In a nutshell, an iterated function system made up of a finite number of iterated mappings on a complete metric space produces a fractal interpolation function. The characteristics and shape of the fractal functions are significantly influenced by the vertical scaling factors, which are significant set of free parameters in the iterated mappings. Not only in the case of affine fractal function but also in the non-affine cases, the vertical scaling factors uniquely determine the corresponding fractal function when the interpolation points are prescribed in advance. In the previous Chapter, various types of fractal interpolation functions are discussed but all are limited within the case of constant vertical scaling factors ( \(\alpha _n\) , constant parameters). Using constant parameters in iterated function system, one can make each iterated mapping possess the same vertical compression ratios on an identical subinterval that belongs to a partition of some closed interval defining the fractal function. This means that the FIFs generated by those IFSs with constant parameters usually have obvious self-similarity character, which could lead to the loss of flexibility, and might cause obvious errors in fitting and approximation of some complicated curves and non-stationary data that show less self-similarity. This complication can be rectified by defining variable or function scaling offering greater advantages. In addition, the concept of optimization of scaling parameters is much more useful as it provides better approximation than both the constant and variable scalings.