I added a second post on my new Patreon, about my plans for a three-dimensional expanding racks design based on the srs net (also known as the Laves graph). See www.patreon.com/posts/135832...

I never got around to posting this animation I made with Saul Schleimer.This animates successively better approximations to a space-filling curve. (Or rather, you can tile the plane with the shape, and that gives the approximation to the space-filling curve.)

Here’s another clip from my video on expanding rack and pinion mechanisms - an expanding pythagorean triple triangle. There’s a reason why it’s easier to make this kind of triangle! Full video at
youtu.be/iWknov3Xpts

New video on some expanding 3D printed designs based on rack and pinion mechanisms:
youtu.be/iWknov3Xpts