Parametric Curve(s)

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