FourierToy
Inspired by Matt Henderson’s post, I created this interactive visualization of the Fourier series in terms of epicycles.
Below, you see 8 components corresponding to the integer frequencies from 1 to 8. The blue circle represents the amplitude and phase of each component. You can change these by clicking and dragging around each box. You can also set the amplitude manually by typing in a value from 0 to 1.
Holding shift will lock the phase in 45° multiples, and holding control will lock the amplitude in place.
The right-click context menu has a few wave presets.
Keyboard shortcuts
Space bar: reset everything to zero
Up / down: speed up and slow down the animation
Left / right: rotate the phases of all components at once
Ctrl + 1-8: set the associated component to zero
T: toggle the blue trace
Ctrl+backspace: clear graph
