# Drawing lattice (say over the integer numbers Z)

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. • This is a very vague question. Nevertheless you can probably do this with tikz. Just scroll through the TikZ & PGF manual or the pgfplots manual. Find something which looks like what you envision than edit it. – Roald Sep 27 '16 at 17:12
• I know I can use tikz, I just have no time for this and thus I asked the help of the community. – Marion Sep 27 '16 at 23:10
• @Roald I have expanded the question and included a picture for better understanding. – Marion Sep 28 '16 at 11:37

Here is a starting point using \foreach loops to iterate over all lattice points. I added also an example condition (i,j) > (2,2):

\documentclass[tikz,border=7pt]{standalone}
\begin{document}
\begin{tikzpicture}
% labels
\foreach \i in {0,...,5}
\path[blue] (\i,-1) node{\i} (-1,\i) node{\i};
% loop over the lattice points
\foreach \i in {0,...,5}
\foreach \j in {0,...,5}{
\draw (\i,\j) circle(3pt);
% check if (\i,\j) > (2,2)
\ifnum \i > 2
\ifnum \j > 2
\fill[red] (\i,\j) circle(2pt);
\fi
\fi
};
\end{tikzpicture}
\end{document} • thanks a lot, I am interested in having both negative and positive axes and coloring out regions (rather than dots). But thanks for your help! – Marion Sep 27 '16 at 23:10