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Orthogonal Decomposition of Fractal Sets

In: Approximation and Computation

Author

Listed:
  • Ljubiša M. Kocić

    (University of Niš)

  • Sonja Gegovska - Zajkova

    (Ss Cyril and Methodius University)

  • Elena Babače

    (Ss Cyril and Methodius University)

Abstract

It is well known that interactive modeling of fractal sets is a very difficult task. The common constructive tool, Iterated Function Systems (IFS) fails to be of big help in this matter. On the contrary, the concept of Affine invariant Iterated Function Systems (AIFS) makes modeling partially possible, and in addition it offers natural algorithms that can generate both fractal (so non-smooth) and smooth, polynomial objects. While IFS is usually based on Cartesian rectangular coordinates, the AIFS is constructed using areal (normalized barycentric) coordinates. Here, we show the existence of the bijective transform between IFS and AIFS, and give explicit formulas in n-dimensional real spaces. Also, we point out that these mappings are based on orthogonal projections, and give characteristic examples.

Suggested Citation

  • Ljubiša M. Kocić & Sonja Gegovska - Zajkova & Elena Babače, 2010. "Orthogonal Decomposition of Fractal Sets," Springer Optimization and Its Applications, in: Walter Gautschi & Giuseppe Mastroianni & Themistocles M. Rassias (ed.), Approximation and Computation, pages 145-156, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-6594-3_11
    DOI: 10.1007/978-1-4419-6594-3_11
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