[math-fun] measuring the irregularity (or salamander-ness) of a planar region

Is there a good measure of how irregular a region of the plane is? something that gives 0, say, for a circular disk, and 1 (or infinity) for a fractal gasket? the motivation is to find a measure of how irregular (or gerrymandered) a congressional district is. Neil -- Dear Friends, I have now retired from AT&T. New coordinates: Neil J. A. Sloane, President, OEIS Foundation 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com