Parametric Curve(s)
$$$
\forall\alpha\in\{0,2\pi\}\quad\;
k_{a}\in \mathbb{R}\quad0.05\leqslant\;k_{a}\;\leqslant0.16$$$
$$$ \left \{ \begin{array}{r c l}
\theta(\alpha)& = &\alpha \\
r(\alpha)& = &k_{a}\times\left(\cos^2{(2.5\cdot\alpha)}-1.5\right)
\end{array}\right .$$$