Abstract
A fractal surface is a set which is a graph of a bivariate continuous function. In the construction of fractal surfaces using IFS, vertical scaling factors in IFS are important one which characterizes a fractal feature of surfaces constructed. We construct IFS with function vertical scaling factors which are 0 on the boundaries of a rectangular grid using arbitrary data set on a rectangular grid and give a condition for an attractor of the IFS constructed being a surface. Finally, lower and upper bounds of Box-counting dimension of the constructed surface are estimated.
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