An interesting quirk of our democracy is that legislatures must reapportion the boundaries of voting districts at regular intervals. This gives the representative considerable power to decide his or her own fate, since they can effectively choose the electoral body that they will "represent". For example, Congressman Black might prefer a district that includes mostly poor minorities, while Congresswoman White would like her district to include the fru-fru, quiche-eating country club types. This can be a mutually beneficial relationship; incumbency is paramount. To the detriment of democracy, since representatives are thus secure, with a consolidated base, and are free to pursue all sorts of dastardly corruption without fear of being unseated or even significantly challenged.

Thus, my motivation for this analysis of gerrymandering of U.S. Congressional districts. "Gerrymander" originated from one Elbridge Gerry, of Massachusetts, who redrew his district so that it resembled a salamander, slithering across the state.

My assumption was this: a non-gerrymandered (GM) district will have a simple shape, like a square or a circle. A GM district, on the other hand, will be oblong and spidery (like Florida's District 22, to the right). A simple metric to capture this difference is the ratio of the area to the square of the perimeter of the district.

Some notes on methodology:
My data set was the 108th Congressional districts, taken from the U.S. census website.Unfortunately there are no maps available for the 109th Congress as of yet. I then identified the region within the district via a few image filters (basically, identifying the border by color and flood-filling it). Most of this could be done computationally; a few (~10) were too complex and required a modest amount of hand-editing.

A notable difficulty is coastlines. First, because district boundaries often extend way off into the water (as with my own), simply for map-drawing convenience), the shape of the district may not accurately reflect its electoral range. That is, there is no reason to include empty water as either area or perimeter, since it could obviously not serve as motivation for gerrymandering. But, second, coastlines have fractal geometries and highly intricate borders, and if I merely subtract away all the water from the district, this leaves an artificially complicated border with an enormous perimeter. A compromise is to subtract water that is far away from land, but count it when it is close to land (effectively smoothing out the coast).

I was not totally meticulous about checking my results, but the method went through three iterations over its development (the past few days, between doing ACTUAL work), and I believe it's roughly error-free, and about as indicative as this simple metric can be. I hope the results speak for their own accuracy.

Since your appetite is now hopefully whetted, here are some results.

Average gerrymandering by state. I've arbitrarily multiplied my score by 1000 to make it more readable; you can catch number of districts in the state as well. I've color-coded by partisan status (based on Congressperson).

MD 6.88793880535598 8 GA 8.50851723977752 13 VA 8.98535082698503 11 WV 9.30040737254421 3 NC 9.68898361365534 13 MA 9.83815278770039 10 RI 10.3367699156752 2 AK 10.4485686714127 1 CA 11.1569187555363 53 PA 11.2178984267845 19 NY 11.3708290869881 29 TN 11.5855566566526 9 NJ 12.0420686498261 13 NH 12.1578267933015 2 LA 12.2445438938043 7 AL 12.4107845305385 7 ME 12.4741193904276 2 SC 12.6619477973961 6 IL 13.1024810826366 19 FL 13.6986245130043 24 TX 14.5563881134424 32 WA 14.5889054246271 9 CT 14.7686056184507 5 OH 16.1212612375961 18 KY 16.4950727687108 6

MO 16.5901389002228 9 NV 16.9636163319575 3 OK 17.0302256381007 5 DE 17.9639557785057 1 MS 18.4056015269158 4 AR 18.6930775427076 4 IN 19.0298976932724 9 ID 19.0611097181691 2 CO 19.190015615601 7 MN 19.668740404658 8 OR 19.8991234034763 5 MI 21.3541582563898 15 AZ 22.1584468774782 8 WI 22.1993707024622 8 IA 23.3256579617634 5 UT 25.1600292963252 3 VT 25.1601919520778 1 NE 25.182095595885 3 NM 25.6531361363256 3 KS 26.0170276559194 4 MT 36.2821268787846 1 HI 39.8850037043964 2 SD 41.9751521430988 1 ND 47.6133854255138 1 WY 53.3433982895139 1

Here's the 15 worst districts in the country. You'll note that it's heavily biased towards Democrats. This is representative; of the top 150 GM districts, 100 are Democrat.

CA_23	2.15392705251479	2496	13419	Capps, Lois	D
FL_20	3.41104498269896	4250	61612	Deutsch,Peter	D
FL_22	1.74145540968764	3760	24620	Shaw, E. Clay Jr.	R
GA_08	2.19182084493442	6264	86002	Collins, Mac	R
GA_11	2.82575367189675	4538	58192	Gingrey, Phil	R
GA_13	2.15803292714407	4904	51899	Scott, David	D
MD_02	1.94030760534665	6024	70411	Ruppersberger, C. A. Dutch	D
NC_03	2.41473482901921	5786	80840	Jones, Walter B.	R
NC_12	2.24523848405671	3984	35637	Watt, Melvin L.	D
NJ_06	2.86701555517374	4198	50526	Pallone, Frank Jr.	D
NJ_13	3.44740247443505	3560	43691	Menendez, Robert	D
NY_08	2.54177448357528	3020	23182	Nadler, Jerrold	D
NY_09	2.98325633510843	3652	39788	Weiner, Anthony D.	D
PA_01	3.26930653336639	4114	55333	Brady, Robert A.	D
PA_12	3.35095973846017	5090	86817	Murtha, John P.	D

And here's the raw data.