Fourier Approximators and your Intuition

I've mentioned before that I'm a real fan of anything that improves your physical intuition. Previously, I noted a nice, compact color-coded form of the Fourier equation. Now, from Ben Grawi comes this very cool visualization tool

It lets you build up a few complex waveforms (square, triangle, sawtooth) with a variable number of terms. If you play with it a bit, you can quickly see just how many (or, how few) terms it takes to get a decent approximation of what you're looking for.

There are three things that I especially like about this. First,  you can isolate different terms, and see what they look like by themselves. Secondly, this provides perhaps the best intuitive insight I've ever seen into "overshoot" (if you are deeply, nerdily interested, then I suggest you follow his link about the Gibbs Phenomenon). I also really like how you can visually see the impact of phase: pick some settings, and then toggle back and forth between "square" and "sawtooth", and you'll see what I mean. 

Anyway, this thing is gorgeous, and a fantastic little intuition pump (especially if you're a visual learner for whom the math itself isn't satisfying).