Modeling cities with formulas that describe social behavior

By James Maynard , Jun 22, 2013 01:51 AM EDT

Cities grow and shrink in size according to regular patterns first suggested researchers in 2007. Now, those same scientists believe that they can model the behavior of people and future of a city by simple mathematical formulas. These simple formulas describe how population levels affect several aspects of cities from land size to rents.

Luis Bettencourt is a professor of complex systems at the Santa Fe Institute in New Mexico. He has been studying the patterns of cities as they grow, trying to identify common patterns.

"A city is first and foremost a social reactor. It works like a star, attracting people and accelerating social interaction and social outputs in a way that is analogous to how stars compress matter and burn brighter and faster the bigger they are," Bettencourt said.

The study assumed four facts to be true about cities. First, the population should be able to travel in order to interact with each other. Second, that the infrastructure of the city grows, allowing larger populations to continue interacting with each other. Third, the city does not grow so quickly that the population leaves, and lastly, that the population actually has social interactions, instead of staying isolated. Cities need to be thought of from a standpoint of social interactions, and not just population.

The aspects of a city which change along with population include economics, infrastructure and the social behavior of a population center. Bettencourt and his team studied data from thousands of cities around the world, at all levels of development.

The simplest relationship between a characteristic of a city and its population would be a linear one - if the population of an area doubled, so would whatever aspect of that city you were examining. Bettencourt found in his earlier study, confirmed here, that certain qualities of a city, for instance economic levels, grows faster than population (superlinearly) while others, like infrastructure grow sublinearly, or slower than population.

Urban planners could use the research developed for this project in planning future growth, which should include making positive social interactions easily available at a small cost in energy or inconvenience to the population.

Looking at present cities, the study found that Riverside, CA and Brownsville, TX could benefit from more contact between their people, while Bridgeport, CT is in need of more efficient transportation to meet the needs of their quickly-growing population.

"It's an entirely new kind of complex system that we humans have created. We have intuitively invented the best way to create vast social networks embedded in space and time, and keep them growing and evolving without having to stop. When that is possible, a social species can sustain ways of being incredibly inventive and productive," Bettencourt said.

The Origins of Scaling in Cities, Bettencourt's article on his research, has been published in the journal Science.

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