Lissajous curves with a finite sum of prime number frequencies

TL;DR

This paper explores Lissajous curves generated by finite sums of sinusoidal functions with prime number frequencies, inspired by the Ulam spiral, to analyze their geometric properties.

Contribution

It introduces a novel method of constructing Lissajous curves using prime number frequencies, expanding the understanding of their mathematical and visual characteristics.

Findings

Distinct geometric patterns emerge from prime-based frequencies

Prime frequency sums produce unique Lissajous curve symmetries

Potential applications in signal processing and mathematical visualization

Abstract

The Ulam spiral inspired us to calculate and present Lissajous curves where the orthogonally added functions are a finite sum of sinus and cosines functions with consecutive prime number frequencies.