Talk:Fractal

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Suggestion

Hopefully this can offer an eventual merge? Sr13 05:48, 20 June 2007 (UTC) Adding a reference for item 34 on the achieved talk page (page2). A reference from the Nexus Journal: Daniele Capo, The Fractal Nature of the Architectural Orders. [1] Nikhil Varma 14:23, 21 June 2007 (UTC) Adding a link to www.fractalguide.com—The preceding unsigned comment was added by 149.254.192.192 (talk • contribs).

I have recently developed a web based fractal viewer. Does anyone think a link to the viewer on the fractal pagewoulds be useful. http://www.webmandel.com is where it can be found. —Preceding unsigned comment added by 199.44.137.1 (talk) 16:41, 9 October 2007 (UTC)

See WP:EL. A new link is not necessary.TheRingess (talk) 16:50, 9 October 2007 (UTC)

Thanks for your opinion —Preceding unsigned comment added by 199.44.137.1 (talk) 19:07, 9 October 2007 (UTC)

There is nothing that would rule out that link in WP:EL, in fact items 3 and 4 of what should be included fit the given site well, and it passes all tests of what not to include. EL is also a style guide, not a strict policy. All that said, I don't like the link simply because of the ugly layout and palette used. Fix that up, and the site would make a great addition to this page. Nazlfrag (talk) 06:28, 31 December 2007 (UTC)

image

I have an image of a real-life fractal. It's from the glass door on a wood-burning stove. The charring on the glass flakes off in a fractal pattern. It's not a great picture, but it is a great example of fractal behavior in a physical process. Does anyone think it would help to contribute it to the article (and to the Commons)? --Cheeser1 07:51, 1 July 2007 (UTC)

"Colloquial usage"

What exactly does the lead sentence mean by "In colloquial usage, a fractal is..."? How is "fractal" a colloquialism? See also colloquial. If the definition is wrong, fix the definition, don't label it a colloquialism. If the definition is correct (albeit rough or vague), then it's fine as-is (minus "colloquial"). --Cheeser1 06:15, 3 October 2007 (UTC)

The point that "colloquial" is trying to make is that what follows is not a mathematically precise definition of a fractal, because it is too vague. "Colloquial" is a flag to say "please don't pick holes in this definition, we know it is not exact". Unfortunately, we cannot put in a mathematically precise definition because there isn't one (AFAIK). Every attempt that I have seen at a precise definition either excludes objects that are generally agreed to be fractals, or includes objects that are generally agreed not to be fractals. But maybe "colloquial" is not the right term here - would "informal" be better ? Gandalf61 08:51, 3 October 2007 (UTC)

There isn't one precise definition of "integral" either. A better example, take "chaos." How about this:

A fractal is generally "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity. The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured".

Does that sound better? I'd also probably want to change "A fractal as a geometric object generally has the following features" to simply "A fractal often has the following features." You think that works? --Cheeser1 14:13, 3 October 2007 (UTC)

So long as it remains clear that the term has no really precise mathematical definition (Well, in fact it does: a fractal set has non-integer dimension!) But the point is that it has a more widely understood vernacular meaning (which is arguably much more important)--C G Strauss 21:20, 6 October 2007 (UTC)

Unfortunately, the "non-integer Hausdorff dimension" definition does not work, because it excludes objects such as the Smith-Volterra-Cantor set (dimension=1) and Peano curves (dimension=2), which are generally considered to be fractals. See List of fractals by Hausdorff dimension for more examples of fractals with integer Hausdorff dimension. Gandalf61 08:08, 7 October 2007 (UTC)

I agree - I think the imprecise definition is actually quite appropriate, given the different uses of the term to describe what are similar (if not precisely the same) phenomena. --Cheeser1 17:07, 9 October 2007 (UTC)

For a formal definition of a fractal, what about a set whose Hausdorff dimension differs from it's topological (Lebesgue covering) dimension? —Preceding unsigned comment added by 82.31.209.115 (talk) 22:21, 2 July 2008 (UTC)

It's one of the properties that a fractal can have. I don't know if there are counter-examples. Actually, the page states that "It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve)". I think that the text between parentheses is mathematically wrong, since the Hilbert curve as a topological dimension of 1 (being a curve) and an Hausdorff dimension of 2. Maybe it remains from an earlier version, where it was only stated that a fractal has a non-integer Hausdorff dimension? -- Clément Pillias (talk) 09:18, 4 November 2008 (UTC)

Links

• XaoS — One of the fastest fractal generators.

