Help with Grid Lines in a pgfplot (Version 2)

This is a follow-up question to Help with grid lines in a pgfplot

I edited the code in that post to get a grid on the Cartesian plane that is closer to what I want.

Here is what I have. By specifying grid=both, and grid style={line width=.1pt, draw=gray!10}, andxmin=-10.5, xmax=10.5, ymin=-10.5,and ymax=10.5 in the axis environment, I think that TikZ draws 20 horizontal gray lines and 20 vertical gray lines. I think major grid style={line width=.2pt,draw=gray!50}, in the axis environment should instruct TikZ to draw some darker help lines. It doesn't. I tried specifying xtick={-10, -5, 5, 10},, ytick={-10, -5, 5, 10},, ticklabel style={font=\tiny,fill=white},, and extra x ticks={-9, -8, -7, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 7, 8, 9}, to get TikZ to draw the "major grid" through x=-10, x=-5, x=5, and x=10. That didn't work.

Here are some features that need to be included. Tick marks at -10, -5, 5, and 10 are to be typeset on both axes and "over the grid lines." Implementing this code, they are all under the grid ... but there is a horizontal white strip below the x-axis and to the left of the y-axis, except for the typesetting of -10, -5, 5, and 10. Why is this horizontal white strip there?

\documentclass{amsart}
\usepackage{tikz}
\usetikzlibrary{calc}

\usepackage{pgfplots}
\pgfplotsset{compat=1.11}

\begin{document}

\begin{tikzpicture}
\begin{axis}[title=An Illustration of Lattice Paths, title style={align=center,font=\bfseries},
grid=both,grid style={line width=.1pt, draw=gray!10},major grid style={line width=.2pt,draw=gray!50},
xmin=-10,xmax=10,ymin=-10,ymax=10,
axis lines=middle,
xtick={-10, -5, 5, 10},
ytick={-10, -5, 5, 10},
ticklabel style={font=\tiny,fill=white},
extra x ticks={-9, -8, -7, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 7, 8, 9},
extra x tick labels={},
extra y ticks={-9, -8, -7, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 7, 8, 9},
extra y tick labels={},
minor tick num=4,
enlargelimits={abs=0.5},
axis line style={latex-latex},
axis line style={shorten >=-7.5pt, shorten <=-7.5pt},
xlabel style={at={(ticklabel* cs:1)},anchor=north west},
ylabel style={at={(ticklabel* cs:1)},anchor=south west}
]

\coordinate (O) at (0,0);
\node[fill=white,circle,inner sep=0.5pt] (O-label) at ($(O)+(-135:10pt)$) {$\scriptstyle{O}$};
\coordinate (A) at (-3,9);
\node[fill=white,circle,inner sep=0.5pt] (A-label) at ($(A)+(-180:10pt)$) {$\scriptstyle{A}$};
\coordinate (B) at (7,-3);
\node[fill=white,circle,inner sep=0.5pt] (B-label) at ($(B)+(-45:10pt)$) {$\scriptstyle{B}$};

\draw[fill] (O) circle (1.5pt);
\draw[fill] (A) circle (1.5pt);
\draw[fill] (B) circle (1.5pt);

%These commands are for drawing a path from O to A.
\coordinate (A1) at (-1,0);
\coordinate (A2) at (-1,3);
\coordinate (A3) at (-3,3);

\draw[line width=1pt] (O) -- (A1) -- (A2) -- (A3) -- (A);

%These commands are for drawing a path from O to B.
\coordinate (B1) at (2,0);
\coordinate (B2) at (2,-2);
\coordinate (B3) at (5,-2);
\coordinate (B4) at (5,-3);
\coordinate (B) at (7,-3);

\draw[line width=1pt] (O) -- (B1) -- (B2) -- (B3) -- (B4) -- (B);

\coordinate (P) at (4,6);
\node[fill=white,circle,inner sep=0.5pt] (P-label) at ($(P)+(45:10pt)$) {$\scriptstyle{P}$};
\draw[fill] (P) circle (1.5pt);

\coordinate (Q) at (-7,-7);
\node[fill=white,circle,inner sep=0.5pt] (Q-label) at ($(Q)+(-135:10pt)$) {$\scriptstyle{Q}$};
\draw[fill] (Q) circle (1.5pt);

\end{axis}

\end{tikzpicture}
• Why did you remove the link to the previous question? – Alenanno May 31 '15 at 0:48
• @Alenanno Sorry. Undo that. – user74973 May 31 '15 at 0:49
• @Alenanno Hit the wrong icon. What is "rollback"? – user74973 May 31 '15 at 0:50
• Rollback reverts the changes to the revision where you clicked rollback. :) – Alenanno May 31 '15 at 0:57
• @Alenanno In this case, I had just put a post on this web site. You modified it. I hit rollback, and this web site returned the post to the way I had it. Is that right? – user74973 May 31 '15 at 15:08

I think major grid style={line width=.2pt,draw=gray!50}, in the axis environment should instruct TikZ to draw some darker help lines. It doesn't.

