Laser-cut Gosper-curve Trivet 2017-12-14

At my university, students can get access to 3D-printers, laser cutter/engraver and other nice and handy tools after a short introduction course for a given machine. Students are then free to use them any time, provided you find and reserve a time slot.

I just finished the short intro course for the laser cutter and engraver. I am now eager to start burning things! I thought coasters and trivets would be good candidates for a first project. Now only to decide what to engrave or cut to make good use of the laser cutter's capabilities.

Space-filling curves are an interesting class of curves, they have a fractal nature which often look very pretty. The fractal nature is used to make the curve fill more and more of a 2D area until the entire area is filled. However, the number of itterations of this fractal behaviour can be limited, allowing us to control how detailed and intricate we want the curve to be.

The Gosper curve is such a space-filling curve, which I find looks very interesting! Having this as a trivet would be nice! The wikipedia article for the Gosper curve has a figure (in svg format) of this curve after 4 itterations. The wikipedia figure also gives the perl script (mirror) that was used to generate the svg file. Here we can simply change the number of itterations from 4 to 3. Giving us the following, less fussy, curve, compared the 4th itteration curve.

Next, I open up the generated .svg file in Inkscape. Here I wish to outline the thick curve lines with a thin red path that the laser-cutter will interpret as the path to use for cutting. This gives me the following svg, ready to be sent to the laser-cutter.

The result...