Talk:Mandelbrot set/Archive 1

message: The opening paragraph is too wordy and too technical. Most Wikipedia articles are:
* Title
* Brief summary
* Table of contents
* Detail
I would have fixed it myself, but I can't think of any good way to summarize it briefly -- which I guess is why it's like this in the first place. Does anyone have any ideas? Ravenswood 16:18, August 3, 2005 (UTC)
:Agreed - I came here looking for a brief summary to copy and edit into the glossary of a paper I'm working on. Instead I'm going to have to mangle my own one. Hope someone picks up on this - I can't see a way to create a clear intro. 62.253.219.238 14:10, 7 December 2005 (UTC)
replies: text: I hope the new opening paragraph is more useful --- it is a more mathematical definition of the Mandelbrot set. Suggestions are welcome. --Lasserempe 17:58, 16 March 2006 (UTC)
replies: text: Having re-arranged the paragraphs in the introduction so the maths comes after some words in plain English, I think it's much better. --CharlesC 23:49, 17 June 2006 (UTC)
replies: text: Yeah, that's fine. It's better to explain what it is in english before diving into the math. Expecially with such an innocuous looking function that turns out to be this complex. No-one knew what it really looked like until about 1980 because it's not really decipherable by simply reading the formula. - Rainwarrior 05:07, 18 June 2006 (UTC)
replies: text: I made the black-and-white rendering of the Mandelbrot set because I looked all over the Web and couldn't find a rendering of the set which included the axes. I have a degree in math, so it bugs me when the mathematical nature of the subject is obscured to the point that people don't realize that the Mandelbrot set is a plain old subset of C, that points are either in or not in the set (laypersons confuse the infinite sequence with the set proper), that the set isn't "special" and in itself does not feature "pretty colors," and -- as one generally does with sets of points in C -- it is not unreasonable to render this set with axes.  I think it's misleading to have a colored picture labeled "Mandelbrot set" at the top of this article, because the Mandelbrot set is not colored -- it's a set, it has a membership operator that maps to the booleans, it's black and white.  However, I'll go along with the colored Mandelbrot image if people like it.  Moreover, the article is currently confusing, as it mashes together the formal mathematics of the Mandelbrot set with the hobbyist's perspective of the Mandelbrot set. I mean, read the introduction: "connectedness locus...family of complex quadratic polynomials...Julia set...connected...critical point...n-fold composition."  While off to the right is a picture from the hobbyist's perspective (labeled "Mandelbrot set," which is formally incorrect, as it's an image made from the "Mandelbrot sequence" and not the set).   I guess I don't really like the edit to the introduction section by User:Lasserempe  and I much prefer a succinct introduction which defines the set M from a sequence, such as .  The formal math stuff can be moved into a formal math section.  The advantage of the "sequence definition" is that it allows the person with only a high school math background to appreciate the beauty and simplicity of the Mandelbrot set's mathematics.  I can add an aside to explain to the reader with little math background that the "Mandelbrot set" itself is "black and white," and that the color is generated by looking at the beginnings of the infinite sequence which determines the "true" Mandelbrot set M.  What do you guys think? - Connelly 03:42, 3 August 2006 (UTC)
replies: text: While I would agree that the black and white image with axes is the best image for demonstrating the mathematical definition of the mandelbrot set, I think the current image is more suitable for this page. The reason I say this is that I think the page should proceed from "layperson" information at the start to "expert" information later on, so that a person who does not yet have the skills to interperet the mathematics of it does not have to sift through technical descriptions to get to the information they want to know. I think most people who come to this page probably want to know something about this pretty thing they've heard of or seen called the mandelbrot, and the best information to leave at the top is maybe a bit of its history, and a general description. (We should have the formula there too, but try to explain it in less technical terms.) After the top couple of paragraphs, we should be free to get mathematical, as it is a very mathematical topic, but we seriously need to tone down the jargon. e.g. We should mention that is is a connectedness locus somewhere, but definitely not in the lead. Put the simplest explanations first, and then introduce technical terms after. - Rainwarrior 04:26, 3 August 2006 (UTC)
replies: text: I agree with Rainwarrior. Also just to say I didn't mean to be rude or dimissive about the black and white image and am aware it is simple and correct and of course it belongs in the article. With the coloured image I was intending to 'draw' people into the subject, then when their interest is piqued they are more likely to get into the maths. -- CharlesC 14:49, 3 August 2006 (UTC)
thread_title:  Opening Paragraph 

