3849, 1999, pp.31. ⟨inria-00000877⟩



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