Box-counting dimension and analytic properties of hidden variable fractal interpolation functions with function contractivity factors

TL;DR

This paper investigates the box-counting dimension bounds and analytic properties of hidden variable fractal interpolation functions, enhancing modeling flexibility for natural phenomena.

Contribution

It provides new bounds for the box-counting dimension of HVFIFs and HVBFIFs, along with analysis of their smoothness and stability.

Findings

Bounds for box-counting dimension of HVFIFs and HVBFIFs are established.

Analytic properties such as smoothness and stability are analyzed.

Enhanced modeling flexibility for natural phenomena is demonstrated.

Abstract

We estimate the bounds of box-counting dimension of hidden variable fractal interpolation functions (HVFIFs) and hidden variable bivariate fractal interpolation functions (HVBFIFs) with four function contractivity factors and present analytic properties of HVFIFs which are constructed to ensure more flexibility and diversity in modeling natural phenomena. Firstly, we construct the HVFIFs and analyze their smoothness and stability. Secondly, we obtain the lower and upper bounds of box-counting dimension of the HVFIFs. Finally, in the similar way, we get the lower and upper bounds of box-counting dimension of HVBFIFs constructed in [21].