message: AugPi, I have an issue with your June 12 edit. The following statement is false, as can be shown by the infinite number of "mini" Manelbrot sets attached to and surrounding the main set: The Mandelbrot set can be divided into an infinite set of black figures: the largest figure in the center is a cardioid. The rest of the figures are all circles which branch out from this central cardioid. Mackerm 05:49, 26 Aug 2004 (UTC)
replies: text: I have included a section on the main cardioid, and the hyperbolic components bifurcating diretly from it. --Lasserempe 17:54, 16 March 2006 (UTC)
thread_title:  Circles, cardioid 

message: Anyone to add a note about this in the article, (it is pretty large and a bit messy so I want try to do that. If I do, somebody (maybe you) WILL change it, I'm sure (because I'm Swedish and my writing in English is not perfect, somebody (maybe you) always change the addings I have done to the fractal articles here at en: ), better you write it from scratch =) // Solkoll 20:58, 8 Jun 2005 (UTC)
replies: text: Every quadratic polynomial is conformally equivalent to exactly one map of the form z^2+c; in particular this is true for polynomials of the form \lambda z(1-z). I may add a comment on this if I have time. --Lasserempe 17:57, 16 March 2006 (UTC)

text: In many of them you can find tiny "copy" mandelbrots, which have a definite thickness, but it is possible to find points that appear to be infinitely thin on the mandelbrot; for instance, the "neck" between the large cardioid and the circle to its left I believe is infinitely thin. So, I'm not sure that your question has an answer one way or the other; there are both infinitely thin points and finitely thin points. - Rainwarrior 23:59, 18 June 2006 (UTC)
thread_title:  Mandel and the bifurcation. 

message: Moved following paragraph from article page, as it consists mainly of questions. Gandalf61 09:30, August 12, 2005 (UTC)
:It is said that the Mandelbrot set is a cardioid, but it is not clear if this is just looks or if theer's some mathmatical definition. It is also unclear why Mandelbrot set is shaped the way it is. Also, it is not widespread a knowledge, perhaps due to its esteric nature and the flood of computing enthusiasts, about the significance of Mandelbrot set in mathematics.
* Why are captial Z and minor z in the formulas mixed?
:: For no good reason. I've changed it now.
* What, exactly, is meant by "infinite set"?
:: Infinite set is a set which is not finite. -- EJ 10:09, 15 August 2005 (UTC)
thread_title:  Questions 

message: One can wonder how long it would take a room full of monkeys with computers to reproduce the works of van Gogh.  He painted with a finite number of molecules of paint which have a finite number of permutations, while the set has an infinite range of coordinates, so they all may be in there somewhere.  Or are there mathematical limits on what a Mandelbrot picture can look like?David R. Ingham
My brother wrote a program to write poetry that had one accepted for publication.  When he admitted how he wrote the poem, the periodical changed its mind and rejected it.David R. Ingham 04:07, 1 December 2005 (UTC)
thread_title:  Scope and limitations of Mandelbrot art 

message: The article contains the sentence: "...the Mandelbrot set is connected, and even simply connected. It is conjectured but unproven to be path connected."
According to the simply connected space, a set is simply connected if it is path connected and all loops can be continuously shrunk to points.  Therefore, it seems absurd to say that the Mandelbrot set is simply connected but may or may not be path connected.  Is this a typo?  Or is there another definition of simple connectedness that does not include path connectedness?
Reedbeta 01:09, 12 December 2005 (UTC)
replies: text: See , . The Mandelbrot set is connected, and any loop can be deformed to a point. This is indeed a weaker definition of "simply connected" than what is given in the simply connected article. -- EJ 15:59, 12 December 2005 (UTC)
thread_title:  Simply connected / path connected? 

message: Except for "accelerator" short cuts, it is a point by point calculation, so it would be best done with parallel arithmetic units.  The the requirements for memory and connectivity are minimal.
David R. Ingham 04:43, 17 December 2005 (UTC)
thread_title:  Ideal computer 

message: (I also posted this question on the Talk:Benoît Mandelbrot page)
The formula as originally presented by BBM was z -> z2 - c but almost every single current reference uses z -> z2 + c. Anybody know when and why this was changed? Khim1 14:23, 17 January 2006 (UTC)
replies: text: Mandelbrot's contribution to The Beauty of Fractals (Peitgen and Richter; 1986) refers to "the quadratic map z -> z2 - c". In 1988 Michael Barnsley uses z -> z2 - λ in Fractals Everywhere. OTOH Peitgen and Richter's 1986 survey article Frontiers of Chaos, also published in The Beauty of Fractals, uses the map x -> x2 + c and includes illustrations of the Mandelbrot set in its "modern" orientation. I don't know why the second form became more popular. Gandalf61 11:55, 23 January 2006 (UTC)
replies: text:  I am not sure about the historic development, but certainly Douady and Hubbard, in the early 80's, defined the Mandelbrot set in its current form. In this parametrization, the parameter c agrees with the singular value of the map f_c\,, which is useful from a conceptual point of view. --LR 22:56, 17 March 2006 (UTC)
thread_title:  Change in formula 

