Discontinuous Fractal Functions and Fractal Histopolation

TL;DR

This paper explores the extension of fractal functions to discontinuous cases and introduces fractal histopolation, advancing approximation methods for real data that often require discontinuous models.

Contribution

It demonstrates that many results on fractal functions can be extended to discontinuous functions and introduces the concept of fractal histopolation for area matching.

Findings

Extension of fractal function results to discontinuous functions

Introduction of fractal histopolation concept

Potential applications in data approximation

Abstract

Fractal functions that produce smooth and non-smooth approximants constitute an advancement to classical nonrecursive methods of approximation. In both classical and fractal approximation methods emphasis is given for investigation of continuous approximants whereas much real data demand discontinuous models. This article intends to point out that many of the results on fractal functions in the traditional setting can be immediately extended to the discontinuous case. Another topic is the study of area matching properties of integrable fractal functions in order to introduce the concept of fractal histopolation.