Parametric Curve(s)
$$$
\forall\alpha\in\{0,2\pi\}\quad\;
0.015\leqslant\;k_{a}\;\leqslant0.34\quad\;$$$
$$$ \left \{ \begin{array}{r c l}
\theta(\alpha)& = &\alpha \\
r(\alpha)& = &k_{a}\times\sin{(\frac{\alpha}{3})}
\end{array}\right .$$$