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We provide a general framework to construct fractal interpolation surfaces(FISs) for a prescribed countably infinite data set on a rectangular grid.Using this as a crucial tool, we obtain a parameterized family of bivariatefractal functions simultaneously interpolating and approximating a prescribedbivariate continuous function. Some elementary properties of the associatednonlinear (not necessarily linear) fractal operator are established, therebyinitiating the interaction of the notion of fractal interpolation with thetheory of nonlinear operators.

On Bivariate Fractal Interpolation for Countable Data and Associated Nonlinear Fractal Operator