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​There Are Only Four Types of City in the World, Says Math

Physicists discover that Brooklyn has a touch of Brussels and that Buenos Aires is in a class all its own.
Lower Manhattan skyline. Image: Jaroslav Thraumb

You wouldn't expect Staten Island to have much in common with the Syrian city As-Suwayda, but according to new research, the two communities share an urban "fingerprint." The similarity is just one of many odd municipal couples mapped out in a study published today in the Journal of the Royal Society Interface.

The study's authors concluded that the 131 cities they mathematically modeled fell into only four categories of urban design: medium-sized rectangular blocks, like Buenos Aires (which is the only city in this category); small blocks with a diversity of shapes, like Athens; larger, more balanced blocks with a diversity of shapes, like New Orleans; and finally, a mosaic of small squares, like Mogadishu.


"In some sense, you can think of this classification being for cities what zoology is for animals or botany for plants, a way to sort some objects according to their similarity," co-author Marc Barthelemy, a physicist at the Institut de Physique Théorique, told me.

 "In the same way, these taxonomies led to the discovery of common causes behind similarities—roughly speaking, DNA—we believe that similarities between two different street patterns hide common growth mechanisms," he continued.

Barthelemy and his colleague Rémi Louf sourced their information from Open Street Map and MapZen, and fed the information into a hierarchical clustering model to sort them into four main families. Naturally, there is significant diversity within each category as well, especially in cities that have preserved historic neighborhoods or other culturally distinct districts.

To illustrate the urban variation that can occur within one city, Barthelemy and Louf modeled each of the five boroughs of New York City independently, resulting in a number of unexpected matches with corollary cities around the world.

"Manhattan is very distinct from all the other boroughs," explained Barthelemy. "These other boroughs are very similar to each other—and similar to Detroit—but with different feels or touches: Brussels for Brooklyn, Miami for Queens, Porto for the Bronx, and As-Suwayda for Staten Island."

"The particularity shared by As-Suwayda and Staten Island is the fact that there are twice as much medium size blocks compared to small ones, and that these blocks, medium and small, are essentially rectangles," he continued.


"For other boroughs, the Bronx for example, there is slightly wider variety of shapes," he said. "Our method 'deconstructs' the cities and does not take into account the arrangement of the blocks, just their geometry. Thus, what we can say is that the blocks that constitute the plans of Staten Island and As-Suwayda are very similar, as surprising as this may seem!"

Like species in the fossil record, the sweep of colonialism imprinted the cities in its wake

Just as categorizing species into clades helps map out a larger evolutionary background, Barthelemy and Louf's typologies expose the cultural development and histories of cities around the world.

The block shapes, sizes, and distributions are a window into a city's past, revealing whether it haphazardly evolved its structure or was laid out with a central planning approach. And just as the migration of certain species can be observed throughout the fossil record, so too does the sweep of colonialism imprint the cities in its wake.

"Self-organization usually leads to regular shapes, rectangles and squares, of smalland medium size," said Barthelemy. "This typically leads to European patterns, constructed at a time when cars were not the main mode of transportation. Some East Coast American cities [like] Washington [and] Boston also have the same type of patterns—which could be the reason why people sometimes say they have a 'European feel.'"

"Central planning can have different consequences," he added. "North American cities which were planned to make driving easier have grid-like patterns. On the other hand, when it superimposes to an existing layout, central planning usually does not respect the existing geometry, and creates 'strange' shapes such as elongated triangles. This is the case for example for Paris and Haussmann works in the nineteenth century where large avenues were created to connect important points, resulting in a large variety of block shapes."

The influence of geological features like rivers, coasts, and mountains also influence street distribution, and historical population trends are also deeply imbedded in the topologies of cities. Barthelemy and Louf are working on categorizing more cities with their models, which will no doubt generate more weird connections between geographically distant cities.

"The list of cities in our dataset contains 131 cities in the world, and we can expect that we might find better matches for a larger dataset," said Barthelemy.

For the time being, it's good to know that a globetrotting Staten Islander might be comforted by the familiar city block layout in As-Suwayda, complete with an ancient Roman amphitheater in place of the RCB Ballpark.