The General Curl
The Theory
The image you posted above is trace visualization for what is known as a divergence free vector field. To demonstrate what that mean, consider particles that move along the lines you see above (The field represents their velocity), if the field is indeed divergence f...
First time I've seriously considered awarding a bounty to show appreciation. The amount of effort put into that answer is insane.
Anways, if there is a hat for awarding a bounty - that'd be a good excuse to get it.