Latex, graphs on millimeter paper

Introduction

In a Latex document, how to create graphs on a millimeter paper ? How to automate millimeter paper backgrounds using Tex macros ?

Code sample

The code for the graph above on the left is the following :

\documentclass[tikz]{standalone}

\usepackage{pgfplots}
\usepackage{amsmath,amssymb,amsfonts}

\pgfplotsset{compat=newest}
\pgfplotsset{every axis/.append style={
                    axis x line=middle,    
                    axis y line=middle,   
                    axis line style={->}, 
                    xlabel={$x$},          
                    ylabel={$y$},          
                    label style={font=\scriptsize},
                    tick label style={font=\tiny},
                    unit vector ratio*=1 1 1,  
   					xlabel style={at={(ticklabel* cs:1)},anchor=north west},
   					ylabel style={at={(ticklabel* cs:1)},anchor=south west}  
                    }}

\begin{document}
 
  \begin{tikzpicture}

   \begin{axis}[
	 name = graph1,     
     ytick distance = 1,
     xtick distance = 1,
     ymin=-1.1, ymax=5.1,
     xmin=-1.1, xmax=5.1,
     grid=both,
     grid style={line width=.1pt,draw=brown!20},
     major grid style={line width=.2pt,draw=brown!40},
     minor tick num=10,
     tick style={draw=none},
   ]
  
     \addplot [domain=0.01:10, samples=500, color=gray!90]
        {sqrt(1/x)}; 

   \end{axis}
   \node[anchor=north] at (graph1.south) {\scriptsize $f(x)=\sqrt {\dfrac{1}{x}}  \qquad x \in \mathbb{R}  ,\; x > 0 $};  

  \end{tikzpicture}

\end{document}

To setup the millimeter paper in the background, the following axis properties are defined :

\begin{axis}[
…
     grid=both,
     grid style={line width=.1pt,draw=brown!20},
     major grid style={line width=.2pt,draw=brown!40},
     minor tick num=10,
     tick style={draw=none},
…
]

Automating millimeter paper in a macro

Macro creation

We don’t want to duplicate the code for each graph.

Create a macro axispapermm defining the millimiter paper axis properties in a sty file :

ppm.sty

\ProvidesPackage{ppm}[2021 Millimeter paper macros]

\newcommand{\axispapermm}{grid=both,
 grid style={line width=.1pt,draw=brown!20},
 major grid style={line width=.2pt,draw=brown!40},
 minor tick num=10,
 tick style={draw=none}
}

Import the package and call the macro axispapermm

\documentclass[tikz]{standalone}

\usepackage{pgfplots}
\usepackage{amsmath,amssymb,amsfonts}
\usepackage{ppm}

\pgfplotsset{compat=newest}

\pgfplotsset{every axis/.append style={
                    axis x line=middle,    
                    axis y line=middle,   
                    axis line style={->}, 
                    xlabel={$x$},          
                    ylabel={$y$},          
                    label style={font=\scriptsize},
                    tick label style={font=\tiny},
                    unit vector ratio*=1 1 1,  
   					xlabel style={at={(ticklabel* cs:1)},anchor=north west},
   					ylabel style={at={(ticklabel* cs:1)},anchor=south west}  
                    }}

\begin{document}
 
  \begin{tikzpicture}

   \begin{axis}[
	 name = graph1,     
     ytick distance = 1,
     xtick distance = 1,
     ymin=-1.1, ymax=5.1,
     xmin=-1.1, xmax=5.1,
     \axispapermm
   ]
  
     \addplot [domain=0.01:10, samples=500, color=gray!90]
        {sqrt(1/x)}; 

   \end{axis}
   \node[anchor=north] at (graph1.south) {\scriptsize $f(x)=\sqrt {\dfrac{1}{x}}  \qquad x \in \mathbb{R}  ,\; x > 0 $};  

  \end{tikzpicture}

\end{document}

Customizing the color

The axispapermm macro is then enhanced to to set the color as an argument.

ppm.sty

\ProvidesPackage{ppm}[2021 Millimeter paper macros]

\newcommand{\axispapermm}[1]{grid=both,
   grid style={line width=.1pt,draw=#1!20},
   major grid style={line width=.2pt,draw=#1!40},
   minor tick num=10,
   tick style={draw=none}
}

\documentclass[tikz]{standalone}

\usepackage{pgfplots}
\usepackage{amsmath,amssymb,amsfonts}
\usepackage{ppm}

\pgfplotsset{compat=newest}

\pgfplotsset{every axis/.append style={
                    axis x line=middle,    
                    axis y line=middle,   
                    axis line style={->}, 
                    xlabel={$x$},          
                    ylabel={$y$},          
                    label style={font=\scriptsize},
                    tick label style={font=\tiny},
                    unit vector ratio*=1 1 1,  
   					xlabel style={at={(ticklabel* cs:1)},anchor=north west},
   					ylabel style={at={(ticklabel* cs:1)},anchor=south west}  
                    }}

\begin{document}
 
  \begin{tikzpicture}

   \begin{axis}[
	 name = graph1,     
     ytick distance = 1,
     xtick distance = 1,
     ymin=-1.1, ymax=5.1,
     xmin=-1.1, xmax=5.1,
     \axispapermm{blue}
   ]
  
     \addplot [domain=0.01:10, samples=500, color=gray!90]
        {sqrt(1/x)}; 

   \end{axis}
   \node[anchor=north] at (graph1.south) {\scriptsize $f(x)=\sqrt {\dfrac{1}{x}}  \qquad x \in \mathbb{R}  ,\; x > 0 $};  

  \end{tikzpicture}

\end{document}