[IgorPartola]

Obligatory: http://xkcd.com/195/

Edit: I wish there was an updated version.

[danielweber]

What is that way of ordering numbers called? If I knew the name I could google it but that's what I'm missing.

[Coincoin]

It's called a Hilbert Curve.

https://en.wikipedia.org/wiki/Hilbert_curve

[tbrownaw]

It's a variety of space-filling curve.

That's enough to find out that this particular one is called a Hilbert curve.

[Cameron_D]

http://internetcensus2012.bitbucket.org/images.html

This page has similar images from 2012