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This is an old revision of this page, as edited by Lowercase sigmabot III (talk | contribs) at 00:18, 3 January 2019 (Archiving 2 discussion(s) from Talk:Mandelbrot set) (bot). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.
Archive 1Archive 2Archive 3Archive 4

Smooth coloring formula wrong

I don't know the right formula (it seems no one does) but the one given here is clearly wrong. Just take P-2, N=2, c=1.8 for example. In that case, one iteration (or two, depending how you count) gives z=5.04, which is over the bailout value of 2. Now, the log formula gives 1.2224, which is not in the range [0, 1) as specified. I wish someone who knows the correct algorithm (if any such person really exists) would fix this. Wikipedia readers are spreading this misinformation all over the web. 70.116.13.152 (talk) 03:31, 28 April 2013 (UTC)

Update: the August 2009 version seems to contain better information (it's certainly a different formula from this one, even after simplification, by at least a factor of 2 inside the outermost log, and it also explains that unusual bailouts are required for the smooth coloring algorithm, a crucial piece of information left out in the very poor article that exists today). I will nonetheless wait for a knowledgeable person to do something about it. 70.116.13.152 (talk) 03:49, 28 April 2013 (UTC)

Limit of. Iteration

Your last sentence of your. second paragraph should say the pixels are colored according to the number the sequence approaches. — Preceding unsigned comment added by Claustro123 (talk • contribs) 04:17, 8 March 2013 (UTC)

That is hardly possible, since the usual coloration is applied to points where the iteration diverges to infinity.--LutzL (talk) 13:55, 11 March 2013 (UTC)

Ugly picture

Look at http://en.wikipedia.org/wiki/File:Blue_Mandelbrot_Zoom.jpg. If you look closer, you can notice, that the rectangle in one picture does not strictly correspond to the following picture. The last picture is completely out of the blue, it has no telation whatsoever to the previous one and also has to few iterations. I find it disturbing. The picture has another version: http://commons.wikimedia.org/wiki/File:Mandelzoom.jpg which is slightly better, but suffers similar issues. Janek37 (talk) 21:21, 19 June 2013 (UTC)

It goes to a "personal" site. Is it ok? Tony (talk) 02:21, 9 July 2013 (UTC)

I know this is a hot topic and I know it has million examples on the web. Yet I believe a live demo that the readers can explore without any knowledge of programming languages or even the need to download anything, has a real value.

Please review this page: Interactive live demo (HTML + Javascript) It is very simple, interactive and totally open source.

Leeron-s (talk) 07:14, 8 September 2013 (UTC)

Relation to Julia Sets

Mandelbrot as classification of Julia sets
My (LL) earlier version of it

Having just finally learned, via sources outside of wikipedia, exactly what the difference between the Mandelbrot Set and Julia sets are, equation-wise, I think that this information should go into the article. I'm just not sure how to word it, or where to stick it in.

  • zn+1 = zn2 + c where z0 = 0 (or c) and you map out the variable c, is the mandelbrot set.
  • zn+1 = zn2 + c where c is a fixed constant complex number and you map out the variable of all z0 points, is the julia set of that given c.

The fact that the equation is the same, but which term is the variable, is of great importance to understanding what on earth the equation IS in the first place, and was the chief hindrance in my prior understanding. Any ideas how to put this into the article? Fieari (talk) 14:19, 21 March 2013 (UTC)

You are right. The basic information that the Mandelbrot set is a classification of Julia sets in that it consists of those parameters c such that the Julia set for c is connected resp. contains interior points resp. has z=0 as interior point is completely missing from this article. I found Alan F. Beardon, Iteration of Rational Functions, (Springer 1991) to be a helpful resource.--LutzL (talk) 11:09, 7 April 2013 (UTC)

This article says the Mandelbrot set is actually part of the Julia Set. Anyone else care to read? http://www.relativitybook.com/CoolStuff/julia_set_4d.html Shroobtimetraveller (talk) 06:08, 21 September 2013 (UTC)

Of course you can do that. But the big set is neither a Julia nor a Mandelbrot set. A certain set of parallel cross section gives the Julia sets and another cross section orthogonal to them is the Mandelbrot set. However, the presentation at the website ignores that the point z=0 is a special point for every Julia set in that it is the root of the derivative of the iteration. And in consequence, the iteration starting at z=0 alone already decides if the Julia set is a connected set. The other cross sections have the same importance as other Mandelbrot related pictures, like the Buddhabrot, log-escape maps etc. They look nice, but hold no further fundamental mathematical insight.--LutzL (talk) 07:51, 21 September 2013 (UTC)

POV?

