Rank clocks

Pulling rank in the city Many distributions, such as the size of cities, companies or the Internet, follow scaling laws that imply an element of stability. A new approach to this type of analysis suggests that a much more turbulent dynamics is at work, but that it is largely hidden when observations focus on a single instant of time. The 'rank clock' is a way of visualizing the behaviour of a system — city size distributions in this case — over long time periods. Tested on three very different city systems over very different time periods, the clocks show that civilizations and cities rise and fall in size many times and on many scales, ruling out universal rank-size scaling at the micro-level and associated models of growth by proportionate effect. But clocks can track significant changes, such as the rise and fall of Rome and the impact of the Industrial Revolution.