Talk:Mandelbrot set

Continuous coloring

The "equations" in the subsection Mandelbrot Set#Continuous (smooth) coloring are actually not equations since there are no equals signs! Thus, it is not clear which quantity should be equal to the expressions shown there.--SiriusB (talk) 08:24, 26 August 2008 (UTC)

You are right - they are formulae, not equations. I have fixed the text. The formulae associate a real number with each point z in the complex plane outside of the Mandelbrot set. This real number can then be linked to a colour gradient in order to colour the pixels in an image. The algorithm does not seem to be prescriptive about exactly how a colour is derived from a real number value. Presumably the algorithm just ensures that points close to one another have similar real number values, so that colour varies "smoothly", avoiding artificial "contours" where one colour changes abruptly to another. Gandalf61 (talk) 10:30, 26 August 2008 (UTC)

I've taken a closer look on these formulas and I am more convinced than before that they are incomplete. What's missing is an detailed and unambiguous description which values have to be inserted. The most important issue is that the formulas are obviously discontinuous since they invoke the non-smooth n values. The fraction without the n is related to the absolute value, |z|, it is radial symmetric, i.e. yields equal values for equal distances from (0,0). The addition of the iteration number adds a discontinuous component that will far from being smooth, e.g. there may be z1 and z2 with |z1|=|z2| but n1!=n2. Unless one manages to get non-integer n these formulas appear to be useless in the posted forms. However, if one already has non-integer ("smooth") values for n there would be no need for an additional formula (but for another clever algoritm that gives us smooth iteration numbers).--SiriusB (talk) 13:43, 4 November 2008 (UTC)

After taking an even closer look on them and their source, I have found (and now fixed) the error. z should be replaced with z_n, i.e. not the starting point of z but its final value. Therefore both parts of each formula are no longer independent. However, it remains to show that the resulting real-valued function of z is really continuous.--SiriusB (talk) 14:13, 4 November 2008 (UTC)

Finally, I've added a symbol $\nu$ for the smoothed value to turn the naked formulas into proper equations. Someone might feel that this edit might be original "research", but at least it is what the author of the cited source seems to expect from the reader.--SiriusB (talk) 14:21, 4 November 2008 (UTC)

In addition: I have tested the algorithm in a self-written Mandelbrot program. As expected, the smoothing function is not continuous. However, the jumps that occur at the classical color borders become small if, as suggested in the article, several extra iterations are done, so that the result looks smooth. However, I do not know whether the article may benefit from this since this would clearly qualify as original research, I think.--SiriusB (talk) 08:29, 8 November 2008 (UTC)

SiriusB please explain what you meant by maganes which is not an english word. Cuddlyable3 (talk) 12:54, 8 November 2008 (UTC)

It seems likely that maganes is a simple typo for manages - Unless one maganes manages to get non-integer... 216.241.205.81 (talk) 19:23, 20 December 2008 (UTC)

Oops, sorry, I missed that. Yes, its just a typo. Although it might disrupt the continuity of this thread, I've fixed it now ;-)--SiriusB (talk) 10:00, 23 December 2008 (UTC)

Animation

Hi. I’m not an expert in Mandelbrot sets, but I’m not bad at making rather compact animations and had a Mandelbrot movie-making application sitting around on my hard drive. I added an animation here in the article. As you can see, it is a rather clumsy physical placement as it disrupts the page layout somewhat. Perhaps someone can find a better location. This 196-frame, 15.33-second animation has a variable frame rate. The main portion of the active zoom runs at 16.6 frames per second. The view zooms in 1.5⁴⁰ fold, or 11,057,332:1. I managed to squeeze the thing into a 1.2 MB file and retain rather high quality color. Also, to help prevent that persistent-motion visual effect and motion sickness, I added some some fixed-frame bookends, 750 ms at the start and 2000 ms at the end, and also added a 1000 ms black loop leader. Greg L (talk) 16:59, 4 November 2008 (UTC)

• I supposed I’ve got the page layout done well enough now. Greg L (talk) 04:12, 5 November 2008 (UTC)

Greg that is a nice compact animation you have made. It shows qualitatively much the same features as the preceding section Image gallery of a zoom sequence shows more quantatively i.e. giving some explanation of key features. I think it would be better not to have so much overlapping information. The example given of what "11 million fold" means in terms of life size (?) and a carbon atom is an unnecessary attempt to be impressive; the zoom-ability of Mandelbrot set details is actually infinite, as far as anyone knows. Cuddlyable3 (talk) 13:35, 6 November 2008 (UTC)

• To your last point first “…Mandelbrot set details is actually infinite”: Yes, that’s why the associated text begins with “Regardless of the extent to which one zooms in on a Mandelbrot set, there is always additional detail to see.” As for “unnecessary attempt to be impressive”, that the zoom actually is an eleven million factor truly is an impressive bit of information and it isn’t easy to intuit from watching the video that the zoom is actually that extensive. The analogy of drilling down to the realm of atoms helps drive home this point.

