First up, we have a variation on the Mandelbrot Set called the Buddhabrot, so named for its resemblance to the seated Buddha. They take the M-set, rotate it 90 degrees, and do some cool probabilistic effects to make it look ghostly. Here’s the result (click to enlarge):
We’ve also got an incredible 10-minute dive into the unfathomably microscopic reaches of the M-Set, right here:
And finally, reader Alex Caswell asked yesterday if I knew of any other sweet fractal patterns besides the M-Set. Absolutely! Here’s one called the Burning Ship Fractal:
Many more pictures of the Burning Ship, even cooler than the one above, are right here.
This concludes Fractal Week. It’s been fun! Have a great weekend. I’ll be back Monday with, I don’t know, something that isn’t about math!
Brian D. Buckley 
Its fairly obvious to me how a fractal can be infinitely complicated… my curiosity lies in the computing power needed to calculate the datasets necessary to generate such a high resolution video of an infinite zoom on the M-set…
Reminds me a little of the V’Ger sequence from Star Trek 1 though far more interesting.
As you might guess there are a couple of factors in the computing power needed:
1) The number of iterations per point: Most Mandelbrot sets use color as a way of representing how fast a point goes toward infinity (or above a certain bound). Once you dig deep you need increasing amounts of iterations to get detail. 500 to 1000 is good for maybe the first minute of the film, then more as you go along. So, for a 720×480 pixel DVD quality render you’d already be talking about 345.6 million calculations per frame.
2) Resolution of floating point numbers: I don’t want to even begin to imagine the number of decimal points they’re diving down, but I have a hunch they’ve gone beyond 64-bit at least. Probably the more microscopic required writing their own floating point math algorithm.
My hunch is we’re thinking render farm, like the one they had at ACCAD. I’ll have to see how deep my little program can go on a single desktop for comparison.
Agreed, they have to have some kind of custom floating point math algorithm going here, because this is way beyond anything you’d get with any standard data types.
Yeah, I was wondering that too. No clue, sorry!