Ha, boring :) I just tried to find a couple of addresses I use/know on the map and it was a nice challenge.
For octets closer to the center of their highest order square it was quite easy by just trial and error. But for octets at the edge of their square like e.g. 149 I admit having used pen and paper...
It says the the intent was to make it similar to https://xkcd.com/195/ , i.e. with a space filling curve that preserves grouping, but actual implementation doesn't seem to do that. For example, the upper left squares are:
0 1
2 3
As opposed to
0 1
3 2
Also, 127.0.0.1 is near the right center edge of the map, while 128.0.0.1 is next row down near the left center edge.
For the visual patterns on the map that does not make a major difference.
* Obviously for all of the same color it makes no difference
* For all 4 of different colors the pattern still does not change, it's just randomly colored
* In case of 2 colors it's highly likely that the first half will have one color and the second one another. Nothing changes.
* In the less likely case the 3 have one color and the remaining one is different the resulting pattern is a triangle. So the direction of the diagonal will flip. But I don't think the overall impression will change.
In higher level squares replace "color" by "pattern", still no significant changes in appearance. Of course the two lower squares always swap their location.
I accidentally stumbled on your project just yesterday evening after reading your comment here https://news.ycombinator.com/item?id=39792381 (Hivekit, hexagons and Hilbert spaces). I posted it on a network operator IRC channel, and now it's on HN again, nice to see how that works.
Something to add, perhaps, is some sort of map marker and compass per zoom level? What part of the IPv4 space am I seeing, and what are the neighbours? Perhaps you've seen https://map.bgp.tools/ as well?
Small feature idea: "find my ip" which zooms to/selects the apparent ip of the current visitor.