message: An anon user User:86.129.85.127 replaced the pseudo code with this (as being more compact):
QBasic code for plotting a Mandelbrot set. 
SCREEN 12 
FOR sy% = 0 TO 479 
   FOR sx% = 0 TO 639 
      x = (sx% - 320) / 160: ox = x 
      y = (sy% - 240) / 160: oy = y 
      FOR c% = 15 TO 1 STEP -1 
         xx = x * x: yy = y * y 
         IF xx + yy >= 4 THEN EXIT FOR 
         y = x * y * 2 + oy 
         x = xx - yy + ox 
      NEXT 
      PSET (sx%, sy%), c% 
   NEXT 
NEXT
I've rolled it back, (and notified the anon) please discuss here. Rich   Farmbrough. 23:46, 21 February 2006 (UTC)
thread_title:  Pseudo code vs QBASIC 

message: That makes the mathematics much more intuitive.  I only wonder whether it is 5 or 6 cases.  David R. Ingham 05:18, 4 March 2006 (UTC)
thread_title:  illustration of sequences 

message: I can't see it, when viewing the Mandelbrot set page, on Safari or Netscape, on my Mac.  (I read that FireFox is more "politicly correct" but have not tried it yet.)
David R. Ingham 05:35, 4 March 2006 (UTC)
replies: text: I can't see it with Safari or Firefox, nor with IE on the PC. I suspect that this is because of the fact that the image is just an empty, transparent 325x235 frame. The file is only 477 bytes in size. Khim1 21:00, 4 March 2006 (UTC)
replies: text: I too first thought it was some temporary error or my browser, so I thought it would be better once my or wikipedias cache was reset. Ah well, I fixed it by changing the size of the thumbnail slightly so Wikipedia had to rerender it. --David Göthberg 23:39, 4 March 2006 (UTC)
thread_title:  Visibilty of Image:Mandelset hires.png 

message: I have removed the reference to the "Burning ship" fractal, of which I have never heard before (which may not say much), and which seems to have been included by one of its originators. However, a general mention of non-analytic dynamics is well-merited, and I have included a paragraph to this effect. This includes a reference to Milnor's 'tricorn', which I believe is the most popular of these objects. --Lasserempe 15 March 2006 (UTC)
: I have also moved this section forward, to keep the mathematical material bundled together. --Lasserempe 18:00, 16 March 2006 (UTC)
thread_title:  Generalizations 

message: I am going to remove the new animation of a cycle, for the following reason. The Mandelbrot set is *not* the phase space of a dynamical system: it lives in the *parameter space* of quadratic polynomials. For every parameter in a hyperbolic component, the corresponding cycle points live in the *dynamical plane*. Plotting these cycles over the Mandelbrot set confuses more than it clarifies, as it gives the impression that there is some dynamical system in parameter space.
The conceptually correct picture would have the dynamical plane of each parameter as a complex *fiber* over the corresponding point of parameter space. However, I suspect that it would require a lot of thought to produce a picture of this type that would really clarify the situation to a layperson.
At some point, when I have more than a few minutes, I might try to write a paragraph on how the position of a parameter in the Mandelbrot set determines the combinatorics of the corresponding Julia set, but to write this in a concise and understandable way is not easy. It might be worthwhile to add a new article "Combinatorics of quadratic polynomials and the Mandelbrot set", but this would require some seriously good expository skills to be useful. (The mathematics behind all this is well-known since Douady and Hubbard's work, although some people have worked to clear it up a bit since then.) --LR 22:44, 20 March 2006 (UTC)
replies: text: I put the picture in because to an engineer like me it is very interesting to see how these cycles evolve. It is interesting from the point of view of a «practical» engineer. But I can understand your point about the parameter/dynamical ambiguity. But anyway are not both the Mandelbrot set and the dynamic systems both represented in the complex plane? I would think that it could be interesting to let the picture stay. Commented by someone like you. But I am not a mathematician so I think it is not for me to decide and that is why I asked if you thought it was useful. Engineers like it, but maybe that is not relevant. Tó campos 11:57, 21 March 2006 (UTC)
replies: text:  I agree that information about the dynamics of different parameters in the Mandelbrot set is interesting, and not just to engineers. In fact, the way that periodic cycles evolve in the parameter plane organize the combinatorial structure of the Mandelbrot set. However, it is not clear what plotting them over the Mandelbrot set will accomplish --- plotting them over the corresponding (filled) Julia set, and indicating where this Julia set arises in the Mandelbrot set, on the other hand, would be useful. --LR 20:39, 21 March 2006 (UTC)

