City street networks are similar to other information networks, such as the Internet or social networks. Street and roads are the links while the crossroads are the nodes of these networks. So it is tempting to use physics to map city complexity, as is reporting Technology Research News. Several physicists from Sweden and Denmark have compared the complexity of finding an address in Manhattan and in several Swedish cities. Not surprisingly, Manhattan, with its checkered grid plan, is easier to navigate than the older European cities. The scientists think their model could be "used to allow city planners to see how street changes affect navigability." But as cities don't change very fast, it's doubtful that this method can be used efficiently anytime soon. But read more.
Here is how Technology Research News describes the method used.
The information needed to navigate in a city can be used to quantify and compare the complexity of cities, said Martin Rosvall, a researcher at Umeå University [in Sweden]. The method could eventually be used to allow city planners to see how street changes affect navigability and could also be used to make other types of networks -- like supermarket aisles and airways -- work more efficiently, he said.
The researchers' model assumes that a person traveling along the streets of the city gets all travel directions in the form of the sequence of roads that lead to the target road. In networking terms, these sequences are sets of nodes linked by intersections. From this perspective, all roads are the same regardless of how long they are. The number of intersections between roads is the measure of the information distance between them. This makes sense intuitively; the more turns there are along a route, the harder it is to follow.
The illustration describes the process used by the researchers (Credit: Martin Rosvall and his colleagues).
This figure illustrates a visitor's perspective of an unknown city (a). The visitor asks a citizen about the way to a specific street. The citizen answers based on its perspective of the city as in (b), or rather the higher abstraction level in (c). This level is the dual map of the city, a network where streets are identified as nodes and intersections between streets as links between the nodes. We use this level to quantify the search information in (d): The minimum number of yes/no questions (bits) the visitor must ask the citizen to find a specific street (log2 36 bits from s to t).
Let's move back to the Technology Research News article.
The model shows each main road as a central hub and each crossroad as a peripheral node connected to the hub. A grid of streets appears as a ring of nodes. Connections between streets form a many-pointed star inside the ring, with each of the star's points meeting the ring at a node.
Like other cities created overnight in the Outlet, Woodward acquired between noon and sunset of September 16, 1893, a population of five thousand; and that night a voluntary committee on law and order sent around the warning, “if you must shoot, shoot straight up!”
—State of Oklahoma, U. S. public relief program (1935-1943)
The researchers' model confirmed the widely-held view that the roads of Manhattan are simpler in terms of information handling than cities with complicated road-construction histories. "Historical cities have an overabundance of short streets that make the cities more complex in the sense that they increase the information distance between streets," said Rosvall.
In "The urban maze," published on August 13, 2004 by Nature, Philip Ball, who read an early publication of this research work, added that you "don't [have to] feel bad if you often get lost in cities."
Rosvall, of Umeå University in Sweden, and his co-workers have tried to figure out why it is so hard for us to find our way around cities. Of course, the obvious answer is that cities have a lot of streets. And particularly if you live in an old city like London or Athens, those streets are messily arranged. But it turns out that the problem is a lot worse than that.
And he explains why the researchers have found it was more difficult to navigate a real city than a randomized one.
The crucial characteristic that complicates cities seems to be their inhomogeneity. A random network is more or less equally random everywhere. But cities, especially ones with a long history, have local "islands" of dense interconnections, containing streets that are hidden away in corners.
The research work has been published by Physical Review Letters on January 19, 2005 under the name "Networks and Cities: An Information Perspective." Here is a link to the abstract.
Traffic is constrained by the information involved in locating the receiver and the physical distance between sender and receiver. We here focus on the former, and investigate traffic in the perspective of information handling. We replot the road map of cities in terms of the information needed to locate specific addresses and create information city networks with roads mapped to nodes and intersections to links between nodes. These networks have the broad degree distribution found in many other complex networks. The mapping to an information city network makes it possible to quantify the information associated with locating specific addresses.
The full paper is also available on line, either in a short version (PDF format, 1 page, 206 KB) or a longer one (PDF format, 4 pages, 237 KB).
My faith is the grand drama of my life. I’m a believer, so I sing words of God to those who have no faith. I give bird songs to those who dwell in cities and have never heard them, make rhythms for those who know only military marches or jazz, and paint colours for those who see none.
—Olivier Messiaen (1908–1992)
The above illustration comes from the short version of this technical paper.
Sources: Kimberly Patch, Technology Research News, June 29/July 6, 2005; and various web sites
Related stories can be found in the following categories.
Networking
Physics
Social Networks
Transportation.