On beautiful math that makes beautiful art

The other day at the office I was talking with some friends about animation, art, code, math. You know, the usual stuff. The subject of beauty came up, and it occurred to me that beauty, in all of these different disciplines, is often associated with elegant solutions to problems. Beautiful math explains complex phenomena with simple formulas, while beautiful animation accomplishes rich and layered storytelling goals with seemingly simple actions.


A couple of days later I stumbled on Daniel White’s amazing 3D fractal images, via my friend Saschka. I’ve been a fan of fractals since reading Mandelbrot’s book in high school. The Mandelbrot set is this rare creature that’s beautiful both mathematically (an elegant formula) and visually (rewarding exploration with endless variety). Like everybody else, I wondered whether something as beautiful could exist in three dimensions (or more, for that matter!) Until recently, though, nothing had turned up. There were beautiful shapes made using complex formulas, and elegant formulas that made ho-hum images, but nothing as sublime as Mandelbrot’s set. This thing, though, looks very promising!

If you like math even a little bit, it’s really worth reading White’s account of how these images got made. The guy wrote his own renderer, for crying out loud!

Daniel White doesn’t seem convinced yet that this object is the “real” 3D Mandelbrot, and I’m inclined to agree: as stunning as it is visually, there’s something a bit unwieldy about the formula, with all its thetas and phis. But what’s wonderful is the way White and his colleagues are conducting their search. They’re not content with just one kind of beauty. It won’t be “real” to them unless it has both!

Another Dragon trailer

I guess there are two different trailers making the rounds. This one is the “international” trailer (which I think really means “not the USA or Canada”.) It’s interesting to see how they pitch the movie slightly differently to different audiences. The same warnings apply: watch this only if you don’t mind spoilers!

How to Train Your Dragon trailer

This is the movie I’ve been working on for the past year or so. I can’t say enough good about this film. By far the best one I’ve ever worked on, I can recommend it without hesitation. Yes, it’s that good!

The trailer is finally up, and it has a bunch of my shots in it! (The freeze frame you see below is one of them.) I have mixed feelings about posting the trailer here: on the one hand, compared to the previous teasers and leaked footage that’s been out there, this does a much better job at representing what the movie’s really like. But on the other hand, it takes a lot of sweet moments and shows them out of context, which could take away some of the surprise and enjoyment when you see it in the theater. So, if you don’t mind spoilers, watch the trailer below. But if you’d rather keep yourself pure and unsullied, just wait ’til March 26th and go see it on the big screen!

And here’s a link to the full-res trailer if you’d like to see it a bit bigger!