Parametric Curve(s)
$$$
\forall\alpha\in\{0,10\pi\}\quad\;
0.5\leqslant\;k_{a}\;\leqslant3.3\quad\;$$$
$$$ \left \{ \begin{array}{r c l}
\theta(\alpha)& = &\alpha \\
r(\alpha)& = &0.25\times\cos{\left (k_{a}\cdot\cos{(2\cdot\alpha)}\times\sin{(k_{a}\cdot \sin{\alpha})}\right )}
\end{array}\right .$$$