Parametric Curve(s)
$$$
\forall\alpha\in\{0,2\pi\}\quad\;
5\leqslant\;k_{a}\;\leqslant40\quad\;$$$
$$$ \left \{ \begin{array}{r c l}
\theta(\alpha)& = &0.2\times\sin{(k_{a}\cdot\alpha)} \\
r(\alpha)& = &0.48\times\cos{(2\cdot\alpha)}
\end{array}\right .$$$