Cities have been compared to living organisms, machines, river networks and insect colonies. Instead, suggests a new study, urban centers are more like stars, fusing human connections as if they were hydrogen atoms.

But only sort of. Using mathematical equations to synthesize mounds of data, a researcher concluded that cities are vastly more complex and open-ended than any system in nature.

Still, by developing a unified theory of urbanization that explains the essence of how cities grow and function, the hope is to help policy-makers and planners design better, more efficient cities that prioritize social connections and induce innovation.

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“At the center of a star, the core is so dense that nuclear interactions take place and as a result, light comes out. And basically, the light that comes out of a star is brighter and reactions are faster the larger the star is,” Bettencourt said. “That’s a little bit like what cities do, too. It’s mathematically different, but the larger the population is, the faster the rates of social interaction.”

“Stars are nuclear reactors and cities are a different kind of reactor,” he added. “They are social reactors.”

Cities have been a source of philosophical fascination since the time of the ancient Greeks. Even Aristotle wrote about the purpose of cities. He observed that people are more political than any other animal and he explored the virtue of public life.

For the past decade, Bettencourt and colleagues have taken a more systematic and quantitative approach to understanding cities by gathering data from a wide variety of disciplines, including economics, urban geography and social psychology.

Instead of focusing on form and what cities look like, Bettencourt said, he was more interested in function and how cities work.

Among other details, he considered land-use, area of roads and other aspects of infrastructure. He collected information on electricity consumption, pipe volumes, and measures of innovation, such as numbers of patents and people in creative professions. And to round out the big picture, he factored in incidences of disease, violence and crime. Then, he crunched the numbers.

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The bigger a city is, the more social interactions become possible, Bettencourt reports today in the journal Science. And, he concludes, the cities that work the best manage to maximize these interactions while minimizing crime, costs and the effort required for people to connect.  

Cities like New York and Chicago, for example, do pretty well at efficiently bringing people together and fostering innovation. Los Angeles scores slightly lower because of the greater amount of effort required to get around and interact with others.

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Places like Riverside, Calif., and Phoenix do much worse, often as a result of growing too quickly. In these places, the costs of mobility often outweigh the benefits of getting places to make connections.

By focusing on planning details that prioritize social connections, Bettencourt suggests, cities could grow in smarter, more deliberate ways.

“In practice, you cannot really manage a city well if you don’t understand its primary function,” Bettencourt said.

“The management of cities often has to do with very practical things -- fix the roads, get the buses running on time,” he added. “All of these things are supportive structures to realize social interactions and promote good ones instead of bad ones. You should think about running the buses on time, but to what extent does this contribute to social interactions that may lead to innovation?”

Experts have long known that cities get richer, both economically and creatively, as they get bigger, with a simultaneous boost in crime rates, congestion, cost of living and other negatives, said Michael Batty, an urban planner at University College London’s Centre for Advanced Spatial Analysis.

The new study begins to pick apart the details of what happens when cities grow, Batty said, offering insight into why some cities function better than others of the same size.

“This theory is explaining why big cities do generate more income and creativity than small cities do,” Batty said.

“The simplest way of thinking about it is that if you think about all the connections you can make in a city, it’s population squared. So if there are 10 people, there are 100 possible links and if there are 100 people, it’s possible to make 10,000 links. We can’t realize all of those links and networks, but generally speaking, big cities give opportunities for more contact.”