# Non-stationary Fractal Interpolation

## TL;DR

This paper extends fractal interpolation by introducing non-stationary iterated function systems, allowing for more flexible fractal functions with varied local and global behaviors, based on recent fixed point theories.

## Contribution

It proposes a new framework for non-stationary fractal interpolation using sequences of set-valued maps and recent fixed point theories, expanding the scope of fractal functions.

## Key findings

- New classes of fractal functions with diverse behaviors
- Extension of fractal interpolation to non-stationary settings
- Application of non-stationary fixed point theory

## Abstract

We introduce the novel concept of a non-stationary iterated function system by considering a countable sequence of distinct set-valued maps $\{\mathcal{F}_k\}_{k\in \mathbb{N}}$ where each $\mathcal{F}_k$ maps $\mathcal{H}(X)\to \mathcal{H}(X)$ and arises from an iterated function system. Employing the recently developed theory of non-stationary versions of fixed points [11] and the concept of forward and backward trajectories, we present new classes of fractal functions exhibiting different local and global behavior, and extend fractal interpolation to this new, more flexible setting.