The results of redistricting in the US have been compared to the patchwork bantustans created under apartheid in South Africa: topological monstrosities whose tentacles and fractured edges serve to create homogenized voting blocs where the notion of a district as a conventional geographic entity is completely lost.
For example, on the right is a map of the Pennsylvania district in the the Vieth v. Jubelirer case - the resemblance to an apartheid homeland is uncanny.
The purpose of this gerrymandering is to ensure that incumbents don't lose their seats. According to the LA Times on 31 Oct 2004, "Of the 435 House elections Tuesday, only about four dozen are remotely competitive. Not one of California's 51 House incumbents is in danger of losing his or her seat."
The result is frequently the social and racial homogenization of electoral districts; for example, according to a Boston Globe article by Frank Phillips on 17 August 2004, "voting rights groups forced a major redrawing of Boston's House districts to increase minority political clout." The story notedthat "A three-judge panel concluded in February that the redistricting plan [...] deprived minorities of their voting rights [because] among other inequities, the House plan packed minority voters into an already heavily minority district in Roxbury, while shifting minority voters from nearby districts."
While the maps look the same, there are striking differences between the US and South African experiences.
In America, coming up with crazy cartography is a consensus activity. Although Left and Right may end up on opposite sides of court cases about the specifics, both engage in it, and feel it helps their constituencies. While often racially motivated, US gerrymandering is driven by party political power, which is as more about financial interests and social values than it is about ethnicity.
The foundations of the American practice are also less stable than the apartheid one. Skin color was all that mattered in South Africa, but while American voting habits may correlate from time to time with ethnicity, it keeps changing. A Wall Street Journal story on October 20, 2004 by Jacob Schlesinger describes "emerging signs that a wide swath of voting blocs -- such as women, Latinos, young voters and rural voters -- could behave in unpredictable ways in next Tuesday's election."
With a little luck, this means that the gerrymanderers' best laid plans will always unravel, and that the electoral lock-ins that they crave will never last.
Will electoral districts will ever contract to more coherent shapes? Demographic analysis will continue to become more sophisticated, and the trend to ever-more complex boundaries seems inexorable. Districts will become ever-more fragmented because they can, not because they should. The courts are a countervailing force; to the extent that they refrain from using demographic information to draw boundaries, they will have to fall back on geography, and thus on simpler shapes.
The geography of gerrymandering presents a fascinating opportunity to explore the intersection between political science and complexity theory. The key parameter to track over time will be boundary complexity (measured as fractal dimension, perhaps). It's grown over the last few decades; will it continue to do so? I expect it will. Fortunately, the "If I can think of it, somebody's already done it" Rule, some enterprising political science student has already written their thesis about this. I look forward to finding it; there's already some work on fractals and redistricting.