Toroidia
Adventures in Toroidal Geometry.

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.