http://corte.si/posts/code/hilbert/portrait/index.html
And you can see what this looks like when used to visualize sorting algorithms at large scale here:
http://corte.si/posts/code/sortvis-fruitsalad/index.html
And here:
I've also published an Open Source project that might be useful to anyone who wants to play with these ideas:
https://github.com/cortesi/scurve
There are some limitations to the process as described - most obviously the fact that I'm using the RGB color space which is not the best match for human color perception. RGB is convenient because it is a regular cube and therefore easy to map onto the Hilbert curve, but with a little work the process could be generalized.