A Constructive Finite Field Method for Scattering Points on the Surface of $d$-Dimensional Spheres

TL;DR

This paper introduces a new constructive method for scattering points uniformly on the surface of d-dimensional spheres, addressing a complex problem with broad applications across multiple scientific fields.

Contribution

The paper presents a novel constructive approach for distributing points on spheres, advancing the methodology for uniform scattering in higher dimensions.

Findings

Method effectively scatters points on spheres in various dimensions

Potential applications in crystallography and molecular modeling

Improves upon existing uniform distribution techniques

Abstract

In this exploratory article, we present a constructive method for scattering points on the surface of $d$ dimensional spheres which we believe is new and of interest. Indeed, the problem of uniformly distributing points on spheres is an interesting and difficult problem with vast applications in fields as diverse as crystallography, approximation theory, computational complexity, molecular structure, and electrostatics.