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

TL;DR

This paper analyzes how perturbations in contractivity factors affect the stability and fractal dimensions of hidden variable recurrent fractal interpolation functions, providing bounds for their box-counting dimensions.

Contribution

It introduces error estimates for perturbations in contractivity factors and derives bounds for the box-counting dimension of HVRFIF and HVBRFIF functions.

Findings

Errors on perturbation of contractivity factors are estimated.

Upper and lower bounds for the box-counting dimension are obtained.

The results enhance understanding of stability and fractal characteristics of the functions.

Abstract

In this paper, we study errors on perturbation of function contractivity factors and box-counting dimension of hidden variable recurrent fractal interpolation function (HVRFIF). The HVRFIF is a hidden variable fractal interpolation function (HVFIF) constructed by recurrent iterated function system (RIFS) with function contractivity factors. The contractivity factors of RIFS determine fractal characteristics and shape of its attractor, so that the HVRFIF with function contractivity factors has more flexibility and diversity than the HVFIF with constant contractivity factors. Stability of interpolation function according to perturbation of the contractivity factors and the box-counting dimension of interpolation function plays very important roles in determining whether these functions can be applied to practical problems or not. We first estimate errors on perturbation of function contractivity factors and then obtain the upper and lower bounds of the box-counting dimension of one variable HVRFIF. Finally, in the similar way, we get the lower and upper bounds of box-counting dimension of hidden variable bivariable recurrent fractal interpolation function (HVBRFIF).