THE Rockefeller Centre sprawls across 89,000 square metres of midtown Manhattan. Curiously, Alcatraz, in San Francisco Bay, the island home of America’s most famous former prison (see picture), has exactly the same area. That coincidence aside, few might imagine the manicured roof gardens and art deco office buildings of the one have much in common with the brutal crags and blockhouses of the other. But they do. For research by Claudio Silva of New York University and his colleagues suggests that the two have a striking resemblance when it comes to the daily ebb and flow of tourists, as judged from the level of activity on Flickr, a photo-hosting site. Dr Silva thinks the peaks and troughs of Flickr activity that his research has discovered in this and other cases are a measure of an area’s “urban pulse”. If so, the Rockefeller Centre and Alcatraz share a pulse.

On October 25th, at a meeting of the Institute of Electrical and Electronics Engineers in Baltimore, Dr Silva plans to present the idea that, like real pulses, urban pulses have useful diagnostic and prognostic properties. He thinks his system to analyse them might help urban planners and architects identify footfall and other patterns that emerge from past developments, and make better choices in future.

At the moment, when such planners try to understand patterns of activity in a district, they do so by conducting surveys, counting the number of people passing important road junctions and measuring traffic volumes. This, though, takes years. One way to speed up the process is to use the reams of data now available from social-media platforms. Flickr, for example, records the location and time of every photograph uploaded to the site. It is especially popular with holidaymakers. Thus, by using the Flickr data as a surrogate measure of their activity, Dr Silva’s program can show in minutes how tourists are moving through a district, and may also highlight areas of activity that conventional methods have missed.

Dr Silva’s work is part of a broader trend, dubbed “smart cities” by some, towards using the vast amounts of data generated by the inhabitants of urban areas to make them better places to live. Carlo Ratti and his colleagues in the Senseable City laboratory at the Massachusetts Institute of Technology (MIT), for example, used mobile-phone records, and also traffic data from 500 pressure sensors on roads, to help guide construction of the new metro system in Saudi Arabia’s capital, Riyadh. And César Hidalgo and Elisa Castañer, who work at MIT’s Media Lab, last year published an algorithm to recommend which types of new business were needed in particular districts, based on the locations of over 1m cafés, bars, shops, schools and so on in 47 American cities.

Dr Silva says that what distinguishes his work from these and other studies is the speed with which he and his team can analyse large data sets such as those from Flickr. The conventional approach is to break such data into chunks for analysis—dividing them up geographically on a grid, for example, or temporally, into days. Researchers then search for patterns by comparing these chunks with each other. The problem is that more detailed analysis requires more such chunks, and the computing time needed to calculate the relationships between them thus spirals.

To avoid this, Dr Silva turned to computational topology—a field that finds algorithms to describe complicated shapes and surfaces as simply as possible. (In this context, “shapes” and “surfaces” are wider ranging than a layman might think, because they can have more than three dimensions.) These algorithms let computers create, analyse and manipulate such multidimensional shapes quickly.

Computational topology is already employed in tasks as diverse as loading goods at dockyards and studying the way protein molecules fold, so many topological algorithms already exist. To take advantage of this trove, Dr Silva’s team had to represent their Flickr data as a topological shape. They did so by calculating, from the number of photos taken there, the level of “activity” at each point in an area of interest. They plotted the results on a grid, to create a three-dimensional representation of tourist activity across a city at a given moment—then added a fourth dimension by repeating the process for every hour of data available. The result was a topological surface whose peaks, troughs, furrows and holes—which could be identified by their algorithms—corresponded to changes in activity over time and space.

This approach means not only that Dr Silva’s programs whizz along much faster than conventional software, but also, because they do not have to filter the data or use a small subset of them, they see patterns that might otherwise slip through the net. Users can compare years’ of Flickr data from whole cities in minutes, thus taking their urban pulses. Indeed, Dr Silva hopes to make these pulses still more accurate, and also extend their analysis beyond tourism, by tapping other sources of information, such as Twitter and Instagram.

Social pulse-taking is not mere theory. Kohn Pedersen Fox Associates (KPF), a firm of architects based in New York, is collaborating with Dr Silva on several as-yet-undisclosed projects. KPF’s past work includes the Shanghai World Financial Centre, the World Bank’s headquarters in Washington, DC, and a recent revamping of Covent Garden, an old fruit and vegetable market, in London. Whether the algorithms of computational topology would show any similarities between those locales is an intriguing question.