Draw multiple polar graphs in different positions on a common coordination system - Tikz

Question

I am trying to plot several polar graphs in a tikzpicture. The idea is to plot the same function but for different parameters. An idea of what I am trying to achieve can be seen below

Although I am able to draw all these individual functions in one single polar plot, I don't know how to draw each if them separately in a common canvas.

So, at the moment I am able to produce the following

using the code seen below

\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots}
\usepgfplotslibrary{polar}

\begin{document}
\begin{tikzpicture}
    \begin{polaraxis}
    \foreach \atwo in {0, 0.4, ..., 2.4}
        \foreach \afour in {-0.6, -0.4, ...,1.8}
            \addplot+[mark=none,domain=0:720,samples=200] 
                {1 + \atwo*(3*cos(x)^2-1)/2 - \afour*(35*cos(x)^4-30*cos(x)^2+3)/8};
    \end{polaraxis}
\end{tikzpicture}
\end{document}

The goal is therefore to draw a set of axes (a2 , a4) and in each node the corresponding polar plot without the polar axes.

Any idea on how to achieve this?

Answer 1

You could move the loops outside the polaraxis environment, and use the at parameter for the axis to move the axes around. The outer axis and ticklabels has to be done manually though. For example:

\documentclass{article}
\usepackage{pgfplots}
\usepgfplotslibrary{polar}
\usetikzlibrary{fit}
\begin{document}
\begin{tikzpicture}
 \foreach[count=\i] \atwo in {0, 0.4, ..., 2.4} {
    \node [below] at (\i,0) {\pgfmathprintnumber[fixed,precision=1]{\atwo}};
    \foreach [count=\j] \afour in {-0.6, -0.4, ...,1.8} {
       \ifnum\i=1
        \node [left] at (0,\j) {\pgfmathprintnumber[fixed,precision=1]{\afour}};
        \fi
        \begin{polaraxis}[
           at={(\i*1cm,\j*1cm)},
           hide axis,
           scale only axis,
           width=1cm,
           name=ax-\i-\j,
           anchor=center
          ]
            \addplot+[mark=none,domain=0:720,samples=200] 
                {1 + \atwo*(3*cos(x)^2-1)/2 - \afour*(35*cos(x)^4-30*cos(x)^2+3)/8};
       \end{polaraxis}
    }}
    \node [draw,fit=(ax-1-1)(ax-7-12)] (ax) {};
    \node [left=1.2cm] at (ax.west) {$\alpha_4$};
    \node [below=1cm] at (ax.south) {$\alpha_2$};
\end{tikzpicture}
\end{document}