On Thu, Mar 15, 2012 at 3:15 PM, Jim Muth <jimmuth@earthlink.net> wrote:

Beyond this, and beyond resolution, lies an area of 2
elements, and then . . . who knows. Does the series continue 1,
1/2, 1/4...? The answer lies well beyond the range of
resolution, but I assume the series comes to an end at 1, with a
minimum of around 40 iterations.

I looked to see what was at the center of symmetry and it did eventually end in a circular area with a bump on one side at a magnification of 3e21. The lowest iteration I saw was 17.