Narrow Results

We construct hidden variable bivariate fractal interpolation surfaces (FIS). The vector valued iterated function system (IFS) is constructed in ℝ⁴ and its projection in ℝ³ is taken. The extra degree of freedom coming from ℝ⁴ provides hidden variable, which is an important factor for flexibility and diversity in the interpolated surface. In the present paper, we construct an IFS that generates both self-similar and non-self-similar FIS simultaneously and show that the hidden variable fractal surface may be self-similar under certain conditions.

We present a method of construction of vector valued bivariate fractal interpolation functions on random grids in ℝ². Examples and applications are also included.