CONSTRUCTION OF FRACTAL SURFACES

Abstract

The paper approaches the construction of fractal surfaces of interpolation and approximation on the basis of a fractal perturbation of any mapping defined on a rectangle. Conditions for the differentiability of these elements are also provided. The fractal surfaces obtained may be used for the approximation of real-world data. The method proposed does not require any restriction on the type of data. Furthermore, the present approach does not imply the solution of large systems of equations. The paper considers both the continuous and the discontinuous case.