Set-valued fractal surfaces for countable data sets: Approximation and fractal dimension

In this paper, we have shown the construction of the set-valued fractal surface for the countable data set. The constructed fractal surfaces are approximated and error bounds between them is calculated. The existence and uniqueness of an invariant Borel probability measure supported on the graph of the set-valued fractal surface map are established. Further, the bounds on the Hausdorff dimension of the set-valued fractal surface is calculated.