Since more than ten years ago, I have wondered about
mysteries in the Cubic Mandelbrot set. I call these:
"the Great Cubic Mandelbrot Mystery", and "the Little
Cubic Mandelbrot Mystery". Now I have illustrated these
mysteries in my chaotic series. Go to:
http://klippan.seths.se/fractals/articles/index.html
and click "24) Mysteries in the Cubic Mandelbrot set".
The first one, "the Great Cubic Mandelbrot Mystery",
I have expressed thus:
"Now let's have a look at the upper Elephant Valley
(figures 7 - 9, Mystery Zoom 2b1-3) in order to see
were the secondary decorations join themini copy on
this side. In "Mystery Zoom 2b3" (figure 9) we see
that the secondary decorations do not join the Elephants
trunks. Neither they join in the top of any hierarchy
of "extra heads" as in the body side of the Seahorse
Valleys (both in the quadratic and cubic Mandelbrot
sets). In fact there are no extra heads in the Elephant
Valley. Instead, and hear is what I call "the Great Cubic
Mandelbrot Mystery", they join in completely undefined
spots...."
The articles: "25) Other Views of the "Great Cubic
Mandelbrot Mystery", and "26) Another zenbuddhistic
koan" are following up articles.
Anyone in this group who has any entlighed comment
of these mysteries, especially the first one, with
probably no solutions.
I have the feeling that both these mysteries may
have something to do with the fact that the Cubic
connectedness Locus", the full analogy to the
Mandelbrot set, is NOT what the great mathematician
calls "locally connected".
--------------------------
Regards,
Ingvar Kullberg
www.come.to/kullberg
|
