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If you’ve ever visited London or Paris, you’ll know how easy it is to spend many a pleasant hour exploring Parisian boulevards and London’s squares. But which is more accessible? Now a group of physicists has worked out how to measure the accessibility of a city and found that the French capital is significantly more accessible than the British.

Luciano da Fontoura Costa at the University of Sao Paulo in Brazil and few pals created a computer model of the street and underground networks in both cities. The networks of Paris and London had 11699 nodes and 6885 nodes, respectively.

They then let loose ant-like agents to crawl the city streets in self-avoiding random walks and watched to see where they ended up. The researchers simulated a total of 10,000 walks for each node in each network.

They then calculated a “diversity entropy” for each node, a number which captures how easily it is to get from one node to others nearby. The results are shown in the pictures above (Londno on top) in which red areas are more easily accessible.

Note in particular that the area of London south of the Thames seems particularly inaccessible while the area of Paris south of the Seine is comparable to the north.

Why the difference? Costa and co say first that the River Thames is much wider than the Seine which has 2.5 times as many bridges crossing it. That significantly affects accessibility. They also suggest that London’s large parks–Hyde Park and Regent’s Park–interfere with the overall accessibility of the city in comparison to Paris.

The study also examined how underground systems affect accessibility (they improve it, unsurprisingly).

The team says the study backs the idea that the diversity entropy is a useful measure of accessibility in cities (although it would be good to know how well self avoiding random walks model real travel patterns). But if we take that as read, this technique (and others like it) could provide a useful tool for city planners to gauge the effects of changes to road networks, public transportation systems and bridge building. Let the planning begin.

Ref: http://arxiv.org/abs/0911.2028: On the Efficiency of Underground Systems in Large Cities

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