Third grade spiral in TikZ - dimension too large

Question

I'm trying to draw a smooth third grade spiral (r^3 = a^3\cdot \varphi) over $60\times 60$mm grid and I'm getting the "Dimension too large"-error if I set $a > 320$ but I need to fill the grid area completely:

\begin{tikzpicture}[x=1mm, y=1mm]

    \draw[step=1, line width=0.1mm, opacity=0.3] (-30, -30) grid (30, 30);

    \draw [domain=0:50, variable=\t, samples=1000] 
        plot ({\t r}:{pow(320*\t, 1/3)});
\end{tikzpicture}

Is there any way to avoid this error?

Answer 1

A different math library helps. For example, library fixedpointarithmetic uses package fp for the fixed point calculations with a much larger number range.

\documentclass{article}
\usepackage{tikz}
\usepackage{fp}
\usetikzlibrary{fixedpointarithmetic}

\begin{document}
\begin{tikzpicture}[x=1mm, y=1mm]

    \draw[step=1, line width=0.1mm, opacity=0.3] (-30, -30) grid (30, 30);

    \draw [domain=0:50, variable=\t, samples=1000]
        plot[fixed point arithmetic] ({\t r}:{pow(600*\t, 1/3)});
\end{tikzpicture}
\end{document}

Answer 2

I would use pgfplots for this for increased math precision and more flexibility for other issues

I've deliberately drew a strange grid and axes lines to show some options other than what you have. And you can change the values to much bigger range.

\documentclass{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[grid=both,xmax=100,ymax=100,xmin=-100,ymin=-100,
axis equal,
xtick={-100,-80,...,100},
ytick={-100,-80,...,100},
minor x tick num=4,
xticklabels={},
yticklabels={}]
\addplot+[no marks,data cs=polar,domain=0:100, samples=1000] 
({deg(x)},{(320*deg(x))^(1/3)});
\end{axis}
\end{tikzpicture}
\end{document}

Answer 3

Mathematically, pow(600*\t,1/3) is equivalent to pow(600,1/3)*pow(\t,1/3)...

Just TikZ and its default math engine:

\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}[x=1mm, y=1mm]
  \draw[step=1, line width=0.1mm, opacity=0.3] (-30, -30) grid (30, 30);

  \draw [domain=0:50, variable=\t, samples=1000] 
  plot ({\t r}:{pow(600,1/3)*pow(\t,1/3)});
\end{tikzpicture}
\end{document}