Univariable affine fractal interpolation functions

An overview of affine fractal interpolation functions using a suitable iterated function system is presented. Furthermore, a brief and coarse discussion on the theory of affine fractal interpolation functions in 2D and their recent developments including some of the research done by the authors is provided. Moreover, the desired range of the contractivity factors of an affine fractal interpolation surface are identified such that it is monotonic and positive for the respective monotonic and positive surface data. All the shape-preserving fractal schemes developed here are verified by numerical experiments.