"The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and as an example of a complex structure arising from the application of simple rules, and is one of the best-known examples of mathematical visualization." -- A little searching would support the popularity of the set (and then documenting it), but is a alleged esthetic appeal really a factor? I find the math great, but the visual image is extremely repugnant to me. It alone almost turned me away from studying fractals. Even today, years later, I get a negative visceral reaction when I see the Mandelbrot set (as opposed to, say, the Julia set).211.225.33.104 (talk) 04:46, 4 October 2013 (UTC)

The whole set is indeed rather boring, the esthetic interest is more on magnifications of the escape map. For an extreme example, I have seen step-colored megnifications as print on a dress. You may argue that those magnifications are close to magnifications of the corresponding Julia set.--LutzL (talk) 07:01, 4 October 2013 (UTC)
Indeed, as soon as you zoom in you'll see variety equivalent to the Julia set, the zoomed-out view is just a starting point. So you can't really say you like the Julia set but not the Mandelbrot, it would be like saying you like trees but don't like forests. Egrange (talk) 10:04, 10 January 2014 (UTC)

I've ran a project last year to pre-compute the Mandelbrot Set as a four Terapixel image:

Terapixel Mandelbrot Set Image

I'm suggesting this as an external link. The difference with the myriad of "classic" exploration programs being the pre-computation, meaning the exploration is fast and interactive even on tables and low-power devices. The raw pre-computed Data is also available through an API and downloads. Egrange (talk) 10:14, 10 January 2014 (UTC)

Possible omission?

Stephen Wolfram uses fractals in a unique way to describe how nature can create complex patterns by repeating a simple algorithm, like a cellular automaton. A sample of images from A New Kind Of Science demonstrates the underlying algorithms similar to that of the Mandelbrot set and fractals in general. Would it be appropriate to mention that herein, or is there a more general Wiki entry on fractals that might benefit from this? http://www.wolframscience.com/downloads/colorimages.html http://www.wolframscience.com/index.html


Hpfeil (talk) 19:22, 28 January 2014 (UTC)

Is the Mandelbrot set a fractal?

Here's what Mandelbrot himself had to say about this: http://www.webofstories.com/play/benoit.mandelbrot/86 — Preceding unsigned comment added by Lbertolotti (talk • contribs) 00:31, 16 February 2014 (UTC)

Dynamically generated DeepZoom image of Mandlbrot (set) fractal

Self similarity type?

The Mandelbrot set is said to possess quasi self-siimilarity, however I am not sure if that applies to the whole fractal or certain regions. Whoever knows the actual answer should make this clear. — Preceding unsigned comment added by 121.72.115.77 (talk) 07:24, 29 April 2014 (UTC)

See the link I provided above:

"The Julia sets again are self-similar; each part is like any other part, but one of the observations made about the Mandelbrot set was the following: that a small corner of the Mandelbrot set looks in many ways like the Julia sets corresponding to it; therefore the Mandelbrot set included as parts of it reduced scale images of an immense variety of Julia sets; therefore it is not self-similar in that respect. It is self-similar in the sense that the islands are like the continent but slightly deformed; but not in a sense that the way in which the islands are arranged, the kind of strings that link them together are the same; in fact, they're different in every point. Therefore the complication of a set goes beyond fractals. Julia sets are self-similar, they are fractals by every definition and by intuition, except when they are just straight intervals which happens for some cases, in which case they are too simple to be fractal. The Mandelbrot set is a complication which includes a huge number of different fractals in its structure and is therefore beyond any fractal. It is a paradox of sorts that this has become the icon of fractality, whereas it does not fit the definition of the concept at all. " Lbertolotti (talk) 14:18, 24 May 2014 (UTC)

All Julia sets?

In the NOVA documentary Fractals, Hunting The Hidden Dimension (around 21:45) the narrator claims the Mandlebrot set represents all the Julia sets with a single formula. If this is true, shouldn't the distinction be made in the lead rather than just saying it is closely related? - Shiftchange (talk) 04:47, 15 June 2014 (UTC)

National varieties of English

In reading this article, I noted multiple varieties of English were used, especially with respect to the spelling "color/colour". The WP Manual of Style guideline recommends consistency. In cases where inconsistent usage is found, it calls for discussion to establish a consensus. When discussion cannot resolve the issue, "the variety used in the first non-stub revision is considered the default."

The first revision using a variety of English was [1] on February 15, 2003. It used the "colour" spelling, but the article was a stub (though not tagged as such) at that time. Subsequent edits over the next year predominantly used the "color" spelling. It's debatable whether or at what point during this time the article ceased to be a stub.

