Well, to be specific, I mean measuring district compactness (a very interesting subject, see these three articles for starters). There are myriad ways of measuring the “oddness” of a shape, including a comparison of the area of the district to its circumcircle, the moment of inertia of the shape, the probability that a path connecting two random points will pass through the polygon, etc.
In today’s Gist, I use the spatstat package to convert Congressional district shapefiles to owin objects, which can be very persnickety — meaning that for our present purposes I have just skipped over districts with overlapping polygons or other owin conversion obstacles. However, spatstat lets us do neat things with owin objects, including the calculation of the area and perimeter of polygons, which I use to compute and then plot a simple Area / Perimeter ratio measure of district compactness.
As you can see in the guilty-pleasure Spectral palette choropleth below (click it for a larger view), the least compact districts are unsurprisingly typically found in high-population-density areas. Also, you can use this map to find your way from Greensboro to Charlotte, via I-85.