Hidden Variable Recurrent Fractal Interpolation Functions With Function Contractivity Factors

Abstract

In this paper, we introduce a construction of hidden variable recurrent fractal interpolation functions (HVRFIF) with four function contractivity factors. In the fractal interpolation theory, it is very import ant to ensure flexibility and diversity of the construction of interpolation function. Recurrent iterated fu nction system (RIFS) produce fractal sets with local self-similarity structure. Therefore the RIFS can d escribe the irregular and complicated objects in nature better than the iterated function system (IFS). Hidden variable fractal interpolation function (HVFIF) is neither self-similar nor self-affine one. The HVFIF is more complicated, diverse and irregular than the fractal interpolation function (FIF). The co ntractivity factor is important one that determins characteristics of FIFs. We present a constructions of one variable HVRFIFs and bivariable HVRFIFs using RIFS with four function contractivity factors.