Recursive Trefoil Knot: Top

Everyone here is familiar with the concept of the Trefoil Knot, right? Topologically, it's the simplest possible non-trivial knot. Well, I like that shape a lot, so I wanted to make one of my own… but this is where the recursion comes in, and this is the cool part: The objects moving along this path are exactly the same shape as the path itself, and they're all interlinked! They each move and rotate along the path while maintaining that linkage the whole time. AWW YEAH HOT MATHS!

I will be posting another perspective of this same scene in just a moment.

I have also prepared a 1920x1080 1 minute looping video of these two perspectives in case you would like to put on some music, fullscreen them, and study them without distraction. I recommend trying this because this animation is hot.

For this design, I chose to learn how to work with moving objects along a Bezier Curve using the Blender Animation Nodes Addon. It took a while to figure out how to move objects along a curve using the “Follow Path” constraint, and then to ditch that approach because it wouldn't allow me to build complete loops in rotation. Then it took me a while to learn how to use the “Evaluate Spline” node, and convert the derivative tangent at that point in the curve into a rotation that I could use to orient my moving objects like the “Follow Path” constraint does. It took me a while longer to figure out that I needed to be performing compound rotation matrix multiplication in order to rotate the shapes along their animated axis first, and then orient them to the direction of that tangent.

See this node setup here.