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This is an old revision of this page, as edited by Gc (talk | contribs) at 21:14, 17 October 2010 (→Example of working code?: new section). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

Mandelbrot Set and applications

Are there any instances of a 3-4 dimensional representation of the Mandelbrot Set actually appearing in reality, and if so, what are the implications of such a representation as regards to its 2-dimensional counterpart, described here? P.S. Should this question be included on the Mandelbulb or what-ever page as well? 71.108.11.25 (talk) 03:40, 26 February 2010 (UTC)[reply]

Actually, this question shouldn't even be here in the article's talk page (see Wikipedia:Talk page guidelines). In short, an article's talk page serves as a forum for discussions about the content or format of the article, not for discussions about the subject of the article. Questions like these belong on one of our reference desks. This one in particular should of course go to the mathematics instance. Good luck! - DVdm (talk) 08:24, 26 February 2010 (UTC)[reply]
Oh, thanks! 71.108.11.25 (talk) 08:45, 26 February 2010 (UTC)[reply]
That reminds me... There is an unusually high amount of images on this particular article, and while they are very intriguing and beautiful 'iterations', they are not completely necessary in understanding the depth of the content, which is why I suggest removing them and instead adding a link next to the headlines instead to get the general idea. I recently commented about how Wikipedia should not include this in its articles. 71.108.11.25 (talk) 09:01, 26 February 2010 (UTC)[reply]
I agree that this particular page is a bit of a mess. So you could propose a list of images for deletion and see if you find wp:consensus for this kind of cleanup. Be prepared to face some opposition. Good luck. - DVdm (talk) 09:09, 26 February 2010 (UTC)[reply]

Images Nominated for Deletion

Here are a few images that I have proposed for deletion, self-explanatory. Anyway, please feel free to add or remove suggestions to the list until the deletion has been enacted. (The first one clearly does not belong on this article.)

  • Buddhabrot Method. Underneath the Computer Drawings headline.
  • Attracting cycle in 2/5 bulb animation. Underneath the Other properties: The main cardioid and period bulbs headline. There are already enough pictures to its right.
  1. I think this one has some merit as it shows a repeating cycle, which is not illustrated well by other images. The Julia sets which are closely related could do with some explanation.--Salix (talk): 09:07, 5 March 2010 (UTC)[reply]
When you say "nominated for deletion", do you just mean that you are proposing to remove these pictures from the article (as opposed to permanent deletion of the image files themselves) ? Gandalf61 (talk) 09:36, 27 February 2010 (UTC)[reply]
Oh, yes, of course. :| TelCoNaSpVe :| (talk) 08:34, 28 February 2010 (UTC)[reply]
User(s) 71.108.11.25 or 71.118.39.219 you (both?) suggest removing many images. Please if possible get an account with a name and sign your posts because that helps us follow who is saying what.
In general I don't think the proposed images should be deleted without a coresponding restructure of text. Images and text are supposed to complement each other. I advise cautiously reviewing case-by-case each image with all the associated text before deleting either. The test is whether a change is a nett improvement for a reader. The article title Mandelbrot set (not Mandelbrot fractal) uses terminology "set" that belongs to mathematics, which should be the tone of the article.
I agree that one of the zoom animations can go. Keep the deeper one. Cuddlyable3 (talk) 17:31, 2 March 2010 (UTC)[reply]
I find that while the pictures do correlate somewhat with the text, that the entire article does not have to be inundated with a repetition of two or more images. Furthermore, I find that other articles which do not have the same amount of images but still contain useful and informative content have the same impact and necessary information a reader needs to know about. So I believe this article needs not rely on an amazing array of images to convey its message to the reader; in fact, if you want to keep the pictures, you could probably provide some sort of link down at the bottom of the page, in some other section (e.g. the 12+ images in the zoom gallery seem entirely useless in light of the zoom animations down below). Wikipedia is not an artistic essay used in conjunction with images to provide some sort of artistic neatness; it is an encyclopedia, and must be treated as such. As stated above, feel free to add or remove suggestions. You could even delete the images right now, read the article again to see if it does not work, and then revert the edit.
And yes I have signed up for an account. This is my current username, right here, without the changing IP addresses: :| TelCoNaSpVe :| (talk) 01:39, 5 March 2010 (UTC)[reply]
Say, why don't we set up some sort of deadline for this kind of thing? Say, how about, April 5-9, since that is a convenient time to review this article again. :| TelCoNaSpVe :| (talk) 01:43, 5 March 2010 (UTC)[reply]

