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Affine Mappings in Iterated Function Systems

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Abstract

Today the reproduction of pictures in journals and books is no longer possible without “information compression”. This important process needs “Iterated Function Systems”-in short IFS. Doing so, affine mappings and their properties play a fundamental role.

In this paper we distinguish between distance contracting and area contracting mappings and we investigate the connections between.

The main goal is to find a criterion which allows to decide if the iteration process of an IFS converges or not.

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Literature

  1. M. Barner — F. Flohr, Analysis II. Berlin (1982)

  2. M. F. Barnsley, Fraktale. Heidelberg (1995)

  3. M. Bernardi — C. Bondioloi, On a problem in the geometry of seifaffine fractals. Rendiconti Istituto Lombardo Milano, Vol. 135, 31–41 (2002)

    MATH  Google Scholar 

  4. G. A. Edgar, Measure, topology and fractal geometry. Berlin (1990)

  5. K. Falconer, Fractal geometry. Chichester (1990)

  6. E. Hutchinson, Fractals and self similarity. Indiana University Math. J. Vol. 30, No 5, 713–747 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  7. H. O. Peitgen — H. Jürgens — D. Saupe, Bausteine Chaos Fraktale. Berlin (1992)

  8. H. Zeitler — D. Pagon, Fraktale Geometrie. Braunschweig (2000)

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Zeitler, H. Affine Mappings in Iterated Function Systems. Results. Math. 46, 181–194 (2004). https://doi.org/10.1007/BF03322880

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  • DOI: https://doi.org/10.1007/BF03322880

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