[Tex/LaTex] control the ‘density’ of a pattern in TikZ

Question

…i.e. I want to control the spacing between lines in a hatch pattern. Is that possible at all with the predefined patterns from the pattern library, like north east lines? Or should I just create my own pattern? I tried the step modifier, but it has no effect as in the minimal non-working example below. 😉

\begin{tikzpicture}
    \draw [step=0.5cm, pattern=north east lines] (0,0) rectangle (1.4,1.4);
\end{tikzpicture}

EDIT: I changed the code a bit, because I would like to control the spacing in any type of pattern and originally in the example was grid.

Answer 1

As Gonzalo says the patterns are not customizable. So, here is one way you can customize the code for the grid pattern to accept a variable that allows you to control the density by adjusting the GridSize=1pt. The default is GridSize=3pt

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{patterns}

\makeatletter
\pgfdeclarepatternformonly[\GridSize]{MyGrid}{\pgfqpoint{-1pt}{-1pt}}{\pgfqpoint{4pt}{4pt}}{\pgfqpoint{\GridSize}{\GridSize}}%
{
  \pgfsetcolor{\tikz@pattern@color}
  \pgfsetlinewidth{0.3pt}
  \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
  \pgfpathlineto{\pgfqpoint{0pt}{3.1pt}}
  \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
  \pgfpathlineto{\pgfqpoint{3.1pt}{0pt}}
  \pgfusepath{stroke}
}
\makeatother

\newdimen\GridSize
\tikzset{
    GridSize/.code={\GridSize=#1},
    GridSize=3pt
}

\begin{document}
\begin{tikzpicture}[grid/.style={pattern=MyGrid}]
   \draw [GridSize=1pt, pattern=MyGrid] (0,0) rectangle (1.4,1.4);
\end{tikzpicture}
\end{document}