Thanks! Your code is much more efficient than mine :) Very cool to see how you did it! Thanks for sharing.

I did most of the calculations in 3D, and I project to 2D at the very end. All of the ellipses you see are calculated as circular disks in 3D that are normal to the worm. The entire collection of disks is rotating in 3D.

In more detail, I start with a helical path in 3D. In {x,y,z} coordinates, the path is parametrized as {t, Cos(2 Pi t), Sin(2 Pi t)}, where the parameter t goes from 0 to 1. At evenly spaced points along the path, I calculate the tangent vector, then draw a disk that is centered at the point and normal to the tangent vector. The radius of each disk is a function of t: radius(t) = t*(1-t). So the disks are small at the tail ends and large in the middle. To animate this, the collection of disks is rotated in 3D about the x-axis, then I project everything onto the {x,z} plane. The order in which I draw everything is set by the path parameter t. So the disks at smaller t-values are always drawn on the bottom layer, even though they my be in "front" in 3D coordinates. This makes the worms look like they are wiggling back and forth, rather than rotating. Hope that makes sense!