The Trond can't help it...

[muon2]

Illinois
1-8 12% of Cook
653,223 .999
9 Will, 3% of Cook
653,223 .999
10 Lake
644,356 .986
11 72% of DuPage
654,140 1.001
12 Kane, 28% of DuPage
654,140 1.001
13 McHenry, Boone, Winnebago, Stephenson, Jo Daviess
651,549 .997
14 La Salle, Grundy, Kendall, DeKalb, Ogle, Lee, Livingston, Ford, Woodford, Marshall, Putnam, Bureau, Carroll, Whiteside, Henry
652,155 .998
15 Rock Island, Mercer, Warren, Henderson, Hancock, Adams, McDonough, Schuyler, Brown, Pike, Calhoun, Fulton, Knox, Stark, Peoria, Scott, Greene
655,346 1.003
16 Tazewell, Mason, Cass, Morgan, Menard, Sangamon, Macoupin, Logan, McLean, DeWitt, Piatt
660,069 1.010 (just under, actually.)
17 Madison, Saint Clair, Jersey, Monroe, Washington, Clinton, Bond, Perry
655,720 1.003
18 Kankakee, Iroquois, Vermillion, Champaign, Edgar, Douglas, Coles, Moultrie, Macon, Shelby, Cumberland
654,716 1.002
19 remaining 29 counties to the South (with an unfortunate northern tip in Christian County)
658,095 1.007

If this were attempted in IL, it would fail at the State Supreme Court which has ruled that there can be no more than 0.5% deviation from the ideal district population. However, if these rules were adopted by Congress to be applied to the states then that decision could be avoided.

[muon2]

New Mexico
Bernalillo can't be paired with either Valencia or Sandoval (nor Santa Fe either) which means it has to extend into quite vast areas. The number of legal combinations within these constraints however is legion - districts as diverse as Bernalillo - Cibola - Catron - Sierra or Bernalillo - Torrance - San Miguel - Dem hold NM1 for ever.
I *think* this map has the lowest pop. variation, although it's right up there in Absurdistan...

1 Bernalillo, Cibola, Torrance, Guadalupe, De Baca
606,104 1.000
2 North of that and as far as Quay and Curry
606,989 1.001
3 remainder
605,953 .999

Yes, the population + county geography combination make splitting counties hard to avoid. Although my old plan did quite well in minimizing that. I only split four counties: Bernalillo because you have to, Sandoval to pick up the northern Urban Area (although if I hadn't hit the population limit I would've then gone south into Valencia to pick up the southern Urban Area), Socorro to nab the Native American Reservation there for CD3, and Colfax to reduce population deviation.

Oh, my version 2 had:
1: 606,359 1.000 Dev. -10
2: 606,421 1.001 Dev. +72
3: 606,266 .999   Dev. -83

Now that is minimal population deviation!

Interesting map there...but it is absurd.

It's interesting to see what happens to Trond's map if you project it to 2010. CD 1 become too large and CD 3 quite a bit to small. To correct it I had to reduce CD 1 to Bernalillo and Cibola only (projected 679.0 K in 2010). CD 2 wraps around Albuquerque and becomes Guadalupe, Los Alamos, McKinley, Mora, Rio Arriba, Sandoval, San Juan, Santa Fe, Taos, Torrance, and Valencia (678.5 K). CD 3 takes in the rest in the south and east (679.5 K).

[muon2]

New Mexico
Bernalillo can't be paired with either Valencia or Sandoval (nor Santa Fe either) which means it has to extend into quite vast areas. The number of legal combinations within these constraints however is legion - districts as diverse as Bernalillo - Cibola - Catron - Sierra or Bernalillo - Torrance - San Miguel - Dem hold NM1 for ever.
I *think* this map has the lowest pop. variation, although it's right up there in Absurdistan...

1 Bernalillo, Cibola, Torrance, Guadalupe, De Baca
606,104 1.000
2 North of that and as far as Quay and Curry
606,989 1.001
3 remainder
605,953 .999

Yes, the population + county geography combination make splitting counties hard to avoid. Although my old plan did quite well in minimizing that. I only split four counties: Bernalillo because you have to, Sandoval to pick up the northern Urban Area (although if I hadn't hit the population limit I would've then gone south into Valencia to pick up the southern Urban Area), Socorro to nab the Native American Reservation there for CD3, and Colfax to reduce population deviation.

Oh, my version 2 had:
1: 606,359 1.000 Dev. -10
2: 606,421 1.001 Dev. +72
3: 606,266 .999   Dev. -83

Now that is minimal population deviation!

Interesting map there...but it is absurd.

It's interesting to see what happens to Trond's map if you project it to 2010. CD 1 become too large and CD 3 quite a bit to small. To correct it I had to reduce CD 1 to Bernalillo and Cibola only (projected 679.0 K in 2010). CD 2 wraps around Albuquerque and becomes Guadalupe, Los Alamos, McKinley, Mora, Rio Arriba, Sandoval, San Juan, Santa Fe, Taos, Torrance, and Valencia (678.5 K). CD 3 takes in the rest in the south and east (679.5 K).

Hmm...interesting indeed. I suspect my map isn't projectable because I split too much of Bernalillo and Sandoval and your projections are only down to the county level...

I can split to smaller levels when there are census estimates. In the NE and Midwest every state is fully broken down to the town level. Elsewhere only incorporated places are estimated by the census.

Thanks to WMS for sending me his precinct files and with some rounding on my part I can make rough projections for WMS' map.

In 2010 the ideal CD is about 679 K in population.
WMS CD 1: 723 K
WMS CD 2: 638 K
WMS CD 3: 677 K
The Albuquerque district has the growth that need to shift to CD 2to then shift to CD 3. The city of Rio Rancho in CD1 in Sandoval county is seeing a growth rate of almost 5% per year.