natural patterns

Patterns pop up in unexpected ways, including one mentioned in a quick column from today's NYTimes. Looking at urban planning from a mathematical perspective:

The mathematics of cities was launched in 1949 when George Zipf, a linguist working at Harvard, reported a striking regularity in the size distribution of cities. He noticed that if you tabulate the biggest cities in a given country and rank them according to their populations, the largest city is always about twice as big as the second largest, and three times as big as the third largest, and so on. In other words, the population of a city is, to a good approximation, inversely proportional to its rank. Why this should be true, no one knows.

This pattern may have been first observed when looking at cities, but it pops up also when looking at elements within those cities, as well: the infrastructure, the people, the cells.

Absolutely astonishing, and very well written article. Definitely worth a few minutes of your time. Steven Strogatz finishes up by noting, "There may be deep laws of collective organization at work here."