Shape of the Figure-Eight Orbit for Alpha

Shape of the figure-eight orbit under the potential $\alpha^{-1}r^{\alpha}$ for $-2 \le \alpha \le +1$.
--A rough estimation--
Points for $\Delta t = T/120$ are shown for each $\alpha$. ($T$ is the period.)
The shape become ``smashed'' as $\alpha$ become large.


Size in X direction is fixed to 2.


Period is fixed to $T=1$.