I began deletion of the proposed images on this day 00:09, 19 March 2010 (UTC)
If anyone has any objections to the deletions, they are free to re-submit the pictures. :| TelCoNaSpVe :| (talk)

TeleComNasSprVen thank you for signing up for an account and welcome to Wikipedia. TeleComNasSprVen you must stop what you are doing. It is clear that you 1) think images should be removed from the article, 2) you have started to delete images and 3) you are deleting images with no corresponding attention to text and with no more care for consensus than saying in effect "Now I deleted it so fix it yourselves if you don't like that." Reactions to the above are 1) That's a fair opinion that can be discussed case-by-case. You must allow that discussion. It is arrogant and unilateral of you to postulate a review deadline (4 weeks) for major deletions from an article that has been 9 years in the making by many editors. ( 1) and 2) are your own statements. ) Your action 3) is most worrying and is how edit warring gets started. You declare the zoom gallery to be "entirely useless" and neglect the facts that there are 15 images each of which is tied to a supporting text about a prominent feature. It is impossible to attach that information to a zoom sequence. Your distaste for the artistic "neatness" of the mathematical set is not the fault of our article about its many noteworthy aspects. If you wish to rail against Wikipedia content about Fractal art see that mentioned article. Cuddlyable3 (talk) 16:02, 31 March 2010 (UTC)[reply]
Okay. "Now I deleted it so fix it yourselves if you don't like that." I'm allowing that to happen because if I delete an image someone posted I may not know how to retrieve it back again if they wished it included. You can explain to me what is wrong with that policy. I believe I had allowed enough time for consensus and discussion, but I could be wrong. I haven't deleted anything Salix challenged, now, have I? I'll concede that I was wrong in posting a deadline; not very Wikipedian of me. But I don't think I am that arrogant; that's an issue for another time. I do not particularly support the 15 images and their content, and if I wanted to I could probably delete the entire section with the accomodating texts: (Step 1..., Step 2..., etc.) But as they are featured images on a featured Wikipedian article, I would leave it alone for article's sake. Nine years in the making by many contributors: I admit I do appreciate the effort being put into the article, and I try to make more perfect whatever endeavor someone has in an article in my own way; but I'm not a deletionist, yet. And please do not mention that in the discussions; I believe that it is a very good article by itself already. I did not know that edit warring can get started in that way, and I am glad that if my actions were to lead into that, that it hasn't happened yet and if so, that it was stopped before it did. And my comment was about the artistic quality of the article itself, not necessarily about the mathematical set. :| TelCoNaSpVe :| (talk) 04:37, 14 April 2010 (UTC)[reply]

I thank User:DVdm, User:Salix alba, User:Gandalf61, and User:Cuddlyable3 for all their help and support. :| TelCoNaSpVe :| (talk) 04:44, 14 April 2010 (UTC)[reply]

In response to your striking of text I have struck out my sentence about "arrogant".Cuddlyable3 (talk) 16:54, 14 April 2010 (UTC)[reply]

Is there a thing like a Mandelbrot set ?