And in general, how about Comparison of fractal software — lim 17:28, 9 October 2007 (UTC)

Wikipedia isn't really a place for software comparisons, unless the comparison is, you know, notable (e.g. the article Windows Vista might include comparisons to its predecessors). I don't think we're in the habit of (basically) reviewing/rating software/games/etc. --Cheeser1 19:22, 9 October 2007 (UTC)

I'm talking about something like this: Comparison of container formats, Comparison of audio codecs, Comparison of SSH clients — lim 10:23, 10 October 2007 (UTC)

What is about making a list of fractal softwares and small discriptions with how to download, and use them.

Vishvax 06:56, 27 October 2007 (UTC)

See this guideline, which explains what I mean when I say that you can't use the existence of one article to justify the existence of another. I see no reason to make such an article, especially since "fractal software" and the features that define such software are poorly-defined. It's not like an audio codec, which can be compared in some more objective/encyclopedic ways. --Cheeser1 21:22, 28 October 2007 (UTC)

• Fractal Geometry at Yale - This is Mandelbrot's definitive online resource on the subject. It is probably reasonable to treat it as being in a category of own with regard to relevant links. --Hjb (talk) 16:18, 23 February 2009 (UTC)hjb

• I know that placing a long list links to fractal generators is discouraged here but I think that the community would benefit from a few good viewers/generators as long as they are vetted by the coordinators. I would like to propose one: http://ladimolnar.com/Fractalia/ BTW, I agree with the fact that a few links like http://classes.yale.edu/fractals/ should also appear here. —Preceding unsigned comment added by 67.160.117.167 (talk) 22:55, 29 August 2009 (UTC)

Fractal-generating software

In the history of this article, a comprehensive list of fractal-generating software is buried. Based on this list, a dedicated article for the list of such software could be created.

See the revision of the article, after which the list of fractral-generating software was removed by the courageous User:Salix alba.

Above, an objection has been raised that "fractal-generating software" is a poorly defined category. I cannot confirm such a statement. To begin with, any program that generates a Mandelbrot set, Julia set, of IFS is a fractal-generating software. Put differently, to the extent to which the term "fractal" is defined, the term "fractal-generating software" is defined too.

--Dan Polansky (talk) 08:11, 23 February 2008 (UTC)

I personally believe that if you really want these links you can probably put them on your user page and reference this fractal page, otherwise I would suggest compiling a list somewhere outside wiki.
Wyvern917 (talk) 14:03, 20 August 2008 (UTC)

verry little math

Altough most Wiki pages about math subjects are unreadable because of the nathlanguage used. This article contains no formula at al. Well that's great its a good read. But perhaps a little bit about the mathematics behind fractals just at a level one can create his own basic version fractal would be nice. —Preceding unsigned comment added by 82.217.143.153 (talk) 16:48, 23 February 2008 (UTC)

I have included a small article about how I recently discovered how to hand draw fractals of anything. I left links showing where to go to see a demonstration. I would like to download a step by step process (in diagrams and an explanation) in which I can show any one (with out using complicated equations), how to hand draw a fractal of any shape. Any help that you could give on how I can download images would be great.--JASONQUANTUM1 (talk) 17:41, 7 July 2008 (UTC)

Yeah I agree about putting more math in this article, I am a student of mathematics and find fractals very interesting. I would really like to know about the math behind a fractal.

Missing from the article seems to be the information that the Koch snowflake is actually Three Koch curves fitted together. Also the Fractal Dimension is on a separate page from the main article. I would say that the importance of fractals comes into play when we try to fit Euclidian geometry onto shapes that are far from Euclidian in nature. Because these shapes are so complex we need to study them in different ways from the Euclidian shapes. Just as there are Euclidian like shapes in nature also we find Fractal like shapes and Euclidian geometry will not help us to understand them. Richardjames13 (talk) 11:01, 11 January 2009 (UTC)

I agree. I think that there definitely could be some more maths in this article. For example, are there equations to represent fractals? Or to find their area?My 2 Cents' Worth (talk) 17:20, 22 May 2010 (UTC)

CD picture of "fractal" referenced to number 7

didn't find any mention in the source that microwaved CD's or DVD's exhibit fractal features. did you find any mention of that? --Kirils (talk) 12:14, 25 September 2008 (UTC)

Fractal software mention

I believe it is necessary to mention fractal generators. A person who knows little about fractals will be none the wiser after reading the four methods of making fractals. What a newcomer most likely wants to know is how fractals are made in practise, rather than in theory.

Further, I think that