The lure of the big city.Percentage of people living worldwide in urban and rural areas between 1950 and 2050 (projected). Unless there are advances in farming technique, and hydroponic factories within cities, we may be headed for a food crisis.[4] (United Nations Data.)[3] |

Two recent papers on arXiv have used mathematics to model the population dynamics of cities.[6-7] One of these looks at the difference between urban mobility and the known trends for long distance travel. Just as in the example that many qualities of city life are exponentially related to population, it was found that that trip length is exponentially distributed.[6]

ItemExponentNew patents 1.27 Inventors 1.25 Private R&D employment 1.34 Super-creative employment 1.15 R&D establishments 1.19 Total wages 1.12 Total bank deposits 1.08 New AIDS cases 1.23 Serious crimes 1.16 Length of electrical cables 0.87 Road surface area 0.83

Distribution of trip distance for four major cities.Data are in blue, and the model is shown in red. (Fig. 3 of ref. 6, modified for clarity, via arXiv.)[6] |

Evolution of a thousand cities after a hundred years..These virtual cities, placed randomly in a 500 kilometer square, had the same initial population. The size of the circle indicates the population after 100 years. (Fig. 3a of ref. 7, via arXiv.)[7] |

- Michael Scherer, "Inside the Secret World of the Data Crunchers Who Helped Obama Win," Time, November 7, 2012.
- Sam Biddle, "Obama's Campaign Ran Millions of Virtual Elections to Predict the Future," Gizmodo, November 7, 2012.
- Population Division of the Department of Economic and Social Affairs of the United Nations Secretariat, World Population Prospects: The 2010 Revision and World Urbanization Prospects: The 2011 Revision.
- Special Report: The Age of Plenty, IEEE Spectrum, 2013.
- Lués M. A. Bettencourt, José Lobo, Dirk Helbing, Christian Kühnert, and Geoffrey B. West, "Growth, innovation, scaling, and the pace of life in cities," Proc. Natl. Acad. Sci. vol. 104, no. 17 (April 24, 2007), pp. 7301-7306.
- Xiao Liang, Jichang Zhao, Li Dong and Ke Xu, "Unraveling the origin of exponential law in intra-urban human mobility," arXiv Preprint Server, May 28, 2013.
- A. Hernando, R. Hernando and A. Plastino, "Space-time correlations in urban sprawl," arXiv Preprint Server, June 16, 2013.