I have never really understood what causes these ghostly high- iteration remnants of the unperturbed M-set to remain in the background of the perturbed sets. I have read explanations explaining that the foreground in images like today's is complex material, while the background is real material, but this doesn't really make sense. My own guess is that regardless of where the iterated points start their travels, if they don't escape first, they will eventually settle into the same orbits as the points that start at 0,0.
That's exactly what happens. There's only the two critical points, infinity and 0, and infinity is always superattracting. Under the Sullivan theorem there can only be one other attractor at most, and it then has to capture 0. So the non-escaping points, if they exist, go to a finite attractor and then 0 goes to that attractor too.Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com