Constructive Approximation

, Volume 2, Issue 1, pp 303–329 | Cite as

Fractal functions and interpolation

  • Michael F. Barnsley


Let a data set {(xi,yi) ∈I×R;i=0,1,⋯,N} be given, whereI=[x0,xN]⊂R. We introduce iterated function systems whose attractorsG are graphs of continuous functionsfIR, which interpolate the data according tof(xi)=yi fori ε {0,1,⋯,N}. Results are presented on the existence, coding theory, functional equations and moment theory for such fractal interpolation functions. Applications to the approximation of naturally wiggly functions, which may show some kind of geometrical self-similarity under magnification, such as profiles of cloud tops and mountain ranges, are envisaged.

AMS classification

26A 28A 41A 44A 60J 

Key words and phrases

Interpolation Fractals Moment theory 


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Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • Michael F. Barnsley
    • 1
  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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