Talk:Mandelbrot set

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).

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)

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)

@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)

I think the original commenter has a point. Yes, you can't describe some concepts without certain terminology, but the emphasis should be firmly placed on making it as easy to understand as possible. I'm not convinced many lay readers would understand this at present and that's a problem that we should at least attempt to minimise. —Preceding unsigned comment added by 94.195.174.51 (talk) 22:08, 18 October 2010 (UTC)

General comments are all very well, but some specific suggestions would be better. For example, how exactly would you suggest the lead section of the article should be simplified ? Or the first paragraph ? Or the first sentence ? Gandalf61 (talk) 12:31, 19 October 2010 (UTC)

I tried to make some changes to the Formal Definition section, which have now been reverted. Some of the set theory notation looks very intimidating to the non-specialist although it actually is almost trivial. For example, the first statement $P_{c}:\mathbb {C} \to \mathbb {C}$ says only that $P_{c}$ is a function that transforms one complex number into another, something that most readers would surely find easier to understand if expressed in words. The following definition is more significant but still depends on the reader understanding the special use of the colon and the $\mapsto$ symbol. Neither uses the same formalism as the algebraic notation in the introduction. The polynomial notation $P_{c}(0)$ is different again. All of this is contrary to the basic principle of starting simple and then developing ideas in a consistent way. Friv (talk) 21:34, 17 December 2010 (UTC)

I made some simplifications to the second paragraph in the "For Programmers" section because it talked about the midpoint in a pixel as if it were something special and because it didn't use the notation that had been set up in the first paragraph. That first paragraph may need similar treatment due to its use of the term "critical point". I would have turned that phrase into a link but I'm not sure that it is the correct term. Cutelyaware (talk) 02:32, 7 March 2011 (UTC)

Came looking for a good introduction to the Mandelbrot Set for my blog readers. The article is still way over spec at the start, and unusable for me. I did some maths at university and I cannot understand anything after "Mandelbrot Set". The article needs to assume no mathematics in the open paragraphs - this is a general encyclopedia, not a reference for mathematicians. Nothing about set theory is "trivial" to me. Nor would it be to, say, a 12 year old school kid. The authors need to think about who Wikipedia is for. By all means bring in the technical stuff lower down, but as it stands the page may as well be in a foreign language - I can read all the connectors, but none of the nouns or verbs. 86.26.1.194 (talk) 07:08, 2 June 2011 (UTC)

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 include a working example in the article, 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)

Adding your own code to the article would be an example of original research, which is strongly discouraged in Wikipedia. Gandalf61 (talk) 21:17, 17 October 2010 (UTC)

However this is good tutorial material for the Wikibook on Fractals. Cuddlyable3 (talk) 07:54, 18 October 2010 (UTC)

Fine, but I think there's a lot of that already in wikipedia. For example in french one you can see a Logo program on bottom of http://fr.wikipedia.org/wiki/Courbe_de_Gosper so why it is ok on some pages and not ok on some others? Gc (talk) 09:41, 18 October 2010 (UTC)

Thx for your code. I have put it here. I think also about adding to wikibooks about fractals page/pages about computer graphic techniques, like drawing on the screen, direct creating image files. drawing in the memory. Your program would be good there. Regards --Adam majewski (talk) 14:34, 18 October 2010 (UTC)

added an informal definition, showing each step, while it lacks math tags it really helps i think. 2011/04/10 (YMD) For Mathamatics, Leave Science behind (talk) 21:32, 10 April 2011 (UTC)

@Gc: Adding your own code is not per se original research. Implementing a well-known algorithm (which is what I think you did) involves no more original research than writing an article about it. Rather less than that. Btw. I like the point you chose, or rather, the journey. Thanks a lot! --84.177.51.103 (talk) 19:00, 30 May 2011 (UTC)

"the Yoccoz parapuzzle"

The basic properties section says:

The dynamical formula for the uniformisation of the complement of the Mandelbrot set, arising from Douady and Hubbard's proof of the connectedness of $M$, gives rise to external rays of the Mandelbrot set. These rays can be used to study the Mandelbrot set in combinatorial terms and form the backbone of the Yoccoz parapuzzle.

The link is to the biographical article on Jean-Christophe Yoccoz, which is barely more than a stub and provides no information about "the Yoccoz parapuzzle". I'm adding a reference to The Mandelbrot set, theme and variations (Tan 2000), which deserves a link here anyway and which has more about it than I can understand (but the expression itself may be due to Tan rather than to Yoccoz). -- Thnidu (talk) 19:14, 27 November 2010 (UTC)

incorrect statement about point i

This (in the 3rd paragraph) is apparently incorrect.

"On the other hand, c = i (where i is defined as i² = −1) gives the sequence 0, i, (−1 + i), −i, (−1 + i), −i, ..., which is bounded and so i belongs to the Mandelbrot set." —Preceding unsigned comment added by 141.210.135.115 (talk) 12:53, 25 March 2011 (UTC)

Is it ? Let's see:

$z_{0}=0$

$z_{1}=z_{0}^{2}+i=0^{2}+i=i$

$z_{2}=z_{1}^{2}+i=i^{2}+i=-1+i$

$z_{3}=z_{2}^{2}+i=(-1+i)^{2}+i=(1-2i+i^{2})+i=1-2i-1+i=-i$

$z_{4}=z_{3}^{2}+i=(-i)^{2}+i=-1+i$

etc.

Looks fine to me. Gandalf61 (talk) 13:07, 25 March 2011 (UTC)

"If you have a complex data type in your programming language, you should use that instead."

That would most likely be less efficient than a purely-real algorithm, even with modern optimising compilers.

217.42.250.131 (talk) 22:27, 26 March 2011 (UTC)

Yes. I have changed "you should use that instead" to "using it can simplify your program". The subject of speed optimization does not belong in the introduction to the pseudocode. Cuddlyable3 (talk) 07:34, 12 April 2011 (UTC)