Those aren't candy or coffee stains. This post is dedicated to the shapely, circular cities of Georgia.
I tried to do some research into why Georgia - and some of South Carolina - have this bizarre pattern, and there is very little out there. Big Think seems to be the only place where someone else thinks this is weird.
There are plenty of reasons why we don't expect administrative boundaries to take on such perfect geometry. Boundaries are usually drawn according to terrain or specific geographic features, or to delineate ethnic and cultural enclaves. Both of these things are rarely so oviform. In fact, there are political scientists who have devoted their work to studying the relationship between administrative boundary geometry and political outcomes. For example, Rutherford, Harmon, and Werfel devised the "Good Fences" theory, postulating that there will be greater political peace among territories separated by significant geographic elements, like rivers and mountains.
In Georgia, there are plenty of cities with nearly perfectly circular boundaries, see circle cities.1, and there are also city boundaries that apparently began as circles and expanded outward haphazardly, probably to incorporate specific desirable plots of land, and resulting in amazing cubist boundaries. See circle cities.2. In circle cities.1, where I layered the near perfectly circular cities above a common centroid, it's interesting that so many cities have the same diameter, most between 2500-3500 m. I'm picturing some omniscient god planner using the duplicate and move tools in his macro-planning toolkit to plop these cities across the country-side...
A few more images for your enjoyment: circle cities.3 shows just how many of circle towns there are in Georgia (in their true location). Circle cities.4 is the same map, but I was struck by how much these circles cities start to looks like constellations when you play with the colors.