Visualizing Rank and Size of Cities and
Part I: England,
Scotland, and Wales,1901-2001
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.
England, Scotland, and Wales:
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.
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
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
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.
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:
- a global view of the UK
- a view of the UK showing national boundaries [see linked material
in reference section to Valery35 and Barmigan]
- a view of the UK showing county boundaries with no labels
[see linked material in reference section to Valery35 and Barmigan]
- a view of the UK showing county boundaries with labels [see
linked material in reference section to Valery35 and Barmigan]
- a view of the UK showing cities and towns with labels; towns and
cities are elevated, as stars perched atop a line, reflecting relative
sizes [see linked material in reference section to Bowman]
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,
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
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.
4a. 1901 population size mapped in Google Earth®.
parallelepiped reflects directly population size of associated town or
here to view a .mov file in
which the reader can control the animation rate.
4b. 1901 population size mapped in Google Earth®.
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
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
- the location
of population clusters in 1901 in England, Scotland, Wales.
understanding of adjacency patterns of these locations
understanding of where places and clusters of places are in relation to
understanding of where places and clusters of places are in relation to
the natural and built environments.
the linked file
(if you have not already done so from the box at the top of this
article) and save it on your computer.
and go to File | Open.
to where you saved the downloaded file.
around in Google
look at data in different subdirectories within the downloaded file. Once this file
subordinate files come up in
Google Earth®, manipulate the Google
Earth navigational devices in the
upper right corner to change viewpoints. Zoom out; drive
around throughout the UK countryside. Double-click a
single layer. Try to determine your position. Look at the
linked Swansea animation
(.mov file) and note that
the parallelepiped is made of tinted glass so that one can see through
the object to keep track of the
landscape. Zoom out to a more global scale to see how much
the Greater London parallelepiped soars above the
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
I: MAKE YOUR OWN PARALLELEPIPED TO ADD TO THE DATABASE.
DOWNLOAD, IN ADDITION, A FREE VERSION
OF GOOGLE SKETCHUP
GIVEN IN TERMS OF EDINBURGH, SCOTLAND, UK.
SUBSTITUTE ANY OTHER CITY/COUNTRY COMBINATION.
the process for successive years in the database simply by calculating
the difference between successive years and
the push/pull by clicking once on the top face of the parallelepiped
typing in that difference, plus or minus.
Google Earth®, the most recent beta version.
to Edinburgh in Google Earth®. Make sure
that the terrain checkbox has a checkmark in it. Make
sure the "sidebar" is visible.
in to about 15,000 feet in Google Earth®, staying directly overhead.
One must get at least this close in order to
be able to bring the Google Earth® image into Google SketchUp®.
open Google SketchUp®, the most recent beta version.
to Google SketchUp® pull-down and select "Current View"--the
with Edinburgh that was visible in Google Earth® now appears in SketchUp®
as a flat image.
the rectangle tool and draw a rectangle to cover the aerial as close to
exact coverage as possible.
the Push-Pull tool to extrude the rectangle AND HOLD DOWN THE LEFT
MOUSE BUTTON AS YOU EXTRUDE IT.
up the population of Edinburgh in 1901 and extrude the rectangle that
number of inches...type in 406368' in the lower right slot, "Distance,"
WHILE CONTINUING STILL TO HOLD DOWN THE LEFT MOUSE BUTTON. Hit Enter.
a large rectangular parallelepiped appears.
the paint bucket to open the Materials picker. Choose
the red glass+transparent material. Dump
the paint bucket into each of the two visible sides of the
to the Google SketchUp® pulldown and choose "Toggle
Terrain"--that action pumps
up the terrain. Adjust the location of the
parallelepiped in relation to the terrain, if needed (not generally an
issue on relatively flat terrain).
the "zoom extents" tool to view the entire parallelepiped.
Color the remaining two sides and top of the Parallelepiped.
to File|Save As and save the file in a folder marked Edinburgh, under
Scotland, under UK and save it as 1901Edinburgh.skp
to File|Export and save the file in the folder marked Edinburgh, under
Scotland, under UK and save it as 1901Edinburgh.kmz -- or,
if you want to see in the context of Google Earth® what you are doing,
folllow the longer sequence of steps below:
go the the Google SketchUp® Pulldown and choose "Place Model"--this
action will place the parallelepiped, adjusted if need be for terrain,
back on the terrain of Google Earth®.
back to Google Earth®.
file will come up in "Temporary Places" as SUPreview2.
on SUPreview2 and choose Rename...rename the file 1901Edinburgh.
with 1901Edinburgh still highlighted, go to File, choose, Save, Save
Place As, and then save 1901Edinburgh in the already-created Edinburgh
folder as 1901Edinburgh.kmz.
.kmz file can then be sent to others, as an e-mail attachment, and
loaded by them into Google
Earth®, by going (in Google Earth®) to
aerial pieces can be brought into the same SketchUp file.
See links on author names in title material for links to publication
Sandra; Batty, Michael; and, Nystuen, John. 2003. Animated
Time Lines: Coordination of Spatial and Temporal Information Solstice: An Electronic Journal of
Geography and Mathematics, Volume
XIV, Number 1, 2003
- Batty, Michael. 2006:
Rank clocks, Nature, Vol.
444, 30 November, 2006, doi:10.1038. Link
Harry. Cities files from
http://bbs.keyhole.com/ubb/showthreaded.php/Cat/0/Number/104614/an/0/page/0 Google Earth® Community. Last accessed
Nov. 27, 2006.
- Tobler, Waldo. The
Development of Analytical Cartography. http://www.geog.ucsb.edu/~tobler/publications/pdf_docs/cartography/Analytic_2.pdf
Edward. 1990. Envisioning
Infomation. Cheshire, CT: Graphics Press, L.L.C.
- Valery35 and Barmigen,
23.02.2006 4:20:46 generated boundary files used here; they were
checked and updated by PriceCollins:
http://bbs.keyhole.com/ubb/showflat.php/Cat/0/Number/324595 Google Earth® Community. Last accessed
Nov. 27, 2006.
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