Back in the 1980s, Stephen Wolfram began experimenting with cellular automata — little rule-sets that govern the “growth” of a collection of dots on an infinitely-sized grid. He’d pick a simple rule, set down a single dot, and then watch to see what sort of colony grew out of it. He expected each rule to produce a simple, repeated pattern — and was surprised when some of the rulesets produced seemingly chaotic, unpredictable shapes. Simple rules, it seems, can produce very complex results, an epiphany that Wolfram spun out into his masterwork A New Kind of Science.

Now he’s turned his automata into something really trippy: Music. He takes a vertical slice of one of his enormous automata grids, lays it horizontal, and uses it as a musical score, with each filled-in cell representing a tone. He calls it WolframTones — man, can anyone create a trademarked name these days that doesn’t include a gratituous internal capitalization? — and intriguingly, the resulting music is strangely tuneful. This, Wolfram says, is because …

… in the computational universe it’s easy to find rules that make complex forms. And that’s how WolframTones manages to create so many different complex musical compositions. Each composition in a sense tells in music the story of some system in the computational universe. And because the system follows a definite consistent rule, the compositions inevitably have a certain internal consistency — which is probably what makes them so effective as music.

Check out that page and you can hear an example. Then you can go to this page where Wolfram’s team has set up a little generator: Pick a musical style — from classical to rock/pop to latin — and it generates an automata, dumps it into the template, and plays the tune. If you like what you’ve done, you can even turn it into a ringtone, which is just the most brilliant thing evah. Let your phone ring with math!

(Thanks to Boing Boing for this one!)