Learn English – word for “back and forth”

Lifting the mouse is perfectly adequate, and is used in the business to describe this exact action. For example, take this excerpt from a magazine review of a mouse:

The ability to tweak lift-off distance is great; we like to lift our mouse a lot, so by setting the M60 to not track at any height, we ended up with solid mousing.

There's also a page by a mouse manufacturer about the related jargon lift-off distance.

It is specific enough because it's about the only reason to lift the mouse.

I do not think that the motion in webs and kaleidoscopes are described by exactly the same phenomenon. I think that Voronoi Diagrams and Delaunay Triangulation would be most interesting to your inquiry about webs. I would call their motion "Voronoi optimizations." Hyperbolic tessellations are more closely related to kaleidoscopes and I would describe their motion as simply "kaleidoscopic."