aequationes mathematicae

, Volume 42, Issue 1, pp 1–22 | Cite as

Vector—valued fractal interpolation functions and their box dimension

  • Peter R. Massopust
Research Papers


We introduce continuous functions f:\(I \subseteq \mathbb{R} \to \mathbb{R}^n ,n > 1 \), whose graphs are the attractors of certain iterated function systems, and which interpolate a given set of data or interpolation points Δ={(t j ,x j ):j = 0, 1, ⋯, M; M >1} according tof(t j ) =x j . The box dimension of the graph of these functions is in general non-integral. We present a formula for this dimension. Applications to the approximation of complicated self-affine functions are indicated.

AMS (1980) subject classification

41 26 


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Copyright information

© Birkhäuser Verlag 1991

Authors and Affiliations

  • Peter R. Massopust
    • 1
  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA

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