text:  You are right, of course. I will try to find some time to make plots over Julia sets arising in different p/q bulbs and put them in the page for you to check, ok? Tó campos 19:23, 23 March 2006 (UTC)
replies: text:  I have tried to add an explanation in the article; I hope it is readable. It might be useful to find some way to emphasize the order in which the cycle is being permuted. For example, instead of connecting the orbit points by lines, one could label them 0,1,\dots,q-1, starting with the critical point. --LR 19:39, 26 March 2006 (UTC)
thread_title:  Cycles/Pictures 

message: It does not seem clear to me that the section on 'Art and the Mandelbrot set' is really adequate for this article. To me, it seems to be presenting one person's pictures of the Mandelbrot set, and just to be a special case of Fractal Art. I feel that this part of the article should either be removed completely, or moved to the Fractal Art article. However, I will wait for other users' comments on this suggestion. --LR 19:39, 26 March 2006 (UTC)
thread_title:  Art and the Mandelbrot set 

message: The article could probably use a discussion of the ideas described at Renormalizing the Mandelbrot Escape.  Basically, the well-known discrete integer iteration count can be elegantly generalized to simple continuous function, which not only yields smooth, accurate color plots of the set, but has useful connections to other areas of mathematics associated with the set.  When i have some free time, i'll try and see where/how it can be worked in.  --Piet Delport 13:45, 5 April 2006 (UTC)
replies: text: The natural way to assign a 'continuous' color-coding of the outside of the Mandelbrot set is given by the Green's function of the Mandelbrot set, which can be 'computed' (or at least estimated) by a simple formula. This is the basis for the 'distance estimate' method of plotting the Mandelbrot set. --LR 23:16, 5 April 2006 (UTC)

text: I have started a new section to cover this (I'm only familiar with the "renormalized" fractional iteration count method). Slowspace 15:28, 4 December 2006 (UTC)
replies: text:  Thanks!  --Piet Delport 22:26, 5 December 2006 (UTC)
thread_title:  Smooth iteration counts 

message: I'm not at all affiliated to Bill Boll or anything like that, but his new DVD "The Amazing Mandelbrot Set" (http://www.mandelbrotset.net/) seems worth mentioning here or in Fractal Art. The DVD contains lots of very deep and nicely coloured deep zooms as well as a tutorial. Would it be ok to add a link to it, and if so, where? Opinions, anyone? --Khim1 06:50, 17 May 2006 (UTC)
thread_title:  Commercial venture of interest 

message: Most wikification needed in the lower half of the article, i.e. fixing heading levels, un-bolding words, fixing references format, all to conform with WP:MoS. J. Finkelstein 17:09, 16 June 2006 (UTC)
replies: text: Fixed heading levels; changed bold emphasis to italic emphasis; changed references to standard in-line citations format; removed wikify tag. Gandalf61 10:16, 19 June 2006 (UTC)
thread_title:  Wikify tag added 

message: The animated zoom picture is nice, but please don't put a 4.5MB image onto the page. It would be better to link to it instead. - Rainwarrior 03:20, 17 June 2006 (UTC)
replies: text: Sorry, didn't realise it was so large! --CharlesC 09:37, 17 June 2006 (UTC)
thread_title:  Animated zoom 

message: What does everyone think about providing links to pages/sites that require a login to access the information? For an example, we currently have "PHP Source Code PHP Mandelbrot Class" listed as an external link. However, in order to actually download this PHP class, one must first register and login. I am against this. Such information should be freely downloadable(?). I don't know. At least, it would be nice to provide a free/open source example as well. Thoughts? --Thorwald 23:10, 28 October 2006 (UTC)
replies: text: Remove the link. - Rainwarrior 03:06, 29 October 2006 (UTC)
thread_title:  Links to sites requiring login 

message: Nice article, but it consists of many mathematical facts and equations which makes it difficult to understand for non professional readers. On the other hand the Mandelbrot set is known in the general public by an extend which is unusual for a mathematical object like this one. Therefore we should add more of the fascinating facts which can be described simply by words. So I have inserted this commented zoom sequence. Perhaps I have some time next weekend for en extended general introduction ;-). --Wolfgangbeyer 23:52, 5 December 2006 (UTC)
thread_title:  Image gallery of a zoom sequence 

message: Elatanatari 02:29, 25 January 2007 (UTC)
replies: text: I assume you mean "people who do not know a lot about mathematics", right? I made an attempt at a layman's description of how to produce a Mandelbrot image, but I believe I failed since it turned out way too verbose. Still, here it is, if someone wants to use it as a starting point or something. Khim1 05:50, 25 January 2007 (UTC)
thread_title:  ? 