  I can hardly see that having the animation detracts whatsoever from the article with “overlapping information”; it’s not at all like adding another set of fixed image gallery images. The image gallery images above the animation are quite impressive in their own right because of their many more colors and the smooth transitions between them. The animation gives readers an entirely different “ah Haa” as to how the Mandelbrot set works and is organized. There is clearly room for both in the article. Greg L (talk) 03:52, 7 November 2008 (UTC)

The subject of the page is the M-set entity and not arbitrary specifics of a zoom. Greg please see WP:POINT as it relates to your wish to "drive home" information that is, as you rightly say, already stated. Cuddlyable3 (talk) 13:09, 8 November 2008 (UTC)

• Cuddlyable3: So you provided a link to WP:POINT (Wikipedia:Do not disrupt Wikipedia to illustrate a point) in a balled faced “If it’s blue, it must be true”-fashion. Thus, you characterized my contribution of an animation and its accompanying text as disruptive!?! If you’re going to post fallacious link-based accusations of improper conduct on my part, I strongly suggest you check out WP:OWN, WP:CIVILITY, and Wikipedia:Please do not bite the newcomers and consider what all three mean.

  As to your very first sentence, yes, the subject of the page is the entire M-set. More to the point, the subject of the section in question is clearly the animation. You are certainly welcome to revise the accompanying text to make it more appropriate and better suited for the greater context of the article if you feel the current text is somehow misleading or incorrect. This is, after all, a collaborative  writing environment. However, your accusation that mentioning the fact that it is an eleven-million-fold zoom is somehow an “unnecessary attempt to be impressive” makes me question your objectivity here.

  In the mean time, addressing your first post where you objected to the very existence of the animation itself (citing pure nonsense of “overlapping information”), please accept the obvious reality that the animation clearly improves the article. I ask that you not be so quick to act as the “Mayor of the Mandelbrot set”, where you undertake the role of censor who decides what contributions you will and will not permit here. Greg L (talk) 23:18, 8 November 2008 (UTC)

Greg L, please chill. Your overheated responses would be poor etiquette even if the accusations that you imagine had been made. They have not. Nobody has characterised your contribution of an animation as disruptive, that is something you have imagined. Nobody has said that its zoom range may not be stated, and that also is an "accusation" that you have imagined. Nobody has "objected to the very existence of the animation", and you misquoted me in that claim. Notwithstanding, there are WP policies that we must respect, or we get nowhere. Using ad hominem terms such as balled[sic] faced, Mayor of the M-set and censor is inappropriate. Seeing that you have made thousands of contributions to Wikipedia since you were welcomed you are far from a newcomer and could benefit from a well earned WP:WIKIBREAK. Cuddlyable3 (talk) 03:47, 9 November 2008 (UTC)

• I do not need to “chill” as you put it, and your suggestion that I should do so does not magically establish you as a calm, wise voice of reason here; particularly when it is you who is quite well deserving of my my calm rebuttals of your fallacious assertions. As to your first claim: “Nobody has characterised your contribution of an animation as disruptive”: nice try, but it was you who invited me to

…please see Wikipedia:Do not disrupt Wikipedia to illustrate a point as it relates to your wish to ‘drive home’ information that is, as you rightly say, already stated.

(13:09, 8 November 2008 post above). Is that or is that not your signature at the end of the above post wherein you more-than-suggest that my defense of the text accompanying the animation is somehow disruptive to Wikipedia? I won’t be baited with such tactics as stating that “WP policies that must be respected”; that was precisely my point with regard to your conduct. So please just pardon me all over the place for asking you to drop the baiting game and the associated patronizing act here; it won’t work (with me anyway) and Wikipedia’s history provides irrefutable proof of precisely what you wrote.

Now, since your arguments here are as elusive as the headless horseman, why don’t you just clearly and precisely explain exactly what you want, or just hold your peace please. Greg L (talk) 06:28, 9 November 2008 (UTC)

• Cuddlyable, the Mandelbrot set et al. is an enduring fascination for me, as a non-expert. I've read what you've written above, and find your arguments against Greg's animation most uncompelling. Greg, the animation is excellent, and adds significantly to the explanatory power of the article. Please retain it. Tony (talk) 09:34, 9 November 2008 (UTC)

Tony I agree with you that the latest animation should be retained. Indeed my arguments against Greg's animation are more than uncompelling, because no such argument exists. Let us keep this nice compact animation (my words emphasized) and turn to responsible editing of text around it.