At present, the "color" spelling outnumbers the "colour" spelling 4 to 1 (47 vs. 12). I would consider that a deciding factor in establishing the American spelling as the de facto standard, but am opening the question for discussion. Unconventional (talk) 16:19, 25 July 2014 (UTC)

Linking to FractalJS

Solendil (talk) 10:06, 8 September 2015 (UTC)  Hi, FractalJS is an open-source interactive fractal explorer in javascript, working right in the browser. It's certainly not the first of its kind, but AFAIK, it's the fastest and most user-friendly. I created FractalJS to promote fractal exploration by everyone : you don't need to install anything, just click, scroll and explore; you can also share links of your favorite places.

I believe FractalJS would be a nice companion to fractal related web pages. I just modified the "Image gallery of a zoom sequence" to include FractalJS links to the same picture. I was wondering if we could add FractalJS in the External Links category of the Mandelbrot article? And how about providing FractalJS links in other relevant articles, like Burning Ship fractal, etc?

This article and Wikipedia "book-creator"

I have a rather obscure problem with this article. As you may know, Wikipedia includes a facility for compiling PDF "books" out of a set of related articles. They do say that the system is "crippled" but I've used it with some very successful results. However, my latest venture was to be on fractals, the first chapter being Wikipedia's "Fractal" article and with subsequent articles on various types of fractals stc. This has all worked fine - except that including the "Mandelbrot set" article causes the book-creation process to fail. (Other articles on fractals are fine.) Does anyone have any idea why this should be? GeoffHope (talk) 10:55, 13 February 2016 (UTC)

I would guess its either the math formula or the total size of the article causing the break. Considering that creating a book is not a widely used feature its probably better to raise it elsewhere. - Shiftchange (talk) 12:33, 13 February 2016 (UTC)

Thanks for such a quick and helpful response. Your thoughts coincide with mine, that it's either the length of the article or the mathematical symbols. I'll follow your suggestion. GeoffHope (talk) 12:52, 13 February 2016 (UTC)

It was caused by a broken HTML fragment. I fixed it and it complies now. — Cheers, Steelpillow (Talk) 15:38, 13 February 2016 (UTC)

Many thanks! I had just logged on to say "It's working now!" GeoffHope (talk) 09:41, 14 February 2016 (UTC)

a question

what program was used to make the images from the "image gallery of a zoom sequence"? — Preceding unsigned comment added by 178.187.248.198 (talk) 11:47, 28 August 2014 (UTC)

Periodicity checking

Dieser Abschnitt ist in mehreren Punkten falsch. Sollten zwei aufeinander folgenden Iterationen die selben Koordinaten haben, dann beträfe das nur das Hauptkartiodit der MBM. Alle anderen Teile innerhalb der MBM haben andere Periodizitäten. Es müßte jede 2. 3. 4. usw. mit der ersten verglichen werden. Innerhalb der MBM werden nie mögliche aufeinanderfolgende Iterationen die exakt selben Koordinaten haben. Die Konvergenz ist unendlich lang. Das Programmbeispiel ist zudem sehr abhängig vom verwendeten Computer-Zahlenformat, was jeweils ein anderes Verhalten zur Folge hat, was aber im erzeugten Bild nicht erkennbar ist. — Preceding unsigned comment added by 178.26.205.207 (talk) 17:39, 18 September 2014 (UTC)

Google-translated: This section is wrong on several points. If two successive iterations have the same coordinates, then would concern only the Hauptkartiodit [main cardioid?] [of] the MBM. All other parts within the MBM have different periodicities. It would have to be compared every second third fourth etc. with the first. Within the MBM never possible successive iterations will have the exact same coordinates. The convergence is infinitely long. The sample program is also very dependent on the used computer numerical format, which each has a different user experience, which is not visible but in the generated image.
AndrewWTaylor (talk) 20:32, 30 September 2014 (UTC)

Query

In technical terms this article goes way beyond my knowledge. But I can tell that it's a really first-rate article.

