Forgery League

Back in high school, I played around with fractals, after finding a writeup about the Mandelbrot set in a back issue of Scientific American. The article had loads of dazzling colour renderings, the likes of which would grace psychedelic CD covers a few short years later: spidery frost patterns, seahorse-like whorls, lighting licking around tiny replicas of the snowman-shaped set.

All that colour and infinite detail came from a mind-bendingly simple equation, calculated over and over: z_n+1 = z_n² + c. The article provided a snippet of pseudocode, which I compiled in C and ran for days on end on the family PC/AT, pumping the raw results through DeluxePaint to colour them. (Later on I added a pause function so my mum and dad could use the computer again.)

It was a window into a mysterious mathematical world: look at the latest image and pick out an interesting looking bit, work out its co-ordinates, and start up the calculations again, and a day or two later, enjoy the results. There was no end to its detail no matter how much you zoomed in on it, and always with those circles upon circles. Similar but never the same: a fractal.

I hadn’t thought much about the Mandelbrot set until a few days ago, when I happened on a link to the Mandelbulb, a recently-discovered 3-D analogue to the old-school set.

It’s… a little creepy.

Its knobbly symmetry gives it the look of some sort of sea creature or single-celled organism, like something Ernst Haeckel might have conjured up in a feverish daze. As you zoom in it proves to be covered in crazy textures: ridges and flowers and macrame tangles. Who could have guessed that a 3-D Mandelbrot set would look so… knitted?

I was fascinated enough by it that I chose an image or two from that web page to use as my desktop at work. And then the other day as I was shutting down for the evening, a co-worker who was stopping by stared and blurted out, “Ew! What is that hideous thing?” She was a bit sheepish about the violence of her reaction – something about the texture, she said – but she’s hardly the only one to feel this way; the comments on MetaFilter and Boing Boing seem to alternate between “hey, awesome”, “whoa, trippy” and “augh, disturbing”.

Kind of amazing, really. It’s just a handful of equations you could fit on the back of a business card. So how can it shake us up so deeply?

One is certainly that texture-phobia. The Unusual Phobias site has collected a number of variations, but clusters and holes (bunches of grapes, honeycombs, crumpets) seem to elicit loathing in a whole lot of people, and just reading their accounts makes me feel it a little bit too.* Is it some ancient fear of wasp nests? Maggot-riddled flesh? Eggs? I suspect bugs are somehow connected.

Worse, if you carry out the calculations to produce higher levels of detail, the Mandelbulb turns out to be surrounded by a “foam” of little spheres, the equivalent of the flat set’s circles-on-circles.

Two: stretchiness. There are places where the virtual fabric of the Bulb seems to be distorted in ways that just look unnatural, like an Evan Penny sculpture.

Three: scale. You can zoom in on this thing to any level and still find it covered with bewildering detail. It never ends. It is arbitrarily large. You could fall into it and never hit bottom.

And finally, there’s the fact that on an actual organism, if there are complex structures it’s because they’ve evolved to serve a function, like metabolism or defense. The Mandelbulb may be born of pure mathematics, but all its bumps and and ridges and spirals look like they’re meant to do something. But what?

Exploring the Mandelbrot set felt a little like exploring a landscape. The Bulb, by contrast, as a three-dimensional object, has a presence – a hair-raising, eldritch presence. Even its discoverers refer to it as “the creature”.

Just look at it… radiating weird malevolence as it sits there, a smug, blobby sea-cucumber. The Mandelbulb: it knows something we don’t.

* My personal horror is intersecting forks – it’s something about the leverage they can exert, thereby bending out of shape accidentally. Maybe I damaged a tooth on a fork as a kid.