This is the bost basic demonstration of what a surface-tiling curve is: a space-filling curve which, when duplicated and transformed (flipped and rotated), tiles the surfaces of an object with an unbroken line.

The examples here are a little fancier than straightforward curves (which don’t have to have visual curves in them – curves in this context can have sharp angles). Each change in direction the curve takes (the corners) has been splined to give each angle a gentler slope and a wavy appearance.