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This is an old revision of this page, as edited by Lowercase sigmabot III (talk | contribs) at 00:07, 29 August 2014 (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)

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