7 Fixed point iteration \(f(x)=x-x^3\) a sink at \(x=0\)

This shows fixed point iteration of \(f(x)=x-x^3\) with 2 seeds, one using \(x_0=0.6\) and one using \(x_0=-0.6\) in the first plot (top left corner plot).

It shows the fixed point interation is stable and converges to the limit \(x=0\) from both sides. Hence \(x=0\) is a sink.

Additional animations shown in the table below, are zoom versions of the same iterations that used the seed \(x=0.6\) in order to obtain better views.

Original version	zoom in more
Pause Play Restart Step forward Step back	Pause Play Restart Step forward Step back