The world's cities are absorbing one million additional people every week—and by 2030, they could consume an extra 1.5 million square kilometers of land, or roughly the area of France, Germany and Spain combined. What would be the best ways for those cities to grow? A new study examines how—before urban planners existed—a group of Italian villages evolved into suburbs outside Milan today. Such studies may eventually help planners optimize future developments.

"We know few things about how cities grow naturally," says Emanuele Strano, a doctoral candidate studying urban geography at Switzerland's École Polytechnique Fédérale de Lausanne who authored the study. "Urban planners believe that with regulations we can control the growth of cities. The question is, how can we control a thing if we don't really know how it behaves?"

The new study takes a step toward that essential understanding. Strano and his colleagues—a group of computer scientists, mathematicians, physicists and urban scholars—teamed up to provide the first quantitative analysis of how unplanned street networks evolve over time. Their results were published March 1 in Nature's "Scientific Reports." (Scientific American is part of Nature Publishing Group.)

"Historically, a lot of these analyses have been done using not such a substantial quantitative basis," says Stephen Marshall, an urban theorist at University College London (U.C.L.) who was not part of the study. "In the areas that I'm familiar with, people might produce a map of a city, and compare and contrast two maps on a more qualitative basis." Marshall also says that this work marks the first time anyone has looked at how those properties change over time.

Strano and his colleagues studied the growth of Groane, an area outside Milan, Italy. Using maps dating as far back as 1833, the researchers modeled the urban sprawl process as Groane developed from agricultural land into a residential and industrial area, and then into a postindustrial suburb of the Milanese metropolis. At seven time points between 1833 and 2007 the researchers used geospatial data and programming script to construct digital maps (shown above) that treat the street system as a network of links (streets) and nodes (intersections).

Network analyses performed on the digitized map revealed that although Groane had never been subjected to large-scale planning efforts, the street network evolved to be more uniform in size and density, and its predominant shape shifted from triangular to rectangular. Rectangular street networks may arise organically, the authors say, simply because they offer more efficient pathways and allow for more organized subdivision of land.

The study also identified two processes of urban growth: one of exploration, where new streets extend into rural areas, and one of densification, where new streets fill in gaps within the existing network. Co-author Marc Barthelemy, a theoretical physicist at the French Commissariat à l'Énergie Atomique explains that although the group has identified some rules that govern the densification process (which tends to make the grid more orderly and square), exploration is less predictable. He says that his team's future studies will take a closer look at the exploratory process to learn what drives urban sprawl. "We ought to understand it because it might give some hints on how to slow it down."

Whereas modes of transportation changed drastically between 1833 and 2007, the original road layouts remained mostly intact. In fact, the researchers found a tendency for older streets to be the more central ones in modern times--90 percent of Groane's most interconnected roads in 2007 had already existed in 1833. Because streets with greater connectivity tend to have higher traffic flows, Barthelemy says urban planners could compute the connectivity on existing or proposed street networks to understand how people will use the space. (Some planners—such as Space Syntax in London and the  University of Strathclyde's Urban Design Studies Unit, of which Strano is a member—are already measuring connectivity to optimize urban designs.)

Planners had already suspected many of the study's findings, but the research provides empirical support for the theories and suggests that natural rules may guide the self-organization of cities. "My suspicion is that some of these rules are working everywhere, because cities are always man-made objects," Strano says.

Marshall cautions that, "to get a complete picture, we need to combine this kind of network analysis approach with an understanding of what's happening on the ground—What are the human actions?" Marshall suggests that factors such as cultural design preferences, the shapes of buildings and small-scale planning efforts may have subtly influenced Groane's street network. Growth patterns also may differ in city centers, rather than at the city's edge, where Groane is located. The authors of the study agree, and they say that answers await further studies of street network evolution in cities of various sizes and geographic locations as well as with differing economic histories.

The implications are important: Correlational studies have suggested that street patterns may impact local economies, physical activity levels, public transportation use, crime rates and social inequality.

"Cities are immensely complex structures," says Michael Batty, a spatial analyst at U.C.L. "When you interfere with a complex system, you get all sorts of side effects." He says that quantitative research such as Strano's could potentially guide planners into enhancing organic growth, rather than stopping it in its tracks—thus helping planners to build better cities and prevent uncontrolled sprawl.