Fractal Continuation

TL;DR

This paper extends the concept of analytic continuation to fractal functions, which are defined as attractors of iterated function systems, broadening the scope of function continuation in mathematical analysis.

Contribution

It introduces a novel method for continuing fractal functions analytically, generalizing traditional analytic continuation techniques.

Findings

Fractal functions can be analytically continued using the proposed method.

The continuation preserves the fractal structure of the original function.

The approach broadens the understanding of fractal functions in complex analysis.

Abstract

A fractal function is a function whose graph is the attractor of an iterated function system. This paper generalizes analytic continuation of an analytic function to continuation of a fractal function.