Last edited 17oct14 by ellingh2@illinois.edu

# Lissajous Curves in the Third Dimension

### made by Graham Ellinghausen for MATH 198 F14

## Abstract

Lissajous curves are figures that can be produced by parametrically plotting two periodic equations. These curves have applications in audio analysis and engineering. By adding a third periodic equation, a Lissajous figure can be brought into the third dimension and can produce a Lissajous knot under certain conditions.

## Proposal

I plan to create several RTICAs in JavaScript to render two- and three-dimensional Lissajous curves from both arbitrary cosine functions and audio signals.

2D Lissajous Figures
Harmonographs

## Updates

10/20/14: I have modified my website to my liking and written a simple interactive page in JavaScript using the canvas to display a 2-dimensional Lissajous curve with custom coefficients, and then modified this file to make another interactive page that could draw a harmonograph figure.

10/31/14: I have started working on a JavaScript page that graphs a Lissajous knot on a canvas object, and I'm working on implementing proper rotation of the figure about three axes.

11/14/14: I have been working on my Lissajous knot RTICA and implementing rotation with the keyboard arrow keys rather than sliders.