User talk:Wolfgangbeyer
From Wikipedia, the free encyclopedia
[edit] Featured Picture
 |
|
Congratulations, and thanks for making it for us. Raven4x4x 07:43, 13 December 2006 (UTC)
Herr Beyer,
Just to let you know that the Featured Picture Image:Mandel zoom 00 mandelbrot set.jpg is due to make an appearance as Picture of the Day on April 4, 2007. If you get a chance, you can check and improve the caption at Template:POTD/2007-04-04. howcheng {chat} 01:39, 5 March 2007 (UTC)
[edit] Mandelbrot set
Hi Wolfang,
I think that, with really large steps, two steps could be enough to show the satellite in the center. I am thinking of a first step with horizontal diameter about 7.2e-13, and a second at about 2.7e-14. I'm not sure, I leave the decision to you.
Your question about the pseudo julia sets is difficult. I think the difference in part quantitative and in part qualitative. If, from step 10, we zoom into a satellite that has the same relation to the first satellite as the first satellite to the main body (that would be a secondary satellite with your terminology, if I understand you right), then we don't get a pseudo julia. So the pseudo julia appears because the second satellite is in a kind of "secondary structure" relative to the first satellite. I have made a couple of experiments:
- A satellite with a "secondary structure" and a "tertiary structure", with different pseudo julias if we zoom in these two structures:
xmin = -0.72856308428204589843; xmax = -0.7285630838980126953; ymin = 0.22332070061377441409; ymax = 0.22332070099780761721;
- Two different pseudo julias around the same satellite:
xmin = -0.6958417956041970825; xmax = -0.69584178771900726315; ymin = 0.36807845039592987059; ymax = 0.36807845828111968993;
--Bernard 18:08, 22 December 2006 (UTC)
- Hi Bernard. Interesting experiments but difficult to interpret. I don’t know how to define "secondary structures" precisely: For instance the "seehorse tail" in the image of step 3 seems to be a primary structure on the first sight. But it can also be interpreted to be an appendix of the antenna of the largest satellite in this image, and this appendix does not occur at the antenna of the main body. So one can conclude that it's a secondary structure. Following this argument, the satellites at the "seahorse tail" should be the centers of pseudo Julia sets. I Think I can identify some of them close to the antenna of the satellite in step 3. They look like Jc with approximately c=-2.5. The pseudo Julia sets expected around the satellite in step 6 should correspond with something like c=-10. Julia set of this kind could be very difficult to recognize because they are very "airy". Are there any "primary structures" at all? Any part of the thin structures is connected to the main body by a path passing satellites. More questions than answers. Unfortunately I don’t know any literature, which discusses the structures of the mandelbrot set by any kind of classification as we do it in our discussion. But I have to admit that I did not searched very much ;-). --Wolfgangbeyer 22:49, 26 December 2006 (UTC)
