On the morphisms of fractal curves that increase their smoothness

TL;DR

This paper introduces a method to transform self-similar fractal curves into smooth curves using self-affine zippers, enhancing their smoothness properties.

Contribution

It presents a novel construction that converts self-similar zippers into self-affine zippers with smooth attractors, advancing fractal curve theory.

Findings

Transforming self-similar zippers yields smooth fractal curves.

The construction applies in -dimensional space.

It broadens the class of fractal curves with smooth properties.

Abstract

We propose a construction which transforms a self-similar zipper in $\mathbb R^n$ to a self-affine zipper $\mathbb R^{n+1}$ whose attractor is a smooth curve.