Here we see the 12th congressional district that was approved in 1994, and which was controversial for being racially "gerry-mandered" . Now, we have to ask ourselves if there is anything wrong with a district having an "bizarre" shape, whether this is somehow giving an unfair advantage. Perhaps requiring that districts be "sensibly shaped" in some way is a reasonable way to ensure fairness. Perhaps not.
Let's also take into consideration that "There's nothing Maryland can do about its bizarre shape," as economist Christopher Chambers said at the AAAS symposium on Fairness and Mathematics. Professor Chambers is one of the authors of an academic article entitled "A Measure of Bizarreness" that will soon be published in the Quarterly Journal of Political Science. So however we may choose to answer the question of "How Bizarre is that shape?" it must take into consideration that the shape may already live in a somewhat bizarre larger one. The way to measure this according the the authors is to use a path-based measure of convexity. Given a district, its bizarreness is determined by the probability that it contains the shortest path within the state that joins two randomly selected points in the district. The higher the probability, the lower the bizarreness.
Here's a January article from Slate magazine concerning this matter.