message: Quick summary:
:GA review (see here for criteria)
#It is reasonably well written.
#:a (prose):  b (MoS): 
#It is factually accurate and verifiable.
#:a (references):  b (citations to reliable sources):  c (OR): 
#It is broad in its coverage.
#:a (major aspects):  b (focused): 
#It follows the neutral point of view policy.
#:a (fair representation):  b (all significant views): 
#It is stable.
#:
#It contains images, where possible, to illustrate the topic.
#:a (tagged and captioned):  b lack of images (does not in itself exclude GA):  c (non-free images have fair use rationales): 
#Overall: 
#:a Pass/Fail: 
In a nutshell, insufficient referencing. MER-C 07:57, 9 March 2007 (UTC)
thread_title:  Failed GA 

message: I reduced the External Links Section extensively. There seems to be a habit of people contributing massive numbers of links to JAVA applets, fractal generator programs and galleries. I believe that there should be, at the very most, two of these. After all, Wikipedia is an encyclopedia, and not a collection of links. Before adding links, please consult Wikipedia:Links and consider whether they add to the value of the article. If you feel that another link of these types should be added, or that one of the present links should be replaced by a more appropriate one (preferable), please discuss on this page first. --LR 15:27, 1 May 2006 (UTC)
replies: text: I don't have time currently to look through your article, but does it add anything that's not already in this wikipedia article? If so, why not consider contributing to this article instead? If you think something is overly technical and could be said more simply, go ahead and change it. Fact is there are thousands of Mandelbrot websites out there, and we can't very well have links to all of them :) You could request to have yours added to DMOZ, and then indirectly it would be linked from here. Ciotog 18:57, 26 March 2007 (UTC)
thread_title:  External Links Section 

message: If Abs(z)=1 the one gets circle of radius 1 centered at the origin . Mandelbrot set has a point c=-2 so it is out of that circle.
IMHO proper definition should be Abs(z)=EscapeRadius where EscapeRadius>=2. (Adam majewski 15:58, 19 April 2007 (UTC)
replies: text: I think we need a specific source for this, to avoid OR. It appears to me that any constant threshold (i.e. |p_n(z)|=k for any k>0) may work to define these curves so that the limit of their sequence is the Mandelbrot set, but I'm no fractal expert.  My guts (via computational experiment) tell me that 1 works: the set grows as n increases, to include points outside of the unit circle.  From a pedagogical point of view, the expression "EscapeRadius" has not been introduced in the article yet at this point.  Doctormatt 20:10, 19 April 2007 (UTC)
thread_title:  Basic properties - lemniscates 

message: [this edit] was made by an ip address. Maths isn't my field, so someone should check that. —The preceding unsigned comment was added by Fluck (talk • contribs) 16:46, 6 May 2007 (UTC)
thread_title:  Someone should check this... 

message: I believe the logistic map should send z to lambda*z*(1 - z), not lambda*z*(z - 1) as it was in the article, so I changed it.  Sorry if I was mistaken on that.  Kier07 16:49, 6 May 2007 (UTC)
thread_title:  Logistic map 

message: Hi Fropuff. The formatting you tried is very space consuming. From esthetical point of view I think it is not a very satisfactory solution, because of the large difference of size for the figure captions. Furthermore it makes it impossible to see all thumbs on one screen. I think its nice to see the initial image and a 60,000,000,000 fold magnification together with all intermediate zoom steps to get a visual idea of this enormous zoom factor. Ok, it makes it somewhat easier to correlate the text with the corresponding thumb, but those who want to understand the text in detail have to open the larger images anyway in order to recognise some of the structures described in the figure captions. In this case they see each images together with a copy of the figure caption from the article and can navigate easily from one image to the next. The only reason why the figure captions should stay also in the article at all is that the figure captions below the large images are not part of the article itself. After all on usual monitors any thumb and the corresponding text fits to one screen without scrolling. Finally you have eliminated the zoom step numbers, but the figure captions refer to them. --Wolfgangbeyer 23:01, 28 December 2006 (UTC)
thread_title:  Formatting of the zoom gallery 

