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Computing Space V: Mapping the Web or Pinging your Way to Infinity


Today’s post is the fifth in a year-long series called,”Computing Space,” which highlights new mapping technologies and new areas for cartographic innovation, along with stories of the lives and work of many of the mostly unknown cartographers, geographers, mathematicians, computer scientists, designers and architects who both now, and in the past, have had a hand in the development of computer cartography and its applications.


Trying to make an accurate map of the World Wide Web is one of the frontiers of cartographic research today and is also one of most fertile grounds for scholars trying understanding the constantly shifting spatial dynamics of human social networks. Maps of the web are be being produced using a wide variety of mathematical and topological techniques and for a whole range of reasons from cyber-security and cyber-warfare purposes, all the way to more traditional studies in the digital humanities that look at both our intimate and casual social network interactions across the globe.

Trying to make a good map of the connections and addresses of the internet is difficult from both an algorithmic and a mathematical perspective, since we are dealing with one of the most complex and vast networks ever created, outside of the human brain itself. In many respects, with the mapping of the web, we have witnessed the creation of a whole new kind of space, and with it, a whole new form of cartography, complete with its own mathematical foundations and unique visualization techniques.

Currently, the most interesting way that today’s researchers are mapping the web comes from looking at the distribution and number of IPv4 addresses that make it up. To do this, researchers at places like the ANT Lab, and other independent and “hacker”oriented programmers, have been pinging IPv4 addresses across the entire web for years and mapping the responses. The maps that they have produced are large, and are most comprehensible when displayed in a a form called a Hilbert Curve or Map, which can be generated recursively.

Small Scale Hilbert Map the Web showing geographic regions. Courtesy ANT lab.

Small Scale Hilbert Map the Web showing geographic regions. Courtesy ANT lab.

Maps employing this technique locate nearby and sequential IPv4 addresses next to each other in a way that forms what is known to mathematicians as a space filling curve. Space filling curves, because they are one-dimensional strings that have the bizarre property of being able to fill spatially a two-dimensional plane, have a number of features that make them ideal candidates for mapping sequential elements that need to be spatially partitioned. The allows huge amounts of data to be easily visualized in a small, finite space.  Geometrically, this means that any consecutive string of IPv4 addresses will be found in a contiguous, single and compact region on the map. The upper left section of the map shown below for example, shows the blocks of IPv4 addresses inhabited by several corporations and government agencies, with the Department of Defense, notably dark, near the middle.

To create massive maps like these,which take in the entire expanse of the web, researchers send out ICMP  echo request packets (Internet Control Message Protocols) that ping IPv4 addresses across the network. As these pings are returned they are color coded depending on the response received. A green pixel in the maps shown below encode a “yes” response to the question, “Are you out there ?”. A red response is a no, which is a message that has most likely been sent back by the security of a firewall. Black, perhaps the most interesting of the responses, encodes “no response”. This means that either there is no address found at the numerical sequence, the message failed somewhere along the way, or that a firewall has opted not to return a message and therefore, remains hidden.

When we look at the structure of these maps one gets a deep sense of the geography of the web, and how is it divided up into “digitally spatial” regions of smaller sub-networks. The sheer size and density of some of these images might also give some readers the eerie feeling that they really do not understand how the web works at all.

Slightly zoomed view of some of the regions of the Hilbert map of the web inhabited by various companies, government agencies and blank repsonse regions. Courtesy ANT Lab

Slightly zoomed view of some of the regions of the Hilbert map of the web inhabited by various companies, government agencies, and you and I. Courtesy ANT Lab.

Every device and computer that is connected to the web has at least one unique numerical address in what is called IPv4 space. This address is a sequence of four numbers separated by a decimal point, for example 1.34.54.78. Each of the four numbers can run from 0 to 255.  In computer terms this is an 8 bit address of which over 4 billion can be made.

Several research groups have made interactive versions of these complex maps and they can be fascinating to explore, tempting the viewer to get lost in the maze of this newly created geographic, but completely non-metric space. In many of these interactive applications one can search your own IPv4 address and locate yourself in this vast digital multiverse.

Zoomed View onan area in North America and encoding the IPv4 ping responses. Courtesy of the ANT Lab.

Zoomed View on an area in North America encoding the IPv4 ping responses. Courtesy of the ANT Lab.

Closer view of an area of the map above showing the structure of responses. Courtesy of the ANT lab.

Closer view of an area of the map above showing the structure of responses. Courtesy of the ANT lab.

Using mapping technology such as this researchers have begun to get a deeper understanding into the complexity of the web, its vulnerabilities, and its detailed topological structure (its connectedness). If we look closely at an area of Washington DC shown below for example, it is apparent there are many unprotected regions, but even more with no response at all.

Hilbert Map of IPv4 space in a region of Washington, DC. Courtesy ANT Lab.

Hilbert Map of IPv4 space in a region of Washington, DC. Courtesy ANT Lab.

Early on in its history users of the web had little understanding of how it evolved and functioned, as its behavior emerged somewhat spontaneously from the millions of users inhabiting a digital space that was very different from that typically mapped by cartographers. Today new mapping tools are giving us, for better or worse, an deeper sense of the dynamics and evolution of this other space that we all inhabit and in which, at least a portion of our modern lives, play out.