Re: Is H-fractal the generator of Mandelberot set?

You seem to have a very good grasp of these things.
It's truely rare...
Adam has sent me Linas' site.
So has Artur...
http://linas.org/art-gallery/farey/farey.html
Good paper that parallels my Weierstrass and Besicovtch -Ursell work
using names for stuuf I've never heard before:
http://linas.org/math/chap-takagi.pdf

The Farey set and phase locking on rational fractional angles is very important to learn.
There is a really good paper by Jeff Lagarias
on the the Farey tree:
A walk along the branches of the extended Farey tree by J.C. Lagarias, C. P. Tresser,
Ibm Journal of Research and Development,
volume 39, Number 3, May 1995
Another good paper that I have is:
Farey Tree and Distribution of Small denominators,
Doug Baney, Scott Beslin and Valerio de Angelis,Topology Procedings, volume 22,1977

What I have learned just lately is that there are higher enengy/ complosite rational functions,
that seem to be unstable even when phase locked.

Julia sets in the interior of the Mandelbrot set are of lower dimension near one ( Ruelle's formula).
Border Julias are the interesting ones.
External ( Fatou set?) Julias are dust like/ Cantor and below dimension one and decay the further away from the M set that you get.

I hope this helps you get further than the rest of us.
Akira Bergman wrote:

Thanks RB.
I was just trying to find that link.

This is kind of related to my question on the topology of the space inside Mandel, when it is considered to consist of a field of infinite Julias. I suppose your method is a way of stitching Julias to get Mandel.


Look here:
http://www.mathematica-users.org/webMathematica/wiki/wiki.jsp?pageName=User:Roger_Bagula
Akira Bergman wrote:




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