The $Z$-Curve as an $n$-Dimensional Hypersphere: Properties and Analysis

TL;DR

This paper introduces an algorithm that projects the n-dimensional Z-curve onto an n-dimensional sphere, creating a new mathematical object and analyzing its properties.

Contribution

The paper presents a novel algorithm for projecting the Z-curve onto a hypersphere and studies the resulting object's properties.

Findings

New mathematical object derived from Z-curve projection

Properties of the n-dimensional hypersphere representation

Potential applications in higher-dimensional analysis

Abstract

In this research, we introduce an algorithm that produces what appears to be a new mathematical object as a consequence of projecting the \( n \)-dimensional \( Z \)-curve onto an \( n \)-dimensional sphere. The first part presents the algorithm that enables this transformation, and the second part focuses on studying its properties.