Bivariate Maps of the Choropleth Persuasion

The depiction of multiple variables on the same map, displayed to highlight a relationship between the two, is no simple feat of cartography.  The choropleth map, in particular, is best suited for indicating the geographic prevalence of a single, or single incidence of multiple, phenomena.  Mapping with varying color shades to indicate the prevalence of two separate variables- the areas where there is a high prevalence of one and not the other, and areas where there is a high prevalence of both- is an ambitious task by any estimation.  

The use of the bivariate choropleth map may be employed for this depiction of two separate variables, and thus indicates the relationship between the two.  Above is a representation of both rates of obesity and physical inactivity, by U.S. county, with the use of two different hues with separate quantitative color progressions.  The legend in the lower left illustrates these with a 9-square color palette, which varies by hue according to the X- and Y-axes, and by lightness progressing across both.  As the colors progress towards the upper right corner of the cube, the colors are meant to indicate a high prevalence of both variables.  Thus, the viewer is able to use the 9 different colors there to visualize the spatial relationship between the two.  The current version of ArcMap in use, though, doesn't support the automated creation of this variety of legend, and it must be assembled by hand.  Though creating a 9-color legend, which varies in hue and lightness along two axes, is no easy feat, it is unarguably a valuable practical lesson in applied color theory.