For instance, the fourth district looks ridiculous:
https://en.wikipedia.org/wiki/Illinois%27s_4th_congressional...
The funky shape ensures that minorities get representation though. The weird path it takes is because of the 7th district, which I live in, which is 54% black. If it was cut any farther East, black people would be a minority.
I think the shape is a bit ridiculous, but it would be possible to make a more fair looking shape that had a white majority in each district, so I think this is the lesser of two evils. There is probably a better way to district this area though, but proportional representation would make the entire situation a bit less ridiculous overall.
The way you've represented what I've said is absurd. If representatives are to be representative of the population you'll have to create some funny looking districts somewhere. If Illinois was really gerrymandering as much as say, Wisconsin, our district map would look like a tentacled monster extending from Chicago and reaching down through the rest of the state.
The article neglected to mention that neither side wants to actually fix the problem, but both sides want to gain an advantage under the guise of fixing the problem. It's like players arguing calls in contemporary sports–it's not based on what's correct, it's based on trying to win at all costs.