Repeat the same TikZ graphic to fill the entire page

Question

What I'm trying to do

I am creating some handwriting drill sheets. In these sheets, the exact same pattern is repeated horizontally and vertically over the entire page. The following 3 images were created using Inkscape, each of them represent the content of a single page that I want to create using TikZ.

What I know

I just learned that I can define a pattern inside \newsavebox.

\documentclass{article}
\usepackage{tikz}
\newsavebox \mybox
\sbox \mybox {%
  \tikz{%
    \draw (0,0) circle (0.2);
    \draw (0,0) circle (0.4);
    \draw (0,0) circle (0.6);
    \draw (0,0) circle (0.8);
    \draw (0,0) circle (1);
  }%
}
\begin{document}
  \begin{tikzpicture}
    \node at (0, 0) {\usebox\mybox};
    \node at (2, 0) {\usebox\mybox};
  \end{tikzpicture}
\end{document}

I also know that I can use loops to repeat the same pattern so that it fills the entire page (without exceeding the page borders).

\documentclass{article}
\usepackage{parskip}
\usepackage[showframe]{geometry}
\usepackage{tikz}
\newsavebox \mybox
\sbox \mybox {%
  \tikz{%
    \draw (0,0) circle (0.2);
    \draw (0,0) circle (0.4);
    \draw (0,0) circle (0.6);
    \draw (0,0) circle (0.8);
    \draw (0,0) circle (1);
  }%
}
\begin{document}
  \begin{tikzpicture}
    \foreach \row in {2,4,...,18} {
      \foreach \column in {2,4,...,14} {
        \node at (\column, \row) {\usebox\mybox};
      }
    }
  \end{tikzpicture}
\end{document}

Sometimes the page dimension is changed using the geometry package. When that hapens, I need to manually update the number of iterations of the loop and see if the number of repetitions don't exceed the page border. I wish the loop automatically stopped when it reaches the right limit of the page or the bottom limit of the page.

I also know how to repeat something until the right limit of the page is reached by using \xleaders. (see this answer). I used that knowledge to repeat the tikz graphic (see minimal working example below). However, the problem is that multiple tikzpicture environment are used. I wished a single tikzpicture is used in order to reduce the complexity of the source code.

\documentclass{article}
\usepackage{parskip}
\usepackage[showframe]{geometry}
\usepackage{tikz}
\newsavebox \mybox
\sbox \mybox {%
  \tikz{%
    \draw (0,0) circle (0.2);
    \draw (0,0) circle (0.4);
    \draw (0,0) circle (0.6);
    \draw (0,0) circle (0.8);
    \draw (0,0) circle (1);
  }%
}
\newcommand\asteriskfill{\leavevmode\xleaders\hbox{%
  \begin{tikzpicture}
    \node at (0, 0) {\usebox\mybox};
  \end{tikzpicture}%
  }%
  \hfill\kern0pt}
\begin{document}
\asteriskfill
\end{document}

I don't know how to repeat a pattern until the bottom limit of the page is reached.

The question

How to repeat the exact same TikZ pattern to use the entire available space in the page without exceeding page limits?

I thought that a possible way to tackle this problem would be to define a pattern using \newsavebox and somehow define a macro that repeats the same box horizontally and vertically until the page limits are reached.

Answer 1

\documentclass{article}
\usepackage{parskip}
\usepackage[showframe]{geometry}
\usepackage{tikz}

\newsavebox{\mybox}
\newlength{\myboxwidth}
\newlength{\myboxheight}

\NewDocumentCommand{\fillPageWithContent}{m}{%
  \newpage
  \sbox\mybox{#1}%
  \setlength{\myboxwidth}{\wd\mybox}%
  \setlength{\myboxheight}{\dimexpr\ht\mybox+\dp\mybox}%
  \noindent
  \begin{tikzpicture}[x=\myboxwidth, y=\myboxheight]
    % "parse=true" \pgfmathparse's the upper bound in the loop
    \foreach[parse=true] \row in {1, ..., \textwidth/\myboxwidth} {%
      \foreach[parse=true] \column in {1, ..., \textheight/\myboxheight} {%
        \node at (\row, \column) {\usebox\mybox};
      }
    }
  \end{tikzpicture}
  \newpage
}

\begin{document}
\fillPageWithContent{%
  \tikz{%
    \draw (0,0) circle (0.2)
          (0,0) circle (0.4)
          (0,0) circle (0.6)
          (0,0) circle (0.8)
          (0,0) circle (1);
    % enlarge bounding box to make some separation
    \path (-1.05, -1.05) (1.05, 1.05);
  }%
}

\fillPageWithContent{%
  \tikz{
    \draw (0, 0) rectangle (2,3)
          (.2, .3) rectangle (1.8, 2.7)
          (.4, .6) rectangle (1.6, 2.4)
          (.6, .8) rectangle (1.4, 2.1);
    \path (-.1, -.1) (2.1, 3.1);
  }%
}

