Post #2063155

You might know that if you make a Sierpinski tetrahedron (by subdividing a regular tetrahedron into four smaller tetrahedra at its corners and a central regular octahedron, removing the octahedron, and recursing) and then stop after finitely many levels, you get a set of vertices that from certain directions projects onto a square grid. But did you know that listing the third (projected out) coordinate for these grid points gives them the structure of a Latin square? And that using a different Latin square than the 2x2 one as the basis for recursion can produce other fractal sets that have the same property of projecting to a square from certain directions? See section 4 of Hideki Tsuiki's "Imaginary Cubes — Objects with Three Square Projection Images", https://archive.bridgesmathart.org/2010/bridges2010-159.pdf