Sierpinski triangle (XOR) snap-fit pieces
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Identical snap-fit pieces that can be snapped together to produce patterns based on XOR such as Sierpinski triangles
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This is a rework of https://www.printables.com/model/882253-sierpinski-triangle-xor-jigsaw-pieces, which is based on 2D jigsaw fittings. The new one has side snaps that are hidden when assembled.
Identical copies of this snap-fit piece, based on a hexagon, can be fit together at 120° rotations to implement an XOR function between neighbors, as shown:
If you start with a single piece with an output of 1 (2nd or 3rd above) and continue down row by row, you will construct a Sierpinski triangle like the one below. Note that this is a synthetic image based on repeats of the top triangle. I would have had to print 366 tiles to make an actual photo of it.
Alternatively, you can begin with other starting states. You will always get patterns with empty regions that are either single or larger triangular assemblies of hexes.
I have three variations of the pieces. One is simply a solid hexagon, leaving no gap at all for smallest 0 values. Another uses a circular indentation to create holes, like the jigsaw version. The one shown above removes an entire rhombus, one third of the hex so that 0s display as hexagonal holes. I think this is the best choice, but I am leaving the others to try out. I also leave a small ledge around the rhombus to make it easier to identify if the piece is facing up.