Rank and Size of Cities and Towns
Part II: Greater London, 1901-2001
Dr. Sandra Arlinghaus is Adjunct Professor at The University of
Michigan, Director of IMaGe, and Executive Member, Community Systems
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.
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.
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
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.
Next, we map the data.
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
There are a number of
interesting patterns one can observe; we invite the reader to add to
these or to challenge them.
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.
- 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
- Early on, the southeast boroughs seemed under-sized in relation
to other bars; later, that changes.
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
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.
limitation in perspective is involved with this procedure. One
see changes over time while driving around within the virtual
distribution of a single time slice. The animation scheme is
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
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
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
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.
- a musical vector
that is relatively high in pitch throughout is one whose associated
region has had relatively high rank throughout the time period (and
- within a
musical vector, be it generally high, low, or middle, the higher notes
represent higher numerals (hence lower ranks) and vice versa.
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.
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!
PROCEDURE USED WITH "A MUSICAL
FREE DEMONSTRATION COPY AND OPEN IT TO FOLLOW ALONG WITH THE DISCUSSION
- Create a matrix showing change in rank, over time, of a city or a
set of cities. We choose "Greenwich" for the sake of example of
procedure. The row associated with Greenwich will be referred to
as its "vector."
- Enter data from the row associated with Greenwich into the
- Direct approach:
- Choose the tab named "Data"
- Click on the letter "N" in order to directly enter numerals
associated with Greenwich.
- Type the numerals, leaving a space between successive
entries, creating a space-delimited file.
- Click "OK" when done. You will then see a small chart
appear in the previously blank left area of the window. The chart
will have the label "data." Change the title to "Greenwich" by
right-clicking and choosing "rename."
- Indirect approach: bring in data directly from Microsoft
(or other software) using directions from the help files of A
- Next, generate music from the data.
- Click to highlight channel 8; it has longer-sounding notes
associated with it than does channel 1.
- Drag the chart entitled "Greenwich" and drop it on top of the
graphic on the "Notes" button.
- Then, hit the "play" button to hear the raw sound of audio
associated with the data for Greenwich.
- Adjust the music. We give the setttings used in the files
for the clickable map of Greater London.
- Set the Tempo to 182: slide the bar.
- Set the number of measures to 10; there are 11 entries in the
- Click on the "Duration" button and set the "Maximum" to 33
(the number of possible ranks) and the "Default" also to 33.
- Click on the "Notes" button. Set the "Minimum" and
"Maximum" to correspond with the minimum and maximum values of the
numerals in the rank vector for Greenwich. A Musical Generator®
allows values from "c" as the Minimum to "g10" as the Maximum. We
use the following assignment pattern to associate musical note value
with rank value, from 1 to 33, assuming after considerable
experimentation that a musical octave, based on Western style with a
"Major" tone scale, is presumed to begin with "c".
- c3=33; d3=32; e3=31; f3=30; g3=29; a3=28; b3=27; c4=26;
d4=25; e4=24; f4=23; g4=22; a4=21; b4=20; c5=19; d5=18; e5=17; f5=16;
g5=15; a5=14; b5=13; c6=12; d6=11; e6=10; f6=9; g6=8; a6=7; b6=6; c7=5;
d7=4; e7=3; f7=2; g7=1. Thus, to cover the entire range of ranks,
one would set the Minimum in the "Edit notes aspect" window to c3 and
the Maximum to g7--as an absolute maximum and absolute minimum for the
- To focus on the general nature of the Greenwich vector,
however, we restrict the focus to the local maximum and local minimum
of the vector itself. The minimum is 13 and the maximum is
20. Thus, set the Minimum in the "Edit notes aspect" window to b5
(assigned to 13) and the Maximum to b4 (assigned to 20). Now, try
playing the associated music once again.
- Save your work both as "Greenwich.tmg" and as
"Greenwich.mid"--the latter is a midi file which plays on the internet
See links on author names in title material for links to publication
- A Musical Generator 3.0, from
Last accessed Nov. 27, 2006.
- Arlinghaus, Sandra and Batty,
Michael. 2006. .Zipf's
Announcement, Solstice: An
Electronic Journal of Geography and Mathematics, Volume
XVII, No. 1.
- Arlinghaus, Sandra and
Arlinghaus, William. 2005 Spatial
Synthesis (Chapter 2, scroll to end for music characterizing
central place hierarchies). Ann Arbor, MI: Institute of Mathematical Geography.
Michael. 2006: Rank clocks, Nature, Vol. 444, 30 November, 2006,
doi:10.1038. Link to
*The City of London population data from
1901 to 1991 is
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.
An Electronic Journal of Geography and Mathematics
, Volume XVII,
Institute of Mathematical Geography (IMaGe).
All rights reserved worldwide, by IMaGe and by the authors.
Please contact an appropriate party concerning citation of this