We generalise the notion of fractal interpolation functions (FIFs) to allow data sets of the form where I = [0, 1] n . We introduce recurrent iterated function systems whose attractors G are graphs of continuous functions f : I → R, which interpolate the data. We show that the proposed constructions generalise the previously existed ones on R. We also present some relations between FIFs and the Laplace partial differential equation with Dirichlet boundary conditions. Finally, the fractal

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... ons of a class of FIFs are derived and some methods for the construction of functions of class C p using recurrent iterated function systems are presented.