I had previously mounted a small UV laser module on the AxiDraw to do cool stuff like light painting and drawing on phosphorescent/glow in the dark vinyl. Searching for other things to expose with the UV laser, I thought on Cyanotype paper (a.k.a. solar paper, sun print paper, etc.). This is light-sensitive paper which turns blue when exposed to light (mainly below about 410nm) and washed with cold water. It's not particularly sensitive, so doesn't require any darkroom precautions for handling the unexposed paper.
I bought my paper from www.cyanotype.co.uk. The paper is coated with a mixture of a ferric salt and potassium ferricyanide. Under exposure to light, the ferric ion is reduced to ferrous, which reacts with the ferricyanide to produce insoluble Prussian blue when the paper is washed. Washing also removes unexposed ferric salt. See the Wikipedia article for more details on the chemistry.
I first tried some simple straight lines to see what sort of speed was required. Results below:
Works very well and produces a really sharp line! I measured about 0.1-0.2mm, depending on the speed. 5mm/s seems pretty good - fast enough to still produce a good visible line. Obviously this will depend on laser power and focal spot size, so you'd need to experiment.
I then fired up the Lorenz attractor script I'd written and tried a full drawing at 5mm/s. Here's the paper just after exposure - you can see a light blue line where the paper has been exposed. The drawing is about 30mm square.
I also did a bigger drawing and included some extra text (drawn via Inkscape). The bold text at the top is shaded using Inkscape's hatch fill extension.
Closeup of the lines - I was afraid they would all blur into a big solid area, but they are all distinct!
Video showing the exposure and washing:
A more powerful laser (e.g. one of those 2W varieties which seem popular on EBay) would obviously expose the paper a lot faster. Deliberately defocusing the beam might produce a wider line, or one with soft edges, which would be an interesting effect.