Visualising Space-Time Dynamics in Scaling Systems: Rank Clocks

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Sometimes you have to take a step back and take a look around a science lab to appreciate the wealth of knowledge and research being carried out. Rank Clocks by Professor Mike Batty here at CASA, The Bartlett, University College London, is a prime example.

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.

Mike has examined the UK urban system from 1901 to 2001, the World System from 430BCE to 2000, and the Ancient World System from 3700BCE to 1000BCE. All these examples show quite regular stability in rank size at the aggregate Zipf Plot level but much greater volatility in terms of the Rank Clocks and this in an of itself throws grave doubt on the issue of universality and regularity in such systems. Moreover it opens up once again the paradox of why systems show such regularity at the macro level when everything is changing at the micro level.

We detail the rank clock illustrating how the rank of cities in the USA changed between 1790 and 2000 below:

Rank clock for US cities from Michael Batty on Vimeo.

In fact for cities and other phenomena such as the distribution of word frequencies, George Kingsley Zipf as long ago as the 1930s characterised such distributions as characterising pure power laws in which the size of an object seemed to approximate the largest object in the set divided by the rank of the object in question. Such strict power laws in fact seem to be the exception rather than the rule but many such rank size distributions seem to follow such laws in their upper tail, and hence these are taken as signs of system stability, self-organisation and universality.

Below we illustrate the animation of a rank clock of the top 100 high buildings in New York change between 1912 and 2008:

Rank clock of the top 100 high buildings in New York from Michael Batty on Vimeo.

However, 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 Software can be downloaded from the CASA, the full paper can be found on Nature.

You can also download CASA Working Paper 152 Visualising Space-Time Dynamics in Scaling Systems. (pdf).

Thanks go to http://gisagents.blogspot.com/

Tweeting from Conferences - Live Criticism and How to Cope

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We write occasionally for the Nature Network, as such we thought readers maybe interested in our latest post on the rise of twitting at events and conferences.

A few weeks ago we presented our latest work 'The Geography of Everything' at the yearly conference organised by the Centre for Advanced Spatial Analysis at University College London. With the work featured in New Scientist and based around a new way of tagging every object in the world via the talesofthings.com site we hoped for a good reception. Indeed the reception was good with an excellent write up in the Guardian and a series of suitably scientific questions fielded and answered. What we were not quite prepared for was the archive of the tweet feed with various audience members 'tweeting' through the event.

Carry on reading over at Urban Nature...

MapTube on Nature Network

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A quick post...

For those interested Nature provides a good coverage of our MapTube site.

Written by Angela Saini you can view the write up direct on the Nature Network.

Rank Clocks - Visualising the Growth of Cities

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Professor Mike Batty CBE - the Director of our lab - published a notable paper in last years November Issue of Nature (444, pp 592-596) examining the growth and decline of cities with data for the top 100 cities in the US urban system for the decades from 1790 to 2000.

Mike has also examined the UK urban system from 1901 to 2001, the World System from 430BCE to 2000, and the Ancient World System from 3700BCE to 1000BCE.

For those new to rank clocks - 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 Editorial of the editions notes that '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'.

Seemingly its all about 'The Long Tail' - the title of a recent book by Chris Anderson (see our Amazon Shop for details). After sitting down with Mike for a bit of an explanation the result was the following diagram:


People assume that the large cities are dominant but in the event of a long enough tail on the log graph there are enough small cities to be influential.

Mikes paper can be read online if you have a subscription to Nature.

You can also download the Rank Clock software in stripped down form with data for the top 100 cities in the US urban system for the decades from 1790 to 2000.