While the computational part of problem 6.4 in the Quadratic Family section is easy enough, I am not sure why the results relate to the features of the graph.

Take part a which states ''Show that the origin is an attractive (or super-attractive) fixed point of $g_\lambda$ whenever $|\lambda|<1$. This observation yields what prominent feature in figure 6.7?''

My computation is as follows

$$g_\lambda(z)=z^2+\lambda z\Rightarrow g_\lambda'(z)=2z+\lambda \Rightarrow g_\lambda'(0)=0+\lambda=\lambda.$$

So by deffinition, if $0<|\lambda|<1$ then the origin is an attractive fixed point.

However, I am not sure how this result relates to the graph. Is it simply the circle around the origin or is there more to it?

Thanks