It does. Try reducing it to .1pt, and you'll still distinguish them from the other lines which are line width=.1pt,gray!10. See image below for a demonstration of this.

I tried specifying xtick={-10, -5, 5, 10},, ytick={-10, -5, 5, 10},, ticklabel style={font=\tiny,fill=white},, and extra x ticks={-9, -8, -7, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 7, 8, 9}, to get TikZ to draw the "major grid" through x=-10, x=-5, x=5, and x=10. That didn't work.

I don't understand why you're trying to do new things, when the code I gave you in the previous question draws the lines exactly through those points. Probably you didn't understand the code (it can happen), but the code already does that. See: The command minor tick num=# is the number of ticks (not tick labels) between each major tick.

So in this case you have 0, 5, 10. If you write minor tick num=4, you'll get four ticks.

So from 0 to 5: 1,2,3,4.
And from 5 to 10: 6,7,8,9.

Four numbers = four ticks. See again image above to see this in action.

Hope this helps.

Edit: In response to your comment:

Suppose that I want a grid on the Cartesian plane with xmin=-52, and xmax=52, and ymin=-11,ymax=17, and that I want the major grid style to be implemented at vertical lines that are multiples of 13 from the y-axis and at horizontal lines that are multiples of 5 from the y-axis.

I can't do that plane here because it's too big, but I'll provide a small example to explain the same concept. If you leave the ticks alone, the default is multiples of 5: {0,5,10,...}, but you can change this for each axis independently. When you set the ticks for a certain axis, those will be considered major ticks for that axis. So if you say {-9,-6,-3,0,3,6,9}, then these will be the major ticks.

Of course, if the ticks are too many but you know the steps, you can simply write xtick={-9,-6,...,9}, and the result is the same. You define starting and ending point, and then the second number is used to define the step. Since between 9 and 6, you have 3 numbers, then the step is 3.

If the two axes are different, we will need to specify the minor ticks for each axis independently using

minor x tick num={4},
minor y tick num={4},

And this is the result: Here is the code:

\documentclass{amsart}
\usepackage{tikz}
\usetikzlibrary{calc}

\usepackage{pgfplots}
\pgfplotsset{compat=1.11}

\begin{document}
\begin{tikzpicture}
\begin{axis}[grid style={line width=.1pt, draw=gray!10},major grid style={line width=.2pt,draw=gray!50},
xmin=-11.75,xmax=11.75,
ymin=-11.75,ymax=11.75,
xtick={-9,-6,...,9},
ytick={},
grid=both,
minor x tick num={4},
minor y tick num={4},
enlargelimits={abs=0},
ticklabel style={font=\tiny,fill=white},
axis lines=middle,
axis line style={latex-latex},
xlabel style={at={(ticklabel* cs:1)},anchor=north west},
ylabel style={at={(ticklabel* cs:1)},anchor=south west}
]

\coordinate (O) at (0,0);
\node[fill=white,circle,inner sep=0pt] (O-label) at ($(O)+(-135:10pt)$) {$\scriptstyle{O}$};

\end{axis}
\end{tikzpicture}
\end{document}
• I understand the code, but I'm not sure how TikZ can adapt it to an asymmetric display. Suppose that I want a grid on the Cartesian plane with xmin=-52, and xmax=52, and ymin=-11,ymax=17, and that I want the major grid style to be implemented at vertical lines that are multiples of 13 from the y-axis and at horizontal lines that are multiples of 5 from the y-axis. (At your suggestion from the other post, I want to include axis line style={shorten >=-7.5pt, shorten <=-7.5pt},.) – user74973 May 31 '15 at 15:04
• @user74973 See edit. – Alenanno May 31 '15 at 15:52
• I appreciate your explanation. Very nice! Please affirm the following paraphrases. If you omit the specification of ticks on the axes or include xtick={\empty},ytick={},, for example, the default for the major grid style is multiples of 5: {... -10, -5, 0,5,10,...}. If you have xmin=-52, and xmax=52 and xtick={-52, -39,..., 52}, and ymin=-11, and ymax=17, and ytick={-9,-6,...,15}, the major grid style will be vertical lines that are integral multiples of 13 from the y-axis and horizontal lines that are integral multiples of 3 from the x-axis. – user74973 May 31 '15 at 18:14
• In case you are not weary of talking about grid lines, I posted another question. The title is "Help with Grid Lines in a pgfplot (Version 3)" – user74973 Jun 1 '15 at 1:14