Adventures in Toroidal Geometry.
You may also be interested in this newer applet on the same theme.
I once met a guy on the Internet who told me that everything in the universe is made of circles of circles of circles.
A circle of circles is a toroid*; a circle of toroids is, for want of a better name, a supertoroid.
What you're looking at here is a spiral on the supersurface of a supertoroid.
This guy told me he knew by direct experience that this is the shape of Things.
One day I realised I knew how to animate it; the mathematics are straightforward enough.
There is still plenty to do with the maths, I think.
There is something strangely beautiful about toroidal convergence.
*This claim deserves some qualification. Specifically, a toroid is the shape made by a circle rotated about a point in the same plane as itself.
Return is the movement
of the Tao.
Yielding is the way of the Tao.
All things are born
Being is born of non-being.
Te Ching, ch. 40.