Fractal Interpolation Surfaces and Perturbations on Vertical Scaling Factors

Abstract: A hyperbolic iterated function system (IFS) whose attractor is the graph of a continuous function f : [a, b] × [c, d] → R that interpolates the given data in R is considered. The function f is called the bivariate fractal interpolation function (FIF) arising from the IFS and the graph of f which is a surface in R is called the bivariate fractal interpolation surface (FIS). By introducing a small perturbation in the vertical scaling factors that are involved in the construction of the IFS, a perturbed iterated function system in R is obtained. Due to perturbation in the vertical scaling factors, there is a change in the FIF. In this paper, the change in the FIF due to the change in the scaling factors of the IFS is primarily studied. An upper bound for the error estimation between the original FIF and the perturbed FIF is also found.