Pairing functions are used to reversibly map a pair of number onto a single number—think of a number-theoretical version of `std::pair`. Cantor was the first (or so I think) to propose one such function. His goal wasn’t data compression but to show that there are as many rationals as natural numbers.

Cantor’s function associates pairs (i,j) with a single number:

…but that’s not the only way of doing this. A much more fun—and spatially coherent—is the boustrophedonic pairing function.