FFT magic explained with animations and smoothies, not equations

Ah, the Fast Fourier Transform. You see it throughout audio and synthesis. And, of course, it’s the thing that … transforms … things. Faster. It’s a fast way of transforming things. Probably a guy named Fourier was involved. Wait – ever wish you knew more about what an FFT actually is and how it works – or even if you do know, wish you had a better visual reference in your own mind and a way to explain to others?