Lissajou pattern, lissajou figure, lissajou curve or lissajous pattern, lissajous figure, lissajous curve. We're talking about the same thing here people. I'm no expert, but the guy's name was Jules Lissajous. Seems to me we should all add the final 's' and stick with lissajous. Cripes, if he didn't know how to spell his own name then who does?
Anywho...these patterns are displayed using smoke and mirrors , oops ... I mean light and mirrors or on an oscilloscope.
They're made by combining two periodic waves - one vertical one horizontal. When the amplitude and frequency of these two signals are identical the resulting figure is a steady circle. As we slowly vary the frequency of one signal, the circle will seem to rotate.
As we vary the strength of one signal the pattern becomes elliptical. So, varying both the strength and frequency gives us rotating ellipses and pretty soon multiple ellipses until it looks like someone just discovered a spirograph.
And guess what? You can't pronounce 'lissajous'. Not no way, not no how. Can't be done. Not only that, but you've seen them over and over again and didn't even know it. All those old sci-fi films, Dr. Who, Star Dreck, old Japanese B-movies -- yep, most of the time there's some old oscilloscope in the background with pretty little spirographic ellipses circling to give the impression that this is some pretty serious science we're doing here.
There are actually practical applications for lissajous patterns. But I think we'll leave that to another noder.