Mandelbrot set in "cross-sections of magnetic field borders" ?

[kram1032]

Which two concepts of infinity are you talking about?

[stereoman]

Which two concepts of infinity are you talking about?

I think we can speak of "open" and closed ".
Correct me if I'm wrong, as is the M-set, can be penetrated to  unthinkable depths , and presumably, with more powerful computers, they can continue to penetrate more and more, ad infinitum, in fact that is what some are doing.
   But in my view, this kind of infinity is not very useful beyond finding more or less attractive frames that differ very little from each other by beautiful they are, I would almost say it's infinitely boring.
   That address has no interest for me, what I want is an approximation to the infinite complexity of the hypersolid, at least, to his behaviour, where all happens trough closed cicles wich support each other.

[kram1032]

Can you elaborate that? What, in your mind, is a hypersolid and how does it relate to any of this?
How does it involve an infinity of any kind, or especially one that can not be dealt with?

[stereoman]

Returning to the design of the gnomon, three circles enclosed within one another, that touch at one point.
 
  They are continuously rotated at different speeds.
   The point where they meet is where the changes occur.
   Suppose that there are certain events scheduled in each cycle, since the speeds are different, the combination of the three series of events will give different results continuously.
    Now, imagine another inner level wich introduces changes into the events series, or  in the various speeds, the direction of time can even change, etc. .
 Of course, this can follow with inner levels that introduce further variations.

 This is the kind of infinity I talk about, and the way the nature works,  the hypersolid is the whole thing, limited by the numbers of cycles and layers, these limits are fixed by the concept of the octave, wich must fulfill all the possibilities , as we see in the musical scale, or the tonal scale, or the color wheel.
 Note that I don´t claim any discovery, the color wheel is one of my daily tools, like the musical scale is the tool for a musician, these tools can´t be changed nor discussed, but one can enter its structure to understand whats going really.

  

[jdebord]

It seems thet recently some scientists have extended the concept of "magnetic fractals" to more general functions :



where m and n are integers (> 1) and a complex parameter.

See for instance :

Fei Yang, Jinsong Zeng, On the dynamics of a family of generated renormalization transformations, J. Math. Anal. Appl. 413 (2014) 361–377

[kram1032]

Link to the paper:
http://arxiv.org/pdf/1312.1617.pdf

[Pauldelbrot]

An old but still great site for information about fractals is
http://www.miqel.com/fractals_math_patterns/visual-math-mandelbrot-magic.html

There I found the following statement:

Also Mandelbrot curves have been discovered
in cross-sections of magnetic field borders,
implying there is a 3-D mandelbrot equivalent that is closely tied to electromagnetism and therefore a deep structural and fundamental
aspect of life, and physical space/time.
(note: I read this in "Turbulent Mirror" can anyone cite a reference for this?

Now THAT would be very cool, as it would mean that fractals are indeed all around and within us, as the earths/suns magnetic field are all around us. Or on tapes, loudspeakers, harddrives... everywhere the m-set?
I knew it's everywhere in nature - but this would add a whole new dimension, in my opinion.

I mailed Miquel if anyone was able to cite a reference for this, but haven't received an answer. This short statement is all I could find on the web.

Does anyone here know more about this?
Or does anyone have the book "Turbulent Mirror" and could cite/scan the part where it says so?

I really need to know this! 

I have had a copy of that for years, of course, and it doesn't. I skimmed the sections to do with magnetism or the Mandelbrot set, finding them with the index; then resorted to a Google Books search of Google's copy. Nothing. Looks like Miqel got a bit confused about where he read that. I know The Beauty of Fractals references fractals arising in the complex-valued version of the Yang-Lee magnetic phase transition mapping, and Mandelbrot fractals appear in the parameter space for this system. They've been commonly implemented in fractal software for a while now, appearing in Fractint as the magnet1 and magnet2 types for instance.

The discussion in The Beauty of Fractals is on pages 129-149.

[stereoman]

Just a footnote,
"formula" is a word wich means " small form", I didn´t knew it, and had real fun