However, these are ideals rather than requirements. In reality, the U.S. Constitution has little to say about how redistricting should occur. Beyond the universal requirement for "one person, one vote", each state is free to determine its own constitutional requirements or statutes for redistricting. For instance, states may have different standards for acceptable deviation from the equal population requirement, and information that is acceptable to use in one state’s process may be explicitly forbidden in another’s. Most states do have a "contiguity rule" requiring districts to be contiguous land areas, but it’s not difficult to find examples of districts that seriously test the limits of this rule.
The equal population requirement is the biggest factor governing the shape and nature of our political districts. However, redistricting experts usually take race, communities of interest, voting history, political affiliation of registered voters, and the home addresses of incumbent politicians into account when drawing political boundaries.
Azavea is building an online software toolkit that would enable citizens to create their own redistricting plans using some of the same data sets that professionals use. The toolkit includes mechanisms for assessing the "fairness" of districts, including generating compactness scores and snapshots of the characteristics of a district's citizenry (population, race, voting history, political affiliation, etc.).