to a variable other than their actual size, the danger is that the features will be distorted to the degree that they are no longer recognizable to map readers, making them less useful. As with map projections, the tradeoffs inherent in cartograms have led to a wide variety of strategies, including manual methods and dozens of computer algorithms that produce very different results from the same source data. The quality of each type of cartogram is typically judged on how accurately it scales each feature, as well as on how (and how well) it attempts to preserve some form of recognizability in the features, usually in two aspects: shape and topological relationship (i.e., retained adjacency of neighboring features). It is likely impossible to preserve both of these, so some cartogram methods attempt to preserve one at the expense of the other, some attempt a compromise solution of balancing the distortion of both, and other methods do not attempt to preserve either one, sacrificing all recognizability to achieve another goal. Area cartograms The area cartogram is by far the most common form; it scales a set of region features, usually administrative districts such as counties or countries, such that the area of each district is directly proportional to a given variable. Usually this variable represents the total count or amount of something, such as total Population, Gross domestic product, or the number of retail outlets of a given brand or type. Other strictly positive ratio variables can also be used, such as GDP per capita or Birth rate, but these can sometimes produce misleading results because of the natural tendency to interpret size as total amount. Of these, total population is probably the most common variable, sometimes called an isodemographic map. The various strategies and algorithms have been classified a number of ways, generally according to their strategies with respect to preserving shape and topology. Those that preserve shape are sometimes called equiform, although isomorphic (same-shape) or homomorphic (similar-shape) may be better terms. Three broad categories are widely accepted: contiguous (preserve topology, distort shape), non-contiguous (preserve shape, distort topology), and diagrammatic (distort both). Recently, more thorough taxonomies by Nusrat and Kobourov, Markowska, and others have built on this basic framework in an attempt to capture the variety in approaches that have been proposed and in the appearances of the results. The various taxonomies tend to agree on the following general types