Clearly there is repetition, i.e. overlapping information, while we have the two sections "Image gallery of a zoom sequence" and "Zoom animation". May we seek to integrate these?

I hope it will become clear to Greg that we have a difference of opinion about whether [edit] enriches the page or is unnecessary. Eleven million has no essential relevance to the M-set. It is obviously a big number. It is not Wikipedia's mission to "drive home" that fact, just because it is the arbitrary range of the animation.

Regrettably I find Greg's confrontational tone on this page disruptive to our editing work. I stand by the letter of what I have posted. I offer my apology for any unclarity found on my part, such as who has signed what. It is alright to say what we feel is impressive in discussion but that must be restrained by WP:NPOV in constructing the article. Cuddlyable3 (talk) 15:48, 9 November 2008 (UTC)

• Regrettably, I find your accusing me of being disruptive immediately after my 03:52, 7 November 2008 post as being beyond fallacious and a breathtaking display of gall and incivility. You can’t possibly expect any editor to assume good faith in another after making several shots across the bow as you chose to do here. Your motives for behaving as you’ve done here are baffling and what you are objecting to makes no sense. And please stop quoting Wikipedia policies while pretending to wisely counsel others about proper etiquette here and spout about how something I’ve done is “disruptive to [your] editing work”. Such posturing is truly laughable. You have much to learn about collaborative writing and dealing with others. I am absolutely done here wasting any further time with you as I find your conduct here exceedingly annoying and entirely unproductive. No one should have to put up with so much crap to just contribute to an article. If you have edits to make, go make them. I would suggest that you first sit back and watch how others on this pale blue dot react to the animation and accompanying text. Greg L (talk) 17:06, 9 November 2008 (UTC)

• Oh… and thanks for weighing in here Tony. Greg L (talk) 03:52, 10 November 2008 (UTC)

• I found the zoom animation a valuable addition to the article. I must admit the maths goes over my head, but the zoom was one of the parts that made things clearer to a non maths person like me. The static pics were usefull in that each shape was described, but I didnt really get what mandelbrots were about until I saw the animated zoom. I'd say keep it. Metafis (talk) 03:34, 25 November 2008 (UTC)

Here's an Flash application which lets you zoom in for your self: http://veclock.deviantart.com/art/Flash-Mandelbrot-set-106531519 —Preceding unsigned comment added by 85.224.88.254 (talk) 18:05, 2 January 2009 (UTC)

probable error in diagram

There appears to be something wrong in the second diagram, containing the Mandelbrot set relative to the axes in the complex plane. The imaginary axis has units 1 and -1, which are located outside the set, whereas i and -i should lie inside the set. Jorn74 (talk) 12:04, 11 January 2009 (UTC)

The points i and -i are right on the boundary of the Mandelbrot set - their Julia sets have an empty interior. They are joined to the main body of the Mandelbrot set by very thin filaments. These filaments show up in some of the images in the article where points are coloured according to escape time. In the first image, for example, you can see two filaments branching off from the top bulb, and i is at the end of the right-hand filament. However, these filaments are too thin to show up in the pure black-on-white image shown in the second diagram. Gandalf61 (talk) 13:27, 11 January 2009 (UTC)

Pseudocode error

There seems to be a problem with the pseudocode.

 while ( x*x + y*y <= (2*2)  AND  iteration < max_iteration ) 

Only the first couple pixels will succeed this comparison. At pixel (1,2) for example, the equation will be: (1)*(1) + (2)*(2) <= (2*2), which of course fails the comparison.

151.112.23.68 (talk) 19:21, 29 January 2009 (UTC)

x and y are not pixel counts, they are the horizontal and vertical coordinates of a pixel. The whole M. set is within the range -2<x<1 and -1<y<1 and only your chosen pixel resolution limits the number of pixels within the set. Cuddlyable3 (talk) 21:13, 29 January 2009 (UTC)

flash mandelbrot set (external)

i stumbled upon this page and i thought it as a good example. It has fantastic zoom but it requires a fast broadband connection.

• [1]

This is a very interesting subject, and if anyone has any more user friendly fractal animations, post them! —Preceding unsigned comment added by 68.209.202.24 (talk) 03:51, 14 February 2009 (UTC)

another external link

I've written another Mandelbrot viewer in Flash: [2] If anyone thinks it warrants inclusion, please add it to the main page. Jamo777 (talk) 17:16, 14 February 2009 (UTC)