REVIEW ON FRACTAL INTERPOLATION FUNCTIONS

The idea of fractal interpolation dates back to the 1980s, however several recent developments on its new types and generalization frameworks have made this domain ripe for extensions, further analyses, and reliable applications. Commencing from the background of Barnsley’s fundamental fractal interpolation function, this review paper summarizes the state of the art encompassing significant contributions in the fractal literature. This paper begins with the review on types of fractal interpolation functions and discusses results on fractional calculus theory emphasizing the relation between scaling factor and fractional order with numerical examples. Special focus is shed on the fractal dimension of fractal interpolation functions and its linear connection with fractional order. Further, the discussion on parameter identification problems highlights the importance of right choice of scaling factors for effective approximation. The paper also reviews differentiable fractal interpolation functions, in addition, encompasses recent advancements related to new contraction maps, shape preserving properties and real-world applications in different domains.