Tikz Random Map with Countries

Question

I like math and I have a young cousin who struggles quite a lot with it. So I am trying to find different fun activities for her to show how interesting math can be.

During my Easter visit to her family, I showed her the Four Color Theorem (I gave her a random map to color in the way it says in the theorem) to show how it all works and bet her that she couldn't come up with one where you need more than 4 colors.

I am no longer visiting but am continuing to send her homework which I compile using LaTeX. I would like to revisit this fun activity but want to be able to draw random maps for her in TikZ, rather than find a picture online.

Something like this, and preferably where I can make several random ones. They don't have to be particularly pretty, just random.

Answer 1

Original attempt

Here's an attempt, which can probably be upscaled to whichever size you want:

\documentclass[tikz,border=2mm]{standalone}
\pgfmathsetseed{\pdfuniformdeviate 10000000} %Credit: https://tex.stackexchange.com/a/212755/117534
\begin{document}    
    \begin{tikzpicture}
    \foreach \i in {0,...,4}
    \foreach \j in {0,...,4}
    \coordinate[] (n-\i\j) at (\i + 0.5*rand,\j + 0.5*rand) {};
    \foreach \i in {0,...,4}
    \foreach \j [count=\jj] in {0,...,3}
    \draw (n-\i\j) -- (n-\i\jj) (n-\j\i) -- (n-\jj\i);
    \end{tikzpicture}
\end{document}

A few outputs:

With Curves

It's a little less controlled now with the curved edges, though. I've added the code:

\pgfmathparse{random(0,60)-30}
\draw (n-\i\j) to [bend right=\pgfmathresult] (n-\i\jj) (n-\j\i) to [bend right=\pgfmathresult] (n-\jj\i);
}

instead, which generates a number from -30 to 30. i.e. it will bend left if the result is negative, right if positive. The full code and example:

\documentclass[tikz,border=2mm]{standalone}
\pgfmathsetseed{\pdfuniformdeviate 10000000} %Credit: https://tex.stackexchange.com/a/212755/117534
\begin{document}    
    \begin{tikzpicture}
    \foreach \i in {0,...,4}
    \foreach \j in {0,...,4}
    \coordinate[] (n-\i\j) at (\i + 0.5*rand,\j + 0.5*rand) {};
    \foreach \i in {0,...,4}
    \foreach \j [count=\jj] in {0,...,3}{%
    \pgfmathparse{random(0,60)-30}
    \draw (n-\i\j) to [bend right=\pgfmathresult] (n-\i\jj) (n-\j\i) to [bend right=\pgfmathresult] (n-\jj\i);
}
    \end{tikzpicture}
\end{document}

Rectangular grids

I added in a few comments, and declared two commands for you to enter how many rows/columns you want. The key difference here from the code above is that I've split up the drawing of horizontal and vertical lines, to accommodate for rectangular grids.

\documentclass[tikz,border=2mm]{standalone}
\pgfmathsetseed{\pdfuniformdeviate 10000000} %Credit: https://tex.stackexchange.com/a/212755/117534
\begin{document}    
    \begin{tikzpicture}
    \pgfmathtruncatemacro{\rownum}{6} % Set number of rows here
    \pgfmathtruncatemacro{\colnum}{3} % Set number of columns here
    \pgfmathtruncatemacro{\rowtemp}{\rownum-1}
    \pgfmathtruncatemacro{\coltemp}{\colnum-1}
    % Place coordinates in a grid like fashion; randomized
    \foreach \i in {0,...,\rownum}
    \foreach \j in {0,...,\colnum}
    \coordinate[] (n-\i\j) at (\i + 0.45*rand,\j + 0.45*rand) {};
    % Draw vertical lines
    \foreach \i in {0,...,\rownum}
    \foreach \j [count=\jj] in {0,...,\coltemp}{%
    \pgfmathparse{random(0,60)-30}
    \draw (n-\i\j) to [bend right=\pgfmathresult] (n-\i\jj);
}    
    % Draw horizontal lines
    \foreach \i [count=\ii] in {0,...,\rowtemp}
    \foreach \j in {0,...,\colnum}{%
    \pgfmathparse{random(0,60)-30}
    \draw (n-\i\j) to [bend right=\pgfmathresult] (n-\ii\j);
    }
    \end{tikzpicture}
\end{document}

A little more 'randomness'

I think this is as far as I can push it with this approach. Here I use an \ifthenelse{}{}{} conditional to remove some of the horizontal lines to give it less of a grid look, and for it to look more organic. Note in the picture below how not all of the nodes are joined by lines.

You can easily modify the code below to remove some vertical lines instead of horizontal lines (not both!). Only thing is that there will be sharp points/corners at random areas, and I have no idea how to make them smooth.

\documentclass[tikz,border=2mm]{standalone}
\usepackage{ifthen}
\pgfmathsetseed{\pdfuniformdeviate 10000000} %Credit: https://tex.stackexchange.com/a/212755/117534
\begin{document}    
    \begin{tikzpicture}
    \pgfmathtruncatemacro{\rownum}{6} % Set number of rows here
    \pgfmathtruncatemacro{\colnum}{3} % Set number of columns here
    \pgfmathtruncatemacro{\rowtemp}{\rownum-1}
    \pgfmathtruncatemacro{\coltemp}{\colnum-1}
    % Place coordinates in a grid like fashion; randomized
    \foreach \i in {0,...,\rownum}
    \foreach \j in {0,...,\colnum}
    \coordinate[] (n-\i\j) at (\i + 0.45*rand,\j + 0.45*rand) {};
    % Draw vertical lines
    \foreach \i in {0,...,\rownum}
    \foreach \j [count=\jj] in {0,...,\coltemp}{%
    \pgfmathparse{random(0,60)-30}
    \draw (n-\i\j) to [bend right=\pgfmathresult] (n-\i\jj);
}    
    % Draw horizontal lines
    \foreach \i [count=\ii] in {0,...,\rowtemp}{%
    \foreach \j in {0,...,\colnum}{%
    \pgfmathtruncatemacro{\randnum}{random(0,60)-30}
    \ifthenelse{\isodd{\randnum/2} \OR \j=0 \OR \j=\colnum}{% <------------------ Ensure end horz lines are drawn
        \draw (n-\i\j) to [bend right=\randnum] (n-\ii\j)}{};
    }}
    \end{tikzpicture}
\end{document}