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In this paper, we study errors on perturbation of function contractivityfactors and box-counting dimension of hidden variable recurrent fractalinterpolation function (HVRFIF). The HVRFIF is a hidden variable fractalinterpolation function (HVFIF) constructed by recurrent iterated functionsystem (RIFS) with function contractivity factors. The contractivity factors ofRIFS determine fractal characteristics and shape of its attractor, so that theHVRFIF with function contractivity factors has more flexibility and diversitythan the HVFIF with constant contractivity factors. Stability of interpolationfunction according to perturbation of the contractivity factors and thebox-counting dimension of interpolation function plays very important roles indetermining whether these functions can be applied to practical problems ornot. We first estimate errors on perturbation of function contractivity factorsand then obtain the upper and lower bounds of the box-counting dimension of onevariable HVRFIF. Finally, in the similar way, we get the lower and upper boundsof box-counting dimension of hidden variable bivariable recurrent fractalinterpolation function (HVBRFIF).

Estimation of errors on perturbation of function contractivity factors  and box-counting dimension of hidden variable recurrent fractal interpolation  function