Parametric Curve(s)
$$$
\forall\alpha\in\{0,4\pi\}\quad\;
0.5\leqslant\;k_{a}\;\leqslant1.2\quad\;$$$
$$$ \left \{ \begin{array}{r c l}
\theta(\alpha)& = &\cos^5{(k_{a}\cdot\alpha)} \\
r(\alpha)& = &0.24\times\sin{\alpha}
\end{array}\right .$$$