Co.Design

Geeky Science Problems Double as Works of Art

Sparse matrices: A lot prettier than they sound

The work you see here is so pretty, you'd hardly guess it's the product of some of the world's biggest math nerds.

The pieces are digital sparse matrices, and scientists and engineers use them to visualize exceedingly complex problems, like whether they can build a working electrical circuit (below, middle) or make a helicopter fly (below, bottom). Think of it this way: Simulating flight on a computer makes a lot more sense than building a physical prototype then trying to fly it yourself (and failing). It just so happens that the simulation is beautiful, too.

Timothy Alden Davis, a computer, information science, and engineering professor at the University of Florida, is a sort of Eli Broad with a pocket protector. He's got the largest open-source collection of sparse matrices in the world, and he shared some examples with us recently.

Here's a visualization of your classic investment puzzler: How do you invest stocks and bonds, so they produce the best return?

Here's a manufacturing problem: If you build a car, will it have annoying vibrations?

This simulates the structural loading of an exhibition hall in Beijing:

This is what a matrix looks like when it doesn't address any issue in particular. Davis calls it a ?random fuzzball."

Davis started collecting matrices years ago, because he develops software people use to make their own matrices, and the best way for him to hone his methods is to see them applied in the real world. But he's also the first to appreciate the matrices on pure aesthetic grounds -- so much so, they've turned him into something of a bard. See what we mean here and here.

[Images by Yifan Hu, AT&T Labs -- Research; courtesy of Timothy Davis]

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