"...Patents are the conventional measure of innovation. Despite their various weaknesses, patents represent a systematic, quantitative measure of innovation and are used by economists as the single dominant measure of innovation. But, as with other measures, economists tend to measure them on a per capita basis.

Innovation Density: Our measure of innovation density is patents per square kilometer. The map below shows the density of innovation based on this measure. The median density of innovation is .008 patents per square kilometer. The densest metros have more than .4 patents per square kilometer, while the least dense have fewer than .001...."