All on their own, ordinary processes can make incredibly convoluted shapes. Consider, for instance the field lines of some magnets moving around each other, as shown in this video by Daniel Piker, who has a great blog of computational gnarl called Space Symmetry Structure.
William Rood has created a somewhat inscrutable—but mind-boggling—gnarl investigating page, just click on the screen-captured image below. It's like flying an alien spaceship, with control buttons that you don't understand. No matter, keep on clicking and gaze your fill.
Owen Maresh, another young investigator, is posting some exceedingly gnarly videos on his YouTube site. Here's one that starts out calm—like an egg—but then goes ape via some folds through the subdimensions.
And finally, how about an explanation from the old Professor himself. Here's my dada video: "What is Gnarl?" (with a narration that's partly in imaginary Norwegian).
You just don't get this kind of information anywhere except on BoingBoing!