Recursive Trefoil Knot - Another Perspective

Higher quality versions: Ello | G+ | 2x@Dribbble | 960x960 + node setup at Imgur

This is an alternate perspective on my original “Recursive Trefoil Knot” design.

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 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.

Zipper Knot

High quality version here: http://imgur.com/gallery/YI4weD2

This design came about entirely by accident. I had been trying to create an animated set of tubular nylon strands like the beauty that is the album artwork for Above and Beyond’s “Group Therapy”, when I turned on geometric displacement and realized that the intensity was set up way too high. Added a Glossy shader, and POW! Happy Accidents!

If you’re not yet familiar with it “Group Therapy”, you should definitely listen to that album - but note that you WILL cry.

This GIF is one in a set named “Knot” - hopefully I’ll be able to create and post more soon - this idea has a lot of unexplored potential.

DIY Celtic Knot Pillow Tutorial from Johanna Rundel.

This pillow is made out of tights filled with polyfill. If you like this DIY, I’d suggest going and looking at the tutorial ASAP because a designer has threatened everyone else (including me) who has posted a DIY knot pillow with legal action saying this pillow design infringes upon her design.