Tie the proverbial knot using math!

I worked on creating a sort of fractal sequence by using two simple transformations: First, I started with a single tetrahedron in space. and I rotate it by a random amount about a random angle. Next, I transform it a small amount outwards to create a long strip of tetrahedrons. This sequence creates the sea urchin look of the thing above.

To make this thing move, I rotate the first tetrahedron in a chain by a tiny amount, then the next, then the next, each time maintaining the coordinate system that the previous rotation created. When done each frame, this causes the tentacles to "curl" inwards, and the severity of the angle and its direction determine how quickly and in which orientation this curling plays out. Here is a series of screens that illustrate the transformation (the coloring is just for effect).


The order of the original structure (even though there is some randomness to how it is shaped) is quickly turned into a chaotic mass of tentacles that curled quickly, eminating grasping tentacles that curled slowly. Thus we have chaos from order!