techblog 

Last year, Duane Wessels published some maps of the IPv4 address space. These were static maps containing one dimensional IPv4 addresses plotted along a 12th order Hilbert curve, resulting in a two dimensional “heatmap”.

In these maps, consecutive networks are grouped nicely together. However, trying to orientate in the map is hard. This is due to the stringent locality preserving properties of hilbert curves. Since we only need to group networks together that share the same prefix, I looked for a curve that has better orientation at the cost of less locality preserving properties. A Morton curve, or Z-order curve does exactly that.

Every pixel represents a /24 network. To cover the entire IPv4 address space, the size of a map is 4096 x 4096 pixes. If this is plotted in three dimensions, the map would be 256 x 256 x 256 pixels.

I’ve created a proof of concept tool to view these three dimensional IPv4 maps. The input is a file with IPv4 addresses, one per line. There are many controls to orientate the cube, select address blocks, highlight problem parts, change focus, zooming, etc.

A few examples:

The 3d image above represents open resolvers on the internet. The more open resolvers per /24, the hotter the color.

The 3d image above shows a small detail of the internet. It shows the open resolvers in 64.0.0.0/8.

Though the data source for the proof of concept was a list of open resolvers, the uses for this vizualizing technique are numerous. The software is available here. Let me know if you’ve created any nice imagery with it.

I gave a presentation about this at the 70th IETF