Summary
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.
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