Friday, September 24, 2010

Space-Time Dynamics in Scaling Systems

To quote from Mike Batty:
"A rank clock is a device for visualising the changes over time in the ranked order of any set of objects where the ordering is usually from large to small. The size of cities, of firms, the distribution of incomes, and such-like social and economic phenomena display highly ordered distributions. If you rank order these phenomena by size from largest to smallest, the objects follow a power law over much of their size range, or at least follow a log normal distribution which is a power law in the upper tail."
The idea behind the Rank Clock is:
"... despite the fact that such distributions are so regular even through time, when one examines how objects within these distributions change over time, it is quite clear that somehow these systems remain stable at the aggregate level but with objects which composes them shifting quite dramatically from time period to time period. The Rank Clock is a device that shows how such distributions change over time and it is a natural complement to the rank size distribution which is called a Zipf Plot."
Below are some movies of the Rank Clock in action (further details can be found here). The first is an animated rank clock showing how the rank of cities in the USA changed between 1790 and 2000.


While the movie below shows an animation of a rank clock showing how the ranks of the top 100 high buildings in New York change between 1912 and 2008.


The Rank Clock Software can be downloaded from the CASA Web Site (here), more information can also be found here and more animations here

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