I have often seen publications include world maps with the areas of
different countries scaled to be proportional to the size of some
reference variable - such as their population or GDP. Where can I find
software capable of producing such a map automatically?

The software would have to, in some way, take as input a list of
countries and associated data (China 1000, Japan 500, US 100, Canada
40) and produce a map where the Area of China was twice that of Japan
and ten times that of the US etc. Any type of graphical file format
is acceptable.

Hi fred120,

Ok, I have good news for you  - software is available but it is not
inexpensive and it will require quite a bit of work on your part to
make your maps. The word "Cartogram" is the key - that is the program
that will allow the map distortion needed to do what you want to do.
Following is a link to a website with a "cartogram" - it is an example
of what can be made with the software I found for you.
http://www.bbr.unl.edu/cartograms/index.html

WHAT ARE CARTOGRAMS ?
"A Cartogram is a map or diagram showing geographical statistical
information (Dorling 1995)... Cartograms differ from traditional maps
as they use a variable other than area to derive the size of areal
units on the map."
http://www.geog.qmw.ac.uk/gbhgis/conference/cartogram.html

Cartograms are also referred to as  "Distortion Maps", "Proportional
Maps", "Diagrammatic Maps", and "Value-by-Area Maps". They are
difficult to make and a large problem with this type of map is they
easily become unrecognizable.

Distortion Map (half way down page):
"Size of polygons are proportional to attribute statistic (such as
population)"
http://faculty.gvsu.edu/hoffmanm/pa644/lectures/thematic/thematic.pdf

To learn more about Cartograms, visit Cartogram Central:
http://www.ncgia.ucsb.edu/projects/Cartogram_Central/

Cartogram software is just a small part of the larger Geographic
Information Systems (GIS) programming.

GIS explained:
"Many computer programs, such as spreadsheets, statistics or drafting
packages can handle simple geographic or spatial data, but this
doesn't make them a GIS. A true GIS links spatial data with geographic
information about a particular feature on a map.
In short, a GIS doesn't hold maps or pictures - it holds a database.
The database concept is central to a GIS and is the main difference
between a GIS and other computer mapping packages."
http://www.geoexplorer.co.uk/sections/gis/gis_explained.htm

SOFTWARE:

GIS: You will first need to purchase ArcView ($1500):
http://www.esri.com/software/arcgis/overview4.html

Once you have ArcView installed on your computer, download the
following:
ArcView Contiguous Cartogram Extension (freeware):
http://arcscripts.esri.com/details.asp?dbid=10509

The two programs above should work for you, however, in addition to
the cost, many hours of work will be needed to produce what you want.
I have spoken to someone who is familiar with GIS and he said it is
not for the faint of heart!

There is a less expensive GIS program which sounds good on the
surface, but unfortunately Manifold cannot produce distortion. One of
their representatives told me that they believe using thematics to
show variables, such as varying color, is easier for humans to
perceive but varying area is harder for humans to perceive.
"Manifold System Release 5.50 Professional Edition": $245
http://www.manifold.net/gis.html

MapInfo is also available but it doesn't seem to be cartogram capable
either and I have been told that it is very complicated to use.
MapInfo Professional®: call for price
http://www.mapinfo.com/products/Features.cfm?ProductID=1044
Contact
http://www.mapinfo.com/products/buying/index.cfm

Sounds like AT&T does has what you are looking for (CartoDraw) but it
seems to be unavailable to the public.
CartoDraw: Contiguous Cartograms:
http://www.research.att.com/~north/papers/01/KNP01.pdf

AT&T Labs Research:
http://www.research.att.com/news/2002/April/DataVisualization.html


Additional Links:

Cartogram history:
http://www.geog.ucsb.edu/%7Esara/html/mapping/election/background.html

GIS explained:
http://www.usgs.gov/research/gis/title.html

"The CyberInstitute Short-Course on Geographic Information Systems":
http://www.ngdc.noaa.gov/seg/tools/gis/referenc.html

http://inside.uidaho.edu/tutorial/software/software.htm

Descartes - available in Germany:
"GIS are typically complex and difficult to operate: significant
training is required."
http://www.iskp.uni-bonn.de/bibliothek/reports/GMD/2000/e-probl/DESCARTE.pdf.

I hope this helps. If you have any questions or if this doesn't
satisfy your request, please post a clarification request before
rating my answer.

A final thought, quoting Steve Demers:
" I definitely prefer for aesthetic purposes, [making a cartogram] by
hand. The time you save automating, you end up using anyway fixing
everything that the computer screwed up. You can see in several places
in the final cartogram where the congressional districts lose
topology. ...there is actually a hole too many things that can go
wrong in automation. Making a cartogram takes a lot of cartographic
licence, style and creativity-things a computer just cant do."
http://www.ncgia.ucsb.edu/projects/Cartogram_Central/goal.html

Thank you and good luck,
hummer

Search Terms:

descarte mapping software
"visual data analysis mapping"
GIS explained
GIS glossary
"visual data analysis maps"
"proportional mapping"
proportional spatial mapping
"statistical mapping" proportional
Cartogram
Value-by-area map
map transformation
anamorphosis
"thematic cartography"
etc

Extremely impressed. A superb, prompt answer to a fairly vague
question - and one which I had asked many others previously with
absolutely no luck.

Dear fred120,

Thank you for your thank you and fine rating, both are appreciated. I
didn't find your question vague at all but finding the answer did
require alot of digging, so don't be too hard on the others. Glad to
hear Google Answers worked for you.

Sincerely,
hummer