Visualizing Rank and Size of Cities and Towns
Part II:  Greater London, 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®:

Greater London:  A Century of Change

Greater London is composed of the City of London (of quite small population) and 32 boroughs that surround the central city.*  As in Part I, we begin looking at changes in the data sets of interest, by decade, over the course of the 20th century.  Rank-size plots are shown in Figure 1; the general pattern is as one might expect.   There appears to be a change in pattern around the time of World War II.

Figure 1.   Rank-size plots of the City of London and 32 surrounding boroughs composing Greater London.  Click here to view a .mov file in which the reader can control the animation rate.

To take a closer look we separate the rank-plots into two sets, in Figure 2.  Figure 2a shows the plots from 1901 to 1941 and Figure 2b shows them from 1951 to 2001.

Figure 2a.

Figure 2b.

Parallel to the Part I case, we note that any given locale is likely to change rank over time.  Thus, we look at the data set in relation to 1901 ranks, for the entire century (Figure 3a) and for the pre-and post-World War II data (Figures 3b and 3c).  The general pattern appears quite wild while the shorter time span ones centered on either side of World War II offer a more organized picture.  Is that picture more organized for Greater London than it is for the entire UK?  These observations are perhaps not surprising.  They do benchmark strategy and might offer interesting visualizations to those doing policy, planning, or historical studies of the study region.

Figure 3a.

Figure 3b.

Figure 3c.

Next, we map the data.   The Google Earth® screenshots of Figure 4 show not only all the population bars for each borough and for the City of London for 1901 but also for each of the other decades up through 2001.  Again, we have animated them so the reader can quickly see such change.  Click on any single image in Figure 4 (a-k) to see a larger image.  Or, keep track of up to nine changing scenes on the screen at a single time. To drive around, download the associated file used to make the images (Figure 4l).

Figure 4a.

Figure 4b.

Figure 4c.

Figure 4d.

Figure 4e.

Figure 4f.

Figure 4g.

Figure 4h.

Figure 4i.

Figure 4j.

Figure 4k.
Open these files in Google Earth:  File|Open and then navigate to where you have stored the files below.

.mov files, user controls animation rate:  1901  1911  1921  1931  1941  1951  1961  1971  1981  1991  2001

Greater London:  all kmz files for each decade.  If you have not already done so from the box at the top, download GreaterLondon.kmz and open it in Google Earth
®, File|Open and then navigate to where you saved GreaterLondon.kmz on your hard drive.

Figure 4l.

There are a number of interesting patterns one can observe; we invite the reader to add to these or to challenge them.
  • Boroughs close to the central city are larger earlier and larger as a group in pre-World War II Greater London.  The general pattern is pyramidal with the apex close to the City of London.
  • Post -World War II sees a flattening of the heights of parallelepipeds across the entire region.
  • The last two decades begin to see some growth back toward the center.
  • Early on, the southeast boroughs seemed under-sized in relation to other bars; later, that changes.
It might be interesting to compare and contrast this situation for London with other major cities, both in the UK and elsewhere, especially in regard to movement patterns in relation to war.  Indeed, one might consider applications for this method for other urban areas in order to study land use planning, circulation, and infrastructure in relation to disasters. 

Tower Hamlets:  A Local View.

The borough of Tower Hamlets is adjacent to the City of London:  it is a "close-in" borough.  Simple animation of the rank-size graph easily shows its changing population/size and rank pattern over time (Figure 5).  In addition, animation from Google Earth® makes it easy to compare and contrast the relative rise and fall in population of Tower Hamlets in relation to Barnet, a "far out" borough (Figures 6a and 6b; again, to take a closer look at either model, click on the image to link to a bigger file).  Thus, scholars investigating patterns associated with sprawl might find this tool to be helpful in a variety of ways.

Figure 5.


Figure 6a.

Figure 6b.

A visual limitation in perspective is involved with this procedure.  One cannot see changes over time while driving around within the virtual distribution of a single time slice.  The animation scheme is useful because it is hard to retain 3D models in the mind and mentally superimpose one time frame on top of another.  The strategy developed above, while apparently useful in many ways, does not allow one to see simultaneously the full picture and also see change over time.  There may be other strategies that fulfill that need. 

Future Directions
Both authors have recently offered a number of different strategies for visualizing data sets over time and also from different periods of time.  In addition, one might imagine that a host of other possibilities will arise given the relative ease of current remarkable visualization techniques.

Add Sound

In order to merge the spatial and temporal concerns, we consider first introducing audio files to supplement the visual.  Click on any of the boroughs in the map below.  A sequence of notes from a musical scale will play.  They represent the rise or fall in rank of that borough during the twentieth century.  Different boroughs will play different notes from the musical vectors serving as a basis for a musical vector space in which both rank and size change through time.  As the reader listens to change over time he/she is free to study simultaneously spatial aspects of the map  Generally, the pattern of the notes works as follows:
The method of construction of the musical vectors, including much detail, appears in Appendix II.  Click on the musical map of Figure 7 and listen to the rise and fall of rank...a guide that those who have vision disabilities may be able to employ.

Figure 7.  Musical map of Greater London.  Click on a borough or the City of London and listen to the general rank pattern and to rise and fall of rank within that general pattern.

Change the Geometry

The methods for looking at spatial change over time outlined above in the context of UK data sets offer exciting prospects for imaginative geometric use of the internet.  What they all have in common is that they are couched in Euclidean geometry.  The most radical, and perhaps the most interesting, approach might well be to change the geometry--to employ the non-Euclidean.  In the last issue of Solstice, we announced our interest in this topic and outlined a research agenda for using non-Euclidean geometry to look simultaneously at spatially disparate rank-size plots from different locales, time frames, or both.  To that agenda it now seems important to add that we should investigate the role of internet mapping and geometry, especially as they draw from Google Earth®.  Might one imagine the Google Earth® "sphere" as a rotating Poincaré Disk on which to embed non-Euclidean views of rank-size plots?  Stay tuned...the answers will be coming soon! 



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

*The City of London population data from 1901 to 1991 is

City of London  26882    19619   14158    11054    5324    4767     4245     5864     5900     4000

Before 1901 the population was likely much higher; indeed, in 1801 the City of London probably had the largest population in the United Kingdom.  London lost more than half its population in the interwar years.  By 1951 the population was very low, never to recover, as it was all employment by then.
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