A cartogram is a map where some other variable is substituted in place of area or distance. The geometery is distorted to convey information about this other variable. It is a particularly useful techniques when the population of the units being mapped varies across the map in a different way than area changes.
For example when mapping variables describing the United States a viewer’s attention is drawn to the large states in the center of the country (the Dakotas, Nebraska etc) which occupy a large amount of the map but have very few people living in them and so are less interesting than smaller but more populous states in the NE of the country.
This document looks at two styles of cartogram that can be implemented easily as part of a web mapping system. Alpha-by-value maps continue to have the same shape as a normal map but make states more (or less) transparent based on their population. Discontinuous cartograms work by scaling the area of the state based on population while keeping the shape the same. This gets around some of the common objections about continous cartograms which is that it is hard to work out which state is being represented.