Journey to the bottom of the Mandelbrot set

If you want to explore the Mandelbrot set, or fractals in general, you have endless options, but you should definitely look at the Xaos Fractal Browser. It’s been super-streamlined for zooming around quickly. Lots of people use it and upload their pictures to Flickr, and Flickr, in turn, makes it easy for me to embed this dandy slideshow.

Zooming around in Mandelbrot space got me thinking about the problem of mathematical exploration in general. I did a little googling and found this news item. (Note: actually I made it up)

WASHINGTON, DC (May 1, 2009)

Government officials were scrambling this morning to put the finishing touches on what’s being touted as the “most significant exploration initiative since Apollo.” The program, called Fractal One, has been established to plant an American flag on the bottom of the Mandelbrot set. Lead mathematician for the program Curt Canneford explained: “The Mandelbrot set is a mathematical object, a fractal set of fantastic richness. The deeper you delve into it, the more mysteries you find. It’s unconscionable that, since its discovery more than twenty years ago, we still don’t know where it stops.”

Bipartisan support has been building for the initiative. As Representative Malcolm Blakey (R, Missouri) explained at a press conference yesterday, “When we heard that the French were funding an expedition to set foot on the bottom of the Mandelbrot set, we realized this was a matter of national pride and competitiveness. Why, in an age when Everest has been climbed, the Marianas trench plumbed, and the moon itself claimed for this great republic, is the Mandelbrot set still hiding secrets? This math resource should be probed and exploited. We might find oil, mineral wealth, or lots of cool pictures for American students to put up in their dorm rooms.”

Late last night, underscoring the urgency of the effort, came word of an imminent Chinese expedition, and there was an unsubstantiated claim that a Russian team was “already there.”

What will it look like at the bottom? It’s hard to say. Lead Mandelnaut Irving Bell was sanguine about the dangers. “We’re talking about extremely small numbers… the linear dimensions alone will measure less than 10 to the minus 128. The computational pressures will be enormous. The iteration counts near the bottom could pin us down for weeks, and a divergent blowout could happen at any time.”

It was a stirring scene as he and his team, against the backdrop of a large American flag, were sealed into the stainless steel Fractal One compute pod and lowered into the complex set.