What I came here to find out is the potential uses of this advance in other areas, whether mathematical or further afield. But alas, there's no section briefly describing that. Tony (talk) 13:32, 28 June 2016 (UTC)

Hi @Tony1: Excellent question. Probably better asked at Wikipedia:Reference desk/Mathematics but I'll give it a shot here.
The Mandelbrot Set is an example of fractal geometric shape: an infinitely complex shape generated from an extremely simple formula. Benoit Mandelbrot, who discovered it, is credited with introducing the general concept of fractal geometry as a means to explain complex shapes in nature, such as clouds, coastlines, tree bark, and so on. The Mandelbrot Set is probably the most famous fractal, but that particular fractal doesn't really have any practical uses that I know of, other than as a pedagogical device. A related formula, the logistic map, has been used as a model of population cycles (and the nodes of the logistic map coincide with the cusps in the Mandelbrot set).
This BBC article] offers a general description of the more practical uses of fractal mathematics. That wouldn't quite be in the scope of this article, however, since this article is about one specific (and famous) fractal object. ~Amatulić (talk) 05:55, 29 June 2016 (UTC)
Update: I found another one that actually shows relationships between real-world phenomena and the Mandelbrot Set here: http://www.sgtnd.narod.ru/science/complex/eng/main.htm -- not easy to understand, but one can get the general idea. ~Amatulić (talk) 06:03, 29 June 2016 (UTC)
Thanks for this. BBC article a little non-specific about the spin-offs (earthquakes, but ... how?). The other link pretty hard to understand, though, for anyone but an expert. But the beauty arising from simplicity is possibly enough to behold! Tony (talk) 07:27, 29 June 2016 (UTC)
My favorite natural fractal that actually looks like a geometric shape, rather than a random thing like a cloud or a coastline, is Romanesco broccoli. I recall reading an article in which someone came up with a 3-dimensional formula to replicate that fractal shape. Unfortunately the Wikipedia article doesn't link to that paper. ~Amatulić (talk) 07:36, 29 June 2016 (UTC)

Please do not remove pseudo-code from this article.

For many people (myself included) it is easier to understand concepts expressed in pseudo-code than mathematical notation.

So far two individuals have reversed removal attempts by 84.249.83.20. Until better reasons can be given, please stop. Thank you. — Preceding unsigned comment added by 173.212.143.233 (talk) 23:02, 12 May 2016 (UTC)

Location in Article

Please feel free to give suggestions as to where the pseudo-code should be located. The section will remain collapsed by default to prevent intrusiveness. — Preceding unsigned comment added by 173.212.143.233 (talk • contribs) 00:21, 14 May 2016‎

Quality

Please feel free to give suggestions for how it could be improved if you feel it is lacking in some way.

These sources were used as guidelines on how to write good pseudocode:

— Preceding unsigned comment added by 173.212.143.233 (talk • contribs) 00:36, 14 May 2016‎

It is definitely misplaced in the lead section. But also, "The section will remain collapsed by default" violates MOS:DONTHIDE. —David Eppstein (talk) 01:55, 14 May 2016 (UTC)
I support the pseudocode removal from the lead section for those reasons, and because it's redundant. There's already sufficient pseudocode in the section Mandelbrot set#Escape time algorithm. ~Amatulić (talk) 21:02, 14 May 2016 (UTC)
I have a problem with "If the above loop never terminates return true". Even in very abstract pseudocode, I don't think you can get away with a test that cannot be implemented in any language. Gandalf61 (talk) 12:21, 15 May 2016 (UTC)
The pseudocode that remains in the article doesn't have this dubious feature. ~Amatulić (talk) 20:52, 15 May 2016 (UTC)
(Pseudocode can be seen in this revision) Jimw338 (talk) 03:43, 5 April 2017 (UTC)

File:Mandelbrot sequence new.gif to appear as POTD soon

Hello! This is a note to let the editors of this article know that File:Mandelbrot sequence new.gif will be appearing as picture of the day on June 15, 2017. You can view and edit the POTD blurb at Template:POTD/2017-06-15. If this article needs any attention or maintenance, it would be preferable if that could be done before its appearance on the Main Page. — Chris Woodrich (talk) 01:33, 3 June 2017 (UTC)

Mandelbrot zoom sequence
A zoom sequence illustrating the set of complex numbers termed the Mandelbrot set. Images of the set, which was defined and named by Adrien Douady in tribute to the mathematician Benoit Mandelbrot, may be created by sampling the complex numbers and determining whether the result of iterating for each sample point goes to infinity. Images exhibit an elaborate and infinitely complicated boundary that reveals progressively ever-finer recursive detail at increasing magnifications. Consequently, the Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and as an example of a complex structure arising from the application of simple rules.Animation: Simpsons contributor
Archive – More featured pictures...
Its lovely, a great example of infinity visualised. Would the addition of one more link be inappropriate? I wanted to suggest changing the text from created to generated and adding the link to Fractal-generating software. - Shiftchange (talk) 06:30, 3 June 2017 (UTC)

Mandelbrot Curves in Desmos

In case anyone finds this useful, I have plotted the first few Mandelbrot curves on the website Desmos. --  Denelson83  04:18, 25 July 2017 (UTC)

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