Here are 4 coasters illustrated with images of the Hilbert curve.

The Hilbert curve is usually generated in stages and the first coaster shows four separate curves of first, second, third and fourth orders.

The other three coasters display fourth order curves where individual lines are replaced by larger and larger rectangles. The effect is to create patterns with interesting symmetry.

The four sets of stl files are:

medley_coaster.stl and medley_pattern.stl four_30_coaster.stl and four_30_pattern.stl four_80_coaster.stl and four_80_pattern.stl four_101_coaster.stl and four_101_pattern.stl

The openSCAD code that created the patterns is hilbert_patterns.scad and the patterns it created are in h_dxf.zip as dxf files. The program that created the coasters is hilbert_coasters.scad.

Jbum, thing:14546, has created an attractive music box with a Hilbert curve on the lid and gadgetguydk's entry, thing:1011, contains an image of a high order Hilbert curve.

Hilbert curves were discovered by David Hilbert in 1891. They are an important part of mathematical history and now widely used. You can read about them on Wikipedia.

The coasters are squares 90 mm on a side. They should be constructed directly on the build surface. I used one shell and five percent infill. If the build surface is well leveled the coasters will have an attractive shiny surface.