Visualizing the IPv4 space using Hilbert Curves
by The Bayesian Observer
The IPv4-heatmap is an awesome little program created by Duane Wessels. It allows the visualization of the entire 32-bit IPv4 address space in 2-dimensions, using the idea of a Hilbert curve, a type of space-filling curve, which are fascinating constructs in and of themselves. Here is an image from Wikipedia showing an iterative process to create higher order Hilbert curves from lower order ones.
Due to the properties of Hilbert curves, the IPv4 heatmap represents IP addresses that are numerically close to one another as physically proximate pixels. Thins of each IP address as a 32 bit integer. Then, 22.214.171.124 is just 1 larger than 126.96.36.199 in value, and the two IP addresses probably belong to the same organization. The program takes in a raw text file containing IP addresses and creates an image like the one below. The particular map below shows the intensity of peer to peer traffic that I measured during one five minute segment. Since large blocks of IP addresses have well known organizations as their holders, the map also displays this information as an overlay.