message: Hi Shiftchange, the chapter "Computer drawings of the Mandelbrot set" deals with algorithms and program code. The main point of the "Image gallery of a zoom sequence" is not to demonstrate algorithms or to show some nice "Computer drawings" but to present different typical geometrical structures and the underlying rules. Therefore I have moved it to "Geometry of the Mandelbrot set". In principle I would prefer a place earlier in front of the chapters with hard mathematics which I guess only few readers will follow ;-). --Wolfgangbeyer 22:47, 24 May 2007 (UTC)
thread_title:  Position of the image gallery 

message: Ok, so this article says that the set is the orbit of 0, but Wolfrom Mathworld on  page defines it as  z_0 = c .  I mean, this is really nitpicky, because both definitions generate the same set, because for  z_{n+1} = z_n + c , if it's the orbit of 0, then  z_1 = c , but if it's the orbit of c, then  z_0 = c , so it's just a difference of the subscripts, but it would be nice to firm that up...  I'm not an expert on the subject, I'm just a high-school math nerd, so forgive me if I'm being stupid.  Sbrools (talk . contribs) 19:10, 4 June 2007 (UTC)
replies: text: The article does not quite say that the Mandelbrot set is the orbit of 0 - it says that it is the set of values of c for which the orbit of 0 is bounded. This is equivalent to the MathWorld definition, because c lies in the orbit of 0, so the fate of the orbit of 0 and the fate of the orbit of c are the same. Mathematical objects can have different but equivalent definitions - the article just happens to use one particular definition (with a source) in its opening paragraph. Gandalf61 04:42, 5 June 2007 (UTC)
replies: text: Yeah, that's what I said.  I was just wondering.  Sbrools (talk . contribs) 11:38, 5 June 2007 (UTC)
thread_title:  Initial value 

message: The image :
http://commons.wikimedia.org/wiki/Image:Demm_2000.jpg
shows the distance estimation method applied to the complement of Mandelbrot set. I don't know why it is strange .--Adam majewski 16:08, 3 July 2007 (UTC)
replies: text: The trouble is that linking directly to a header doesn't give the reader an explanation of what the image represents.  Perhaps you could explain how this image differs from other Mandelbrot images, so it is more clear what the "distance estimation method" does.  Cheers, Doctormatt 17:15, 3 July 2007 (UTC)
thread_title:  Distance estimates 

message: I noticed that the infinite zooming feature of the Mandelbrot Set is hinted at but it's never shown to its best possible degree.
A 6*1010× magnification is no problem for any modern computer to calculate and antialias. I've got an image, albeit not antialiased, on my desktop at a magnification of 21050×≈1.206×10316×. At this level of magnification, I've noticed all the self-similar features that have been zoomed into begin to "stack up" on each other with every new center zoomed into having several "rings" around of smaller julia sets from lower zoom levels. Hopefully, this makes sense I'm not an expert in fractal theory, but I do enjoy exploring them, so I'm sorry if I've misused any terms. I'm not exactly a layperson in math and programming either though, but I am a newbie wikipedian, so I wouldn't dare upload the image without some expert advice though. I do feel, though, that this would be a nice, probably small addition to the article. Any comments especially expert comments would be greatly appreciated.--Plynch22 21:09, 12 July 2007 (UTC)
thread_title:  Infinite Zooming Feature 

message: User:Shiftchange made the following changes (in bold) to the second paragraph of the lead section:
:Unlike traditional shapes of geometry, Mandelbrot set equations are generally impossible to deduce a shape from. The Mandelbrot set, which is usually shown in black, ...
I reverted these changes and User:Shiftchange has asked for an explanation of my reversion. I reverted the changes because:
#The term "traditional shapes of geometry" is vague, and not well defined.
#It is clearly not "impossible" to deduce a shape from the definition of the Mandelbrot set - there is a straigthforward algorithm for determining whether a given point is a member of the set and there are many illustrations in the article showing parts of the set and its borders.
#The Mandelbrot set is sometimes shown in black, but to claim this is "usual" is too much of a generalisation. Indeed, there are many illustrations in this article in which the Mandelbrot set is shown in blue.
Gandalf61 09:33, 18 July 2007 (UTC)
thread_title:  Changes to lead section 

message: Hi, I made this generator  some time ago. Now I come to the conclusion, that I can share it:) I'll be glad when people will be used and enjoy it:)
 
