Last edited 17oct14 by

Lissajous Curves in the Third Dimension

made by Graham Ellinghausen for MATH 198 F14


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.


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


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.