Graph Directed Coalescence Hidden Variable Fractal Interpolation Functions

TL;DR

This paper introduces a graph directed approach to coalescence hidden-variable fractal interpolation functions, expanding the understanding of their self-affine properties and interpolation capabilities for multiple data sets.

Contribution

It develops a graph directed iterated function system framework for generalized data sets, demonstrating that attractor projections interpolate data via CHFIFs.

Findings

Projections of attractors are the graphs of CHFIFs.

The approach handles multiple data sets simultaneously.

It generalizes existing fractal interpolation methods.

Abstract

Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated function system (IFS) corresponding to the data set is the graph of the FIF. Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) is both self-affine and non self-affine in nature depending on the free variables and constrained free variables for a generalized IFS. In this article graph directed iterated function system for a finite number of generalized data sets is considered and it is shown that the projections of the attractors on $\mathbb{R}^{2}$ is the graph of the CHFIFs interpolating the corresponding data sets.