Paul Bourke has, amongst other wonders, some scary renderings of Julia fractals over the quaternions. Here’s one of them:

Aaargh!

What you see is only a 3D slice of the true horror, as the quaternions form a 4-dimensional algebra. (You didn’t think it stopped at complex numbers, did you? And it doesn’t stop at quaternions either; there are octonions, sedenions, and indeed Cayley-Dickson algebras of dimension 2^n, for all n right up to infinity. Or su’ink.) If you’re not thinking fourth dimensionally, you can use time as your other axis and make pretty animations, and with the right colour scheme, all the scariness goes away. Maths imitates racism.

In a fit of true cosmic coincidence, not only was yesterday Gaston Julia’s birthday, it was celebrated by Google with a holiday logo which googledotted the above page. And as if that wasn’t enough, I find Haddock, via Plasticbag, linking to the Buddhabrot image, created with code by - that’s right - Paul Bourke! Sometimes I think a global consciousness will arise as an emergent phenomenon of the clickpaths around various net resources.