Visualizing Rank and Size of Cities and Towns
 Part I: 
England, Scotland, and Wales,1901-2001

Sandra Arlinghaus and Michael Batty

Dr. Sandra Arlinghaus is Adjunct Professor at The University of Michigan, Director of IMaGe, and Executive Member, Community Systems Foundation.
Dr. Michael Batty is Bartlett Professor of Planning at University College London where he directs the Centre of Advanced Spatial Analysis.

Please set screen to highest resolution and use a high speed internet connection.
Please download the most recent free version of Google Earth
®Make sure the "Terrain" box in Google Earth® is checked.

Download the following file to use in Google Earth®:
1901 United Kingdom file

England, Scotland, and Wales:  Rank-size Plots, 1901-2001

Rank-size plots have been used for years in a number of contexts:  large sizes have small numeric ranks--the largest city in a region has rank 1 (the smallest numeral).  Discussions of these plots, merits and drawbacks, example suited and not suited for application, and a host of related matters persist in the social scientific (and other) literature.   Our focus in this internet paper is on the geometric visualization of rank-size relations:  not only as plots but also in other ways that have come about as a result of contemporary electronic and internet capability.  Figure 1 shows a rank-size plot, done in the classical manner, of data for 459 towns and cities in the United Kingdom.  Each separate plot shows the rank-size curve for a particular year.  The data set is ordered for each of 11 decades as noted in the legend of Figure 1.  The goal is to look at change over time.

Figure 1.  Rank-size plots of the UK data by decade.

The curves in Figure 1 each display the general pattern one expects in rank-size plots.  They are similar to one another yet some variation is apparent.  What is often deceptive about these plots, when portrayed as in Figure 1, is that it is not always the same city that has the number one (or any other) rank as one moves through time.  When considering rank-size plots over time, this factor is a critical one.  Thus, when the data set is plotted showing the rank-size plot of 1901 as a benchmark against which to plot remaining decades, the pattern becomes quite different.  The animation in Figure 2 shows the data set arranged and graphed according to 1901 rankings. 

Figure 2.  Envisioning fluctuations in the UK data set based on changes of individual city or town ranks over time.  This animation shows the 1901 rank-size plot as the benchmark against which to visualize other decades.

In 1901, Glasgow City has the highest rank (City of London and its boroughs are each separate in this data set; there is no figure for Greater London) .  Clearly, by 1961 (at least), Glasgow no longer has the highest rank; Birmingham, for one, has surpassed the population size of Glasgow.  Naturally, there are numerous other fluctuations of this sort within this 11 by 459 matrix over the period of a century.  Indeed, it is difficult, looking only at the data, to envision the pattern of such fluctuation.  Animation, not possible in conventional publication, does permit one to look at change over time in imaginative ways. 

Rank changes over time; if one wishes, however, to understand why such changes occur it may be important to know where the cities and towns are in relation to each other and in relation to other variables such as the natural and built environments.  Geographical Information System (GIS) technology permits the association of databases with maps:  a change in the underlying database produces an associated change in the map (and vice versa).  Flat maps made using GIS technology can be "inflated" to have a 3D appearance, and saved as Virtual Reality (vrml) files and viewed on the internet using a plug-in for the browser.  Terrain can be introduced and databases can be viewed against terrain models (such as Triangulated Irregular Networks).  What this approach cannot do is place the spatial model on a globe:  it is conceived with flat maps.

Base Maps on the Globe:  England, Scotland, and Wales

To overcome this noted limitation of GIS software, we use Google Earth®.  As a first step, we create an inventory of base maps of the United Kingdom from materials already available on the Internet.  The materials listed below are presented in an animation in Figure 3 to give the reader a sense of how boundaries fit together and of how towns and cities are arranged within those boundaries.  In order, the frames of the animation of Figure 3 are:

Figure 3.  Base maps of the UK from Google Earth.  Click here to view a .mov file in which the reader can control the animation rate.

Rank-size Data on the Globe:  England, Scotland, and Wales, 1901.

The image in Figure 4 shows size data, from Batty's extensive database, for a selection of towns in England, Scotland and Wales for 1901.  At a glance one can see the location on the globe of large cities in relation to small towns.  The parallelepipeds anchored on town or city location are scaled according to town or city population.
  A town with a population of 125,367 is, for example, represented by a parallelepiped of height 125,367 feet, located at appropriate position on the Google Earth® ball.   The result is shown in Figure 4a.  Notice that Glasgow indeed has the tallest structure while the City of London and its boroughs show the densest concentration of population.  If one wishes to add a single figure for all of Greater London, the result is shown in Figure 4b.   All the 1901 population bars are shown on the animated base maps of Figure 3.

Figure 4a.  1901 population size mapped in Google Earth®.  Height of parallelepiped reflects directly population size of associated town or city.  Click here to view a .mov file in which the reader can control the animation rate.

Figure 4b.  1901 population size mapped in Google Earth®.  Height of parallelepiped reflects directly population size of associated town or city.  A single figure for Greater London has been added to this image from Figure 4a above and this parallelepiped rises far above the edge of the image.  Click here to view a .mov file in which the reader can control the animation rate.

The Greater London parallelepiped actually rises far above the edge of the animation.  One gets, from this animation, simultaneous views of:
Those factors, alone, make it worthwhile to view databases on animated screenshots of the globe.  A far richer experience can be gained, however, by downloading the files used to create these animations and drive around in them in Google Earth®.    

As has Batty's recent article in Nature on "Rank clocks," the images in Figure 4 give new meaning to the base plot of the 1901 rank-size curve of Figure 2.  They are rich in information and capture, as well, adjacency and positional information not present in Figure 2.  When one considers them in Google Earth, itself, the opportunity to extend these advantages to all geographic scales, from the local to the global, is an automatic addition as is the opportunity to view them as virtual reality over which the user has total control. 




Repeat the process for successive years in the database simply by calculating the difference between successive years and adjusting the push/pull by clicking once on the top face of the parallelepiped and then typing in that difference, plus or minus.

Multiple aerial pieces can be brought into the same SketchUp file.

See links on author names in title material for links to publication lists.

Solstice:  An Electronic Journal of Geography and Mathematics, Volume XVII, Number 2
Institute of Mathematical Geography (IMaGe).
All rights reserved worldwide, by IMaGe and by the authors.
Please contact an appropriate party concerning citation of this article:
Hillingdon Harrow Barnet Brent Enfield Ealing Hammersmith and Fulham Hounslow Richmond upon Thames Kingston upon Thames Merton Sutton Croydon Bromley Bexley Havering Redbridge Waltham Forest Barking and Dagenham Haringey Newham Greenwich Lewisham Southwark Lambeth Wandsworth Kensington and Chelsea Westminster City of London Tower Hamlets Camden Islington Hackney