Benoit B. Mandelbrot constructed his sets M in this way: for a family of iterations and two critical points and for (see Julia set), M is the set of points c such that the two sequences of iteration starting in the critical points, do not have the same terminus. The very first set he constructed was for the family and two critical points that were opposite real numbers, and the iterations were towards finite cycles. The picture was "blotchy", but "It sufficed to show that the topic was worth persuing, but had better be persued in an easier context". He ended up with the family having the two critical points 0 and ∞, and iterations towards ∞ outside M.

I say this, because I have had a controversy with Cuddlyable3, who has deleted a remark of mine in the article Multibrot set (now to be found on Talk:Multibrot set) on the grounds that "The term Mandelbrot set must be reserved for set(s) actually introduced by Benoit Mandelbrot. It is incorrect to call other iterated sets "mandelbrot sets" without reputable sources". If you are of the same oppinion as Cuddlyable3, you should contribute to corrections in Wikipedia articles. I have seen several places where "Mandelbrot set" is used for "generalized Mandelbrot set", but I would prefer that the latter term is reserved for a construction that differs from Mandelbrots idea. (Gertbuschmann (talk) 12:33, 28 April 2010 (UTC))[reply]

Only the set that Mandelbrot ended up with: has attained such notability that it now bears his name and its own Wikipedia article. Benoit Mandelbrot is also known for coining the word "fractal". Do we have consensus on the following naming?
  • Maps of many iterated polynomials of a complex variable show fractal characteristics. We do not claim that Benoit Mandelbrot was ever unaware of any of them but it is incorrect to call them all Mandelbrot sets. I agree with Gertbuschmann that some corrections to articles are needed to redact unsourced mentions of Mandelbrot. I see a difference between "a generalization of the Mandelbrot set" and "generalized Mandelbrot set".
  • Reappearances of the characteristic cardioid-plus-circles shape in magnified images present a naming problem. In the section "Image gallery of a zoom sequence" they are consistently called satellites. I have seen them called mandelbrots or mini-mandelbrots; a capital M seems inappropriate here. IMHO our encyclopedia should not lead a rush to turn a living person into a noun, or to paraphrase Winston Churchill (unsourced): [Some] have spoken of [him] in terms that a fellow ought not expect to hear until after he is dead". Cuddlyable3 (talk) 11:57, 1 May 2010 (UTC)[reply]

High resolution image

Please provide high resolution image of Mandelbrot set, so I can see all the details. 188.123.243.103 (talk) 08:28, 2 May 2010 (UTC)[reply]

You can never see all the details of the Mandelbrot set, because it is a fractal. The section of the article headed "Image gallery of a zoom sequence" shows a sequence of increasingly magnified images of one part of the Mandelbrot set's border - the final magnification is about 10,000,000,000 to 1. Gandalf61 (talk) 08:52, 2 May 2010 (UTC)[reply]
You might enjoy making your own program using the pseudocode in the "For programmers" section that will let you enlarge for viewing any of the details of the set. I remember my delight when I first wrote a few lines of BASIC that made the beautiful Mandelbrot fractal appear on my PC screen. Cuddlyable3 (talk) 13:18, 2 May 2010 (UTC)[reply]

3d Mandelbulb

I notice the 3D Mandelbulb section got moved to a separate article.[1] (Note, the section was originally added by me a few months ago, and I changed an article someone had created at that time into a redirect to the section). IMO splitting the section to a separate article was not really necessary, so my inclination would be to move it back. The separate article makes the most sense if quite a bit more external sourcing has appeared since the section was written (which is possible) and expansion is planned based on the new sources. Even with a separate Mandelbulb article, I think it's still worth having a summary-style description in the main article, rather than just a "see also" cross-reference. 69.228.170.24 (talk) 19:56, 27 May 2010 (UTC)[reply]

Deep Magnification

Any way we can get http://vimeo.com/12185093 into the article? Particularly noteworthy and definitely interesting. 68.38.100.91 (talk) 06:36, 15 August 2010 (UTC) Here is better animation fractal 2 throught not for an article. Edo 555 (talk) —Preceding undated comment added 13:46, 11 September 2010 (UTC).[reply]

