I wasn't proposing that district boundaries would end up regular polygons or that their size would be fixed...that would defeat the whole purpose of normalizing population across districts. My idea was to start with a hexagonal (or other regular polygon) grid and then warp it to the minimum degree required to equalize population. The more refined suggestion was to start with a much finer grid, say down to the block or acre level, and then make your districts by including whatever number of smaller polygons are needed. In the latter case, I was looking at construction rules, such as "no more than three sides exposed", that would prevent highly irregular districts.

The reason I thought it necessary to have a starting grid is that an algorithm needs something to work with, an initial state from which to evolve. Alternatives like start in Alaska (the "upper-left corner") and fill down (south) and to the right (east) I'd expect to get pretty damn snarled by the time you get to Florida--errors would accumulate with that kind of algorithm. Networks or meshes start out uniform and distribute errors equally across the surface, so that no one area has a greater error than any other.

I agree that natural features such as rivers and mountains would trump an abstract grid. The small-grid method would allow an algorithmic solution: Define certain hexagons as anchored, or as boundary hexagons, perhaps by designating sides that cannot be joined. Good GIS software can do that easily enough by identifying those natural features.

There will always be a residual amount of human intervention required; no algorithm will cover all cases. But reducing the need for manual intervention to a minimum reduces the opportunity for gerrymandering as well. When the adjustments are infrequent, people will notice and keep an eye on the process.

Which is to say, I think we're in close agreement.