As simple as it could possibly get...

[gumboot]

... and yet still highly amusing:

http://www.flashpedia.net/linesuperfollow.swf

Don't neglect the buttons at the bottom of the screen.

[Kelloggs]

Aha! Inertia!

(as I realised upon wondering why the blobs were orbiting the mouse... it's a thing on a spring!)

[piku]

That works really well if you whizz the mouse around quickly

[gumboot]

Original link's dead. Google points to: http://gprime.net/game.php/linesuperfollow


But was looking for this thread because http://arstechnica.com/ had an advert on a similar theme (seems to be gone, now, and people with lo-tech browsers posted a lot of hate about it). Too lazy to check the source, I found someone else had and it points back to:

http://codepen.io/nikrowell/pen/BNdaKV

Again, still too lazy to read the source, even with it right there in front of me on my screen, I figured that the way I'd do that would be to record mouse position history and to apply an asymmetric, steep low-pass or band-pass filter, maybe with some extra gain above DC, to that data before re-plotting it. Extra-extra gain to separate the individual filaments.

But it looked a bit like later samples were filtered differently from older samples, giving that decay back to flatness and stability. Rather than running various filters (although that shouldn't necessarily cost more than a single FIR) I'd probably lerp between filtered and unfiltered.

But on a quick scan through the source it looks like a trivial IIR with overshoot expressed in a funny way.