The Penrose tiles by pleppik got me thinking and I decided they would be cooler if they held together on their own. The snap shapes enforce the matching rules (as long as all the pieces are right-side up), which means any pattern you make out of them will be aperiodic.
Print lots of each rhombus. Turn off fill in order to print just the perimeter (this makes them print fast and snap together easily). Using Multiply, I managed to cram 16 of rhomb1 onto a TOM build platform and 18 of rhomb2 (it helps to use some negative separation with rhomb2). This would be a perfect use for an Automated Build Platform, but mine isn't attached right now. I can still print upwards of 30 tiles per hour.
Assemble. It's easy to get stymied (for instance, nothing can attach to certain parts of the black star). The arcs also represent the maching rule, so lining up arc segments helps to figure out where pieces can go. The arcs are formed by thin slices out of the STLs; they only go halfway up so you can tell which side is the top. As the pattern gets larger, the ratio of rhomb1 to rhomb2 tiles will approach the golden ratio (~1.618), because math is awesome.
The OpenSCAD file is fully parametric in case you want to modify these.