Needs re-writing for the non-mathematician

The authors of this page are so clever and brainy and it's nice that they've been able to show off by writing in a language only comprehensible to other mathematicians - but this page is probably now (the day that Benoit Mandelbrot sadly passed away) being visited by non-mathematicians who would like to find out more about the great man's work. They wil learn precisely nothing from this page, since it assumes a colossal amount of mathematical knowledge and mastery of advanced mathematical terminology. What a shame. 90.207.65.50 (talk) 09:20, 17 October 2010 (UTC)[reply]

Can you be more precise ? Start with the first section of the article - the "lead". Where exactly does this assume "a colossal amount of mathematical knowledge and mastery of advanced mathematical terminology" ? Granted it assumes that the reader knows what complex numbers and the complex plane are - but without assuming this much knowledge, you can't say much more than "The Mandelbrot set is a pretty shape". Gandalf61 (talk) 09:42, 17 October 2010 (UTC)[reply]
@90.207.65.50, Wikipedia has fine articles about the great man Benoit Mandelbrot and about the Fractal. I think that an average reader would find both those articles accessible. However the title of this article "Mandelbrot Set" should have tipped you off at the beginning that it is about a mathematical concept. If you want to see this described with a minimum of math jargon, see this and this at Simple Wikipedia. Cuddlyable3 (talk) 13:20, 17 October 2010 (UTC)[reply]

Example of working code?

In my opinion, what makes the Mandelbrot set so particular and fascinating for programmers, is how easy it is to write a program that will exhibit so beautiful color shapes. In light of this, how would it be to post a working example, like the following? The algorithm here is naive and sub-optimized, but it's easily understandable and pretty powerful for easily experimenting at home... 

  #include <SDL.h>
  	
  #define DIM 400.0
  	
  int main() {
       SDL_Surface *screen = SDL_SetVideoMode(DIM, DIM, 0, 0);
       SDL_Surface *surface = SDL_CreateRGBSurface(SDL_SWSURFACE, DIM, DIM, 24, 0xFF, 0xFF00, 0xFF0000, 0);
  		
       double fact = 2;
       double cx = -0.74364500005891;
       double cy = 0.13182700000109;
  		
       while (fact > 1e-18) {
            double xa = cx - fact;
            double ya = cy - fact;
            int y;
  			
            for (y = 0; y < DIM; y++) {
                 Uint8 *pixline = surface->pixels + y*surface->pitch;
                 double y0 = ya + y/DIM*2*fact;
                 int x;
                 for (x = 0; x < DIM; x++) {
                      double x0 = xa + x/DIM*2*fact;
                      double xn = 0, yn = 0, tmpxn;
                      int i;
                      for (i = 0; i<512; i++) {
                           tmpxn = xn*xn - yn*yn + x0;
                           yn = 2*xn*yn + y0;
                           xn = tmpxn;
                           if (xn*xn + yn*yn > 4)
                                break;  // approximate infinity
                      }
                      if (i == 512) {
                           // in Mandelbrot set
                           pixline[x*3] = pixline[x*3+1] = pixline[x*3+2] = 0;
                      } else {
                           // not in Mandelbrot set; use escape iteration value to set color (grades of blue then white)
                           pixline[x*3] = pixline[x*3+1] = i < 256 ? 0 : i - 256;
                           pixline[x*3+2] = i < 256 ? i : 255;
                      }
                 }
            }
  			
            SDL_BlitSurface(surface, NULL, screen, NULL);
            SDL_Flip(screen);
            fact /= 2;
       }
  		
       SDL_Quit();
       return(0);
  }

That is easily compiled and run under Linux with "gcc `sdl-config --cflags --libs` -O3 mandelbrot.c && ./a.out" (and probably as easy under Windows, if someone wishes to tell how).

Gc (talk) 21:14, 17 October 2010 (UTC)[reply]

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