  Understanding demographic and migrational patterns constitutes a great
challenge. Millions of individual decisions, motivated by economic, political,
demographic, rational, and/or emotional reasons underlie the high complexity of
demographic dynamics. Significant advances in quantitatively understanding such
complexity have been registered in recent years, as those involving the growth
of cities [Bettencourt LMA, Lobo J, Helbing D, Kuehnert C, West GB (2007)
Growth,. Innovation, Scaling, and the Pace of Life in Cities, Proc Natl Acad
Sci USA 104 (17) 7301-7306] but many fundamental issues still defy
comprehension. We present here compelling empirical evidence of a high level of
regularity regarding time and spatial correlations in urban sprawl, unraveling
patterns about the inertia in the growth of cities and their interaction with
each other. By using one of the world's most exhaustive extant demographic data
basis ---that of the Spanish Government's Institute INE, with records covering
111 years and (in 2011) 45 million people, distributed amongst more than 8000
population nuclei--- we show that the inertia of city growth has a
characteristic time of 15 years, and its interaction with the growth of other
cities has a characteristic distance of 70 km. Distance is shown to be the main
factor that entangles two cities (a 60% of total correlations). We present a
mathematical model for population flows that i) reproduces all these
regularities and ii) can be used to predict the population-evolution of cities.
The power of our current social theories is thereby enhanced.
