On the Bernstein Affine Fractal Interpolation Curved Lines and Surfaces

Abstract

In this article, firstly, an overview of affine fractal interpolation functions using a suitable iterated function system is presented and, secondly, the construction of Bernstein affine fractal interpolation functions in two and three dimensions is introduced. Moreover, the convergence of the proposed Bernstein affine fractal interpolation functions towards the data generating function does not require any condition on the scaling factors. Consequently, the proposed Bernstein affine fractal interpolation functions possess irregularity at any stage of convergence towards the data generating function.

Keywords

• attractor
• Bernstein polynomial
• bivariate surfaces
• dynamic system
• fractal interpolation
• iterated function system