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!
Rudy Rucker is a writer, a mathematician, and a computer scientist--with thirty-two published books. In the 1980s he received two Philip K. Dick awards, for his cyberpunk novels Software and Wetware, which are available as part of the Wares tetralogy. Rucker has a Ph.D. in mathematics, and he worked as a computer science professor at San Jose State in Silicon Valley for twenty years. He took up painting in 1999, and he's had three shows of his pop-surreal works in San Francisco. Rucker's latest publication is his autobiography, Nested Scrolls. Nested Scrolls received the Emperor Norton Award for "extraordinary invention and creativity unhindered by the constraints of paltry reason."