Is there an easy way to number a hexagonal spiral?

Question

I created a hexagonal spiral, but ran into a problem while trying to number it. The spiral is created in 2 sections. I can manually number the whole thing, as I did below, but I haven't been able to find an easier method.

I read about a way to number a spiral, iterating through the rings, but it didn't seem to work very well with how TeX generates the shapes. Here is that method:

function cube_spiral(center, radius):
    var results = [center]
    for each 1 ≤ k ≤ radius:
        results = results + cube_ring(center, k)
    return results

My hexagonal grid is a variant of this grid.

What is should look like:

Code to generate the hexagonal spiral (with partial manual numbering):

\documentclass{standalone}
\usepackage{tikz}
\usepackage{ifthen} % if else statements
\usetikzlibrary{shapes} %allows hexagons

\begin{document}
\begin{tikzpicture} [hexa/.style= {shape=regular polygon, regular polygon sides=6, minimum size=1cm, draw, inner sep=0,     anchor=south, fill=darkgray!85!white, rotate=0},numbr/.style= {white},arro/.style= {draw,red,thick}]
\pgfmathsetmacro\radius{4}
\pgfmathsetmacro\diameter{\radius*2}
\pgfmathsetmacro\shortdiameter{\radius*2-1}
\pgfmathsetmacro\largeradius{\radius+1}
\pgfmathsetmacro\shortradius{\radius-1}

% base hexagon (created in 2 sections and rotated 90 degrees)
\begin{scope}[rotate=90]
\foreach \j in {0,...,\radius}{%
  \pgfmathsetmacro\end{\radius+\j} 
  \foreach \i in {0,...,\end}{%
    \node[hexa] (h\i;\j) at ({(\i-\j/2)*sin(60)},{\j*0.75}) {}; %{\i;\j};
  }
}

\foreach \j in {0,...,\shortradius}{%
  \pgfmathsetmacro\end{\shortdiameter-\j}
  \foreach \i in {0,...,\end}{%
    \node[hexa] (h\i;\j) at ({(\i+\j/2-\shortradius*0.5)*sin(60)},{\j*0.75+\radius*0.75+0.75}) {}; %{\i;\j};
  }
}

% color change(s)
\node[hexa, fill=blue!20!white] (h\radius;\radius) at ({(\radius-\radius/2)*sin(60)},{\radius*0.75}) {};

% manual numbering
\node (h4;4) at ({(4-4/2+0.5)*sin(60)},{4*0.75}) {0};

\node[numbr] (h4;3) at ({(4-3/2+0.5)*sin(60)},{3*0.75}) {1};
\node[numbr] (h3;3) at ({(3-3/2+0.5)*sin(60)},{3*0.75}) {2};
\node[numbr] (h3;4) at ({(3-4/2+0.5)*sin(60)},{4*0.75}) {3};
\node[numbr] (h3;0) at ({(3+0/2-\shortradius*0.5+0.5)*sin(60)},{0*0.75+\radius*0.75+0.75}) {4};
\node[numbr] (h4;0) at ({(4+0/2-\shortradius*0.5+0.5)*sin(60)},{0*0.75+\radius*0.75+0.75}) {5};
\node[numbr] (h5;4) at ({(5-4/2+0.5)*sin(60)},{4*0.75}) {6};

\node[numbr] (h5;3) at ({(5-3/2+0.5)*sin(60)},{3*0.75}) {7};
% ... etc ...

% special shape(s)
\pgfmathsetmacro\arrowlen{0.2}
\foreach \i in {4,...,7}{%
  \draw[arro, ->, to path={-- (\tikztotarget)}]
    ({(\i-4/2+0.5)*sin(60)+\arrowlen/2},{4*0.75-\arrowlen}) to ({(\i-3/2+0.5)*sin(60)-\arrowlen/2},{3*0.75+\arrowlen});
}

\end{scope}
\end{tikzpicture}
\end{document}

Answer 1

Here is one possible solution.

\documentclass[border=7pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric}
\tikzset{
  hexagone/.style={
    draw, thick,
    fill=blue!7,
    shape=regular polygon,
    regular polygon sides=6,
    outer sep=0, inner sep=0,
    minimum size=1cm,
    label={[red]center:#1}
  }
}
\begin{document}
  \begin{tikzpicture}
    \node[hexagone=0] at (0,0){};
    \foreach \r in {1,...,3}
      \foreach \t in {0,...,5}
        \foreach[evaluate={\l=int(\r*(\r-1)*3+\r*\t+\u)}] \u in {1,...,\r}
          \scoped[rotate=-\t*60]
            \node[hexagone=\l] at (0+.75*\u,{0.43301270189*(2*\r-\u)}){};
  \end{tikzpicture}
\end{document}

Note: I haven't checked what is the maximal possible number of "rings", but for 21, \foreach \r in {1,...,21}, it works :)