Hi, I was going to add this google video "Fractals - The Colors of infinity"  by Arthur C. Clark to the "external links".
But I was met with some very unfriendly directions telling me to post here first - so I'll do that and let it be up to you guys if you find it relevant - because clearly you are the ones to be the judge of that. ;)
--80.196.177.35 17:14, 1 August 2007
:According to Wikipedia:Spam#Tagging_articles_prone_to_spam these directions are a preemptive measure against spam. I like to suggest to post the link Animations of the zoom sequence corresponding with the image gallery in this article again, which is obviously no spam but closely related to the article content. Unfortunately it can not be uploaded to Wikipedia because with 37MB due to 1024x768 pixel it exceeds the 10MB limit for media size. --Wolfgangbeyer 21:36, 30 August 2007 (UTC)
replies: text: Obviously no objections ... --Wolfgangbeyer 15:21, 2 September 2007 (UTC)
thread_title:  External links of interest? 

message: I was so happy I've found the formulas, implemented them in a program, and seen them to really work, that I just had to add them to the main page. Feel free to improve typesetting, or move them around, but I feel it should not be deleted as it's pretty hard to find.
The babbling about integer multiples of p0 and the error arising is all mine, found through experiments with my program. It should also be mentioned that the interior distance estimate can in fact be negative for points at boundary of the Mandelbrot set, e.g. -2 or 1+i. I haven't found any explanation for this. Milan va 01:22, 1 December 2007 (UTC)
replies: text: Do you have any sources for these formulas? Wikipedia is not a place for original research, so your estimations found by a program might be hard to keep, unless you write a book or publish them in an article. Paxinum 09:19, 1 December 2007 (UTC)
replies: text: My official source would be Bounding the Area of the Mandelbrot Set but it's somewhat hard to understand the meanings of the variables in the equations. That paper in turns points to "Fisher, Y. (1988): Exploring the Mandelbrot Set. The Science of Fractal Images, Peitgen, H.-O., Saupe, D., Editors, Springer-Verlag, New York, pp. 287-296." but that's not to be found anywhere. Milan va 15:42, 1 December 2007 (UTC)

text: How do you open this paper? (I usu GSView without effect)--Adam majewski 07:01, 2 December 2007 (UTC)
replies: text: I downloaded it and decompressed with Total Commander. WinRAR will work as well, and maybe other decompressors too.  —Preceding unsigned comment added by Milan va (talk • contribs) 11:10, 3 December 2007 (UTC)

text: I have tried to use Total Commander 6.56 : error in archive file . ??--Adam majewski (talk) 20:33, 13 December 2007 (UTC)

text: Sadly, I know nothing about the external rays. My main goal was to speed up the painting of inner pixels, by detecting a period as early as possible. I want to rewrite my program to Java applet and write a page about it, but I think that will take some time. Currently it's written in Delphi 7, if anybody is willing to translate. I've uploaded it to a free webspace if anybody's interested but it needs much work to be usable by common folks. Just left-click and right-click in the image to navigate. Milan va 19:22, 1 December 2007 (UTC)
thread_title:  Distance estimates 

message: The mathematical notation in this section uses F^n_c but the rest of the article uses f^n_c. Is there a reason why to use capital F? Paxinum 16:12, 3 December 2007 (UTC)
thread_title: Notation

message: I think a separate article where the different algorithms (especially colouring algorithms etc) can be added. This article should focus more on the mathematical view on mandelbrot, and the hobby/aesthetical views on mandelbrot fractal can be moved to this new article. Paxinum 12:18, 3 December 2007 (UTC)
replies: text: For myself, I would just drop the whole algorithms section apart from the initial glossary list with internal links. The rest of the section is unsourced and tends towards POV descriptions of "my favourite algorithm". A lot of it appears to be original research. It is interesting, but I am not convinced it is enclyclopedic. Gandalf61 12:48, 3 December 2007 (UTC)
replies: text:  I actually partially agrees, the article as it is now is quite bloated, and those (partially including me), that are interested in documenting good drawing algorithms and colouring parameters could do so in the wikibook here. Paxinum 15:54, 3 December 2007 (UTC)
thread_title:  New article? 

message: I've noticed that there is a substantial lack of sources for the majority of the "Other Properties" section on this page, and was wondering if there was a reason for it.  Would it be reasonable to request that a source (or sources) for the information in that section be provided?  AtramentousAmaranth (talk) 12:21, 30 December 2007 (UTC)
thread_title:  Sources for "Other Properties"? 

