From the examples you’ve drawn — population GDP and zombies — I think you must have a funny character :) Thank you for going graphics, metaphores really help to figure out equations.

Question, what difference in using L1 Vs L2 (square norms) ? Is it to reduce computation? I look at the plot of norm L1 on a plane, and that would turn to be a triangle in positive X, Y coordinates. But missing the link on why preference VS L1, since the changes to have tips at zeros would be even less (only 3 vertex out of 4).