Linkage

Daniel Lemire speeds up binary search using parallel data-comparison instructions (\(\mathbb{M}\), see also). Presenting only the surname of an author is inconvenient, especially for authors from some East Asian cultures with a few very popular surnames. As posted by Joanna Ko, who has one of them. 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 (\(\mathbb{M}\))? And that using a different Latin square than the \(2\times 2\) 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…