In which environment can I draw a 2d lattice (say over Z) and maybe colour various parts (e.g. excluding all points for which (x,y) > (2,2)?
Maybe tikz is a solution but I am not sure where to start from (e.g. how to define a lattice with an origin etc). There is a similar question but does not help a lot.
I upload a picture so that I make clearer what I want to do. The blue axes are the usual (x,y) axes but I also want to draw lines or exes beginning at other points and I want to exclude regions by coloring them. The arrows are not important. Also I do not mind if the lattice points appear too, actually that would be useful.