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In this paper, we introduce a construction of hidden variable recurrentfractal interpolation functions (HVRFIF) with four function contractivityfactors. In the fractal interpolation theory, it is very important to ensureflexibility and diversity of the construction of interpolation function.Recurrent iterated function system (RIFS) produce fractal sets with localself-similarity structure. Therefore the RIFS can describe the irregular andcomplicated objects in nature better than the iterated function system (IFS).Hidden variable fractal interpolation function (HVFIF) is neither self-similarnor self-affine one. The HVFIF is more complicated, diverse and irregular thanthe fractal interpolation function (FIF). The contractivity factor is importantone that determins characteristics of FIFs. We present a constructions of onevariable HVRFIFs and bivariable HVRFIFs using RIFS with four functioncontractivity factors.

Hidden variable recurrent fractal interpolation function with four function contractivity factors