The Petrovsky Flux is a magnificent site in Second Life that you should see as soon as you can: Click this SLurl teleport link to do so. It's a beautifully weird steampunk contraption that self-assembles into a floating city of rusty pipes and iron-latticed apartments and more. And after it has done creating itself, it begins to disassemble in mid-air. And the process begins again.
The creation of two Residents named blotto Epsilon and Cutea Benelli, the Petrovsky Flux is the successor to the Bogon Flux, which they made in 2008, but it is far more grand: "We just turned the dogs loose there a little over a week ago," as Mr. Epsilon put it to me. "There are five independent structures that grow among each other, each with different boundaries... the highest goes up to about 350 meters, I think."
There's more to know about the Petrovsky Flux, listen:
Named after a Soviet mathematician, the Flux is inspired by a paper he wrote, "on the lacunae that occur in the region where the solution of a hyperbolic partial differential equation vanishes." What you see in Second Life, the creators explain in a delightfully unhelpful notecard, is "the effluent that results from squishing a Petrovsky lacuna (a findng involving pliers, single malt scotch, and kitten sausage)". So it's got that going for them.
"The branches all grow independently," Epsilon tells me as we dangle hundreds of meters up, "so when it gets very branchy, we are right up against the grey goo fence limits. The number basic components is fairly small, but the direction of growth is totally random... the compexity comes when the branches weave among each other. The branches are opportunistic about seeking space to grow into."
Here is a YouTube machinima to occupy your time before seeing the Flux first-hand, or if (as might happen), lag from so much math occasionally grinds it to a halt. And once again, here is the link to click to take you there as an avatar. You'll notice that it's hosted on a sim called the Spencer Art Museum, because it's the SL presence of a gallery of the same name that's located on the campus of the University of Kansas. However, when you get to the Petrovsky Flux, you'll realize that you are decidedly not in Kansas anymore.
Update, 11/13: Toxic Menges also shot an expressionistic machinima of the Flux, that's really beautiful, probably best viewed after you've seen the object in-world: