Those not able to see the video, the computer is Albert Michelson's (1852 - 1931) Harmonic Analyzer to perform Fourier Analysis, and is part one of a four part series (staggered upcoming release dates for next three installments). I do wish he'd have all the segments in the series uploaded or at least show a bit more of the mechanical operation as that seemed to be quite ingenious. The clips shown of the mechanical operation either seemed slowed down or altered/shot at an artsy angle which while visually appealing make it hard to appreciate "how it works" overall.
It's not quite what you're looking for (a simulation of the machine, which would be amazing to see in its own right), but according to this video [3], it looks like they've built a neat webapp for the purpose of having a sort of fourier synthesis playground.
Unfortunately, there's just the demo video, with no link to the site itself, and searching turned up nothing. They may plan to release it later on in the series.
[1] http://vimeo.com/engineerguy/videos
That version can run most processing apps within the browser with no plugins or setup, thus letting interested users just visit a link to use the app.