An $\infty$-gon with points on a conic

Move the slider and the pink points.

If we take the construction of the previous animation and place the initial points on a conic, then all subsequent points will lie on three conics. Adjusting the parameters carefully can generate Poncelet $m$-gons and associated $(n_4)$-configurations.

You can move the initial points as well (the pink ones). Since the construction is numerically very sensitive the movement of your mouse will only be transfered with a tiny fraction to the position of the points.