Shape Preserving Zipper Hidden Variable Fractal Interpolation Function

TL;DR

This paper introduces a new class of shape-preserving fractal interpolation functions created via a zipper hidden variable iterated function system, expanding the diversity and generality of fractal interpolation methods.

Contribution

It develops a novel zipper hidden variable iterated function system and constructs univariate zipper fractal interpolation functions with shape-preserving properties.

Findings

Conditions on vertical scaling factors ensure boundedness, positivity, and shape preservation.

Examples demonstrate the effectiveness of the proposed methods.

Abstract

In this paper, we study a new class of zipper fractal interpolation functions (ZFIFs) constructed using a zipper hidden variable iterated function system (ZHVIFS). ZFIFs have more diverse shape than usual fractal interpolation functions, and the hidden variable iterated function system is more general than the iterated function system. Firstly, we introduce a ZHVIFS and construct univariate ZFIFs using the ZHVIFS. Next, we find the conditions on vertical scaling factors for the ZFIFs to preserve boundedness, positivity and piecewise slop of the data set, which are demonstrated through examples.