Hidden variable recurrent fractal interpolation function with four function contractivity factors

TL;DR

This paper introduces a new construction method for hidden variable recurrent fractal interpolation functions with four contractivity factors, enhancing flexibility and diversity in modeling irregular natural objects.

Contribution

It presents a novel approach to constructing one and bivariable HVRFIFs using RIFS with four contractivity factors, expanding the capabilities of fractal interpolation.

Findings

Enhanced flexibility in fractal interpolation functions.

Ability to model more irregular and diverse structures.

Improved description of natural objects' complexity.

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 important to ensure flexibility and diversity of the construction of interpolation function. Recurrent iterated function system (RIFS) produce fractal sets with local self-similarity structure. Therefore the RIFS can describe 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 contractivity 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.