Implementing a Hilbert map of the Internet

Question

In the XKCD comic 195 a design for a map of the Internet address space is suggested using a Hilbert curve so that items from a similar IP adresses will be clustered together.

Answer 1

Essentially you would decompose the number, using pairs of bits, MSB to LSB. The pair of bits tells you if the location is in the Upper Left (0) Lower Left (1) Lower Right (2) or Upper Right (3) quadrant, at a scale that gets finer as you shift through the number.

Additionally, you need to track an "orientation". This is the winding that is used at the scale you are at; the initial winding is as above (UL, LL, LR, UR), and depending on which quadrant you end up in, the winding at the next scale down is (rotated -90, 0, 0, +90) from your current winding.

So you could accumulate offsets :

suppose I start at 0,0, and the first pair gives me a 2, I shift offsets to 0.5, 0.5. The winding in the lower right is the same as my initial one. The next pair reduces the scale, so my adjustments are going to be 0.25 in length.

This pair is a 3, so I translate only my x coordinate and I am at .75, .5. The winding is now rotated over and my next scale down will be (LR, LL, UL, UR). The scale is now .125, and so on and so on until I run out of bits in my address.