Covers of Fractal Interpolation Surfaces with Finite Families of Octahedrons

Abstract In a previous work (Chaos Solitons Fract 173:113674, 2023), we presented a method for finding a finite family of closed balls whose union contains the attractor of a given iterated function system. In this paper, for the particular framework of fractal interpolation surfaces, we provide an improved version of it. This approach is more efficient, from the computational point of view, as it is based on finding the maximum of certain sets, in contrast to the previous method which uses a sorting algorithm.