message: Why is here critical point not equal to zero ? I t should be zero !!!!--Adam majewski (talk) 10:23, 6 January 2008 (UTC)
replies: text: This was an incorrect edit by Cyclone231 - I have fixed it. Gandalf61 (talk) 17:26, 6 January 2008 (UTC)
thread_title:  formal definition 

message: Hi. Thx for new item. 
* Can you add the code to the wikibooks ?
*As I know continues escape time uses low ierations ? Is it true in your version ?
* Can you write more about gradients ?
--Adam majewski (talk) 17:55, 28 December 2007 (UTC)
thread_title:  Continuous (smooth) coloring 

message: "Note that this new equation is simpler than the first, but it only works for Mandelbrot set's with a bailout radius of 2 and a power of 2."  I dont know about Mathematics too much, but I think the bailout radius of the formula should be e, not 2.--Luzi82 (talk) 16:34, 2 February 2008 (UTC)
thread_title:  smoothing 

message: There are many change in code. Evrey change is intresting and I think that should be described. Maybe in wikibooks.--Adam majewski (talk) 12:25, 17 February 2008 (UTC)
replies: text: There is a wikibook about fractals, where pseudocode is encouraged! Paxinum (talk) 07:13, 18 February 2008 (UTC)
replies: text: so please add coomment to this book if you are making changes (:-))--Adam majewski (talk) 09:10, 19 February 2008 (UTC)
thread_title:  for programmers 

message: what about linking http://sourceforge.net/projects/quickman ? it's an open source mandlebrot set generator 151.57.77.203 (talk) 22:06, 18 February 2008 (UTC)
thread_title:  External Link 

message: Ok, we all know the behavior of the primary satellites: Zoom in on a fiber with two other fibers extending out almost perpendicular to the first and you will see 8 fibers, then 16, 32, till they finally degenerate into this smaller version of the original set that is almost broken off from the original except for that first fiber connecting it. Well, in looking around the set, I've noticed that these satellites are almost exactly similar to the original except for the fact that it has all these fibers from the original forming it. They even have their own satellites placed in the same analogous location to the original, but these satellites could have differently shaped fibers from the satellite their "orbiting" along with the fibers from the original set all degenerating into them. As a matter of fact, the Julias seem to be simply an amalgamation of this compound degeneration. The largest two amoebal structures in the Julias seem to be simply a largely exaggerated version of the fibers emanating from the primary bulbs, but these smaller bulbs would have a periodicity of something like a million instead of just 3. Zoom deeper and the amalgamation continues leading to more and more complex structures, because of this, when you zoom in on any detail of any structure, every detail zoomed into after that, must show a sign of that original structure it's inside of. Because of this, if you know how to read them, every picture obtained from the original Mandelbrot set will tell you the story of how it was zoomed in upon.
I guess my point is: Shouldn't we expand this section to show how the mandelbrot set is used to create fractal art. Any ideas? Plynch22 (talk) 00:32, 28 August 2008 (UTC)
replies: text: This page ostensibly about the mathematical object is already overstretched by extra matter about renderings and generalisations, while Fractal art needs more good material. This Wikibookhas an incomplete chapter 10 Applications which would benefit from a contribution about artistic fractals. See also  Cuddlyable3 (talk) 18:39, 28 August 2008 (UTC)
thread_title:  "Quasi-"self-similarity? 

message: The content about Generalisations with other exponents than 2 has been moved to Multibrot sets where there is also new material. Discussion of multibrots has been moved to Talk:Multibrot_sets. Cuddlyable3 (talk) 11:16, 29 September 2008 (UTC)
thread_title:  Multibrot sets - new page 

message: Sorry to be a bother, but would someone kindly describe the set's convex hull?  This would make mentally visualizing the set much easier, at least for me.  Thanks!  --24.29.87.24 (talk) 23:49, 15 July 2008 (UTC)
replies: text: This animation may help.  Cuddlyable3 (talk) 17:46, 9 October 2008 (UTC)
thread_title:  Requesting: Convex Hull 

message: This image shows a Mandelbrot set occuring in a very different process: the analysis of Newton's method for cubic polynomials by means of the fate of their critical point. Maybe it's interesting for the article because this M does not originate in z→z²+c but comes from a meromorphic function. The M in the closeup has its bulbs and buds at places that are a bit different from these of the original M, but it is complete with all bulbs, buds, antennas, filaments, etc. of the original M. The main cardioid is linked to an attractive cycle of period 2. This is very astonishing because the body of M has period 1 and the only part of M which has period 2 is the "head". -- Georg-Johann (talk) 17:25, 23 October 2008 (UTC)
thread_title:  Universality of M 

message: User 66.188.104.173 had reverted by XLinkBot a link to a video on www.youtube.com. There are art works based on the Mandelbrot set at http://www.jonathancoulton.com/songdetails/Mandelbrot%20Set# Tab: Images. Is this a link we can use? Cuddlyable3 (talk) 06:35, 20 May 2008 (UTC)
thread_title:  In Popular Culture