This folder has some animated expansions of state boundaries as complex partial Fourier series.
They are in MP4 video format -- the next format will be animated SVG.
A classical epicycle is almost the same as a term in the Fourier series,
except that 2 terms in the Fourier series can have the same period
but different orientations - one clockwise and the other counterclockwise.
The number of epicycles is always even.
The constant term does not count as an epicycle.
In the first plot, x is the real axis and y is the imaginary axis.