\fillPageWithContent{%
  \tikz{
    \draw (0, 0) rectangle (1,1);
    \draw[rotate=30] (0, 0) rectangle (1,1);
    \draw[rotate=60] (0, 0) rectangle (1,1);
    \draw[rotate=90] (0, 0) rectangle (1,1);
    \draw[rotate=120] (0, 0) rectangle (1,1);    
  }
}
\end{document}

To make the pattern centered within text area, both horizontally and vertically, I

• add inner sep=0pt to tikzpicture in \fillPageWithContent and
• use \path <coordinate>; to enlarge the tikzpicture from north and west, by the needed amount of shifting. This is tricker than classic \centering and \vfill way, but it works for any size of target rectangle to fill.

\documentclass{article}
\usepackage{parskip}
\usepackage[showframe]{geometry}
\usepackage{tikz}
\usetikzlibrary{calc}
\newsavebox{\mybox}
\newlength{\myboxwidth}
\newlength{\myboxheight}
\NewDocumentCommand{\fillPageWithContent}{m}{%
  \newpage
  \sbox\mybox{#1}%
  \setlength{\myboxwidth}{\wd\mybox}%
  \setlength{\myboxheight}{\dimexpr\ht\mybox+\dp\mybox}%
  \noindent
  \begin{tikzpicture}[x=\myboxwidth, y=\myboxheight, inner sep=0pt]
    % "parse=true" \pgfmathparse's the upper bound in the loop
    \foreach[parse=true] \row in {1, ..., \textwidth/\myboxwidth} {%
      \foreach[parse=true] \column in {1, ..., \textheight/\myboxheight} {%
        \node at (\row, \column) {\usebox\mybox};
      }
    }
    \path
      let \n{xshift} = {\textwidth-\myboxwidthint(\textwidth/\myboxwidth)},
          \n{yshift} = {\textheight-\myboxheightint(\textheight/\myboxheight))}
          % Only north and west sides of current bounding box are enlarged,
          % since if all four sides are enlarged, the resulting tikzpicture
          % might be slightly larger than the target rectangle due to rounding
          % errors. May fail in RTL scripts.
          % Also the "pt" following ".5" is important: it makes the x- and
          % y-coordinate with units, so the unit-vectors (which we altered with
          % "x=\myboxwidth, y=\myboxheight") won't be applied.
      in  ([shift={(-.5pt\n{xshift}, .5pt\n{yshift})}]
           current bounding box.north west);
  \end{tikzpicture}
  \newpage
}
\begin{document}
\fillPageWithContent{%
  \tikz{%
    \draw (0,0) circle (0.2)
          (0,0) circle (0.4)
          (0,0) circle (0.6)
          (0,0) circle (0.8)
          (0,0) circle (1);
    % enlarge bounding box to make some separation
    \path (-1.05, -1.05) (1.05, 1.05);
  }%
}
\fillPageWithContent{%
  \tikz{
    \draw (0, 0) rectangle (2,3)
          (.2, .3) rectangle (1.8, 2.7)
          (.4, .6) rectangle (1.6, 2.4)
          (.6, .8) rectangle (1.4, 2.1);
    \path (-.1, -.1) (2.1, 3.1);
  }%
}
\fillPageWithContent{%
  \tikz{
    \draw (0, 0) rectangle (1,1);
    \draw[rotate=30] (0, 0) rectangle (1,1);
    \draw[rotate=60] (0, 0) rectangle (1,1);
    \draw[rotate=90] (0, 0) rectangle (1,1);
    \draw[rotate=120] (0, 0) rectangle (1,1);
  }
}
\end{document}

Answer 2

Knuth designed TeX, perfectly for this. You can avoid all calculations by using both horizontal and vertical leaders.

\documentclass{article}
\usepackage{fontspec}
\usepackage{tikz}
\setmainfont{symbola}
\def\phone{☏}
\def\bullseye{\tikz\draw (0,0) circle (0.2)
          (0,0) circle (0.4)
          (0,0) circle (0.6)
          (0,0) circle (0.8)
          (0,0) circle (1);}
\begin{document}
\newbox\mybox
\setbox\mybox\vbox to .3\textheight{%
\null
\xleaders\hbox{\strut\Huge\kern.2em\bullseye\kern.2em}
\vfill
}
\usebox\mybox
\null\xleaders\hbox{\usebox\mybox}\hfill\null
\end{document}

As you can see from the code, by replacing the \bullseye with the \phone, it will also react to sizing commands such as \Huge or \large. I would recommend to change all coordinates to relative units. Adding also an \fbox to the leader, you get the image I have shown.

\def\bullseye{\tikz\draw (0,0) circle (0.2)
          (0,0) circle (0.4em)
          (0,0) circle (0.6em)
          (0,0) circle (0.8em)
          (0,0) circle (1em);}