Answer 2C


The Mandelbrot Set Explorer


Answer 2C:

The orbits of E and H apparently wander around the boundary of the filled Julia set without tending to infinity or to the 2-cycle. The orbits of F and G are fixed points that seem to lie in the boundary. Therefore these seeds seem to be in the Julia set. Of course, with the limited resolution shown, it is impossible to determine whether these seeds actually lie on the boundary or are merely very, very close to it.

It appears that orbits that lie in the Julia set of x2 - 1 have the property that they remain forever on the boundary. This in fact is true: the boundary of the filled Julia set is "invariant" in the sense that any seed in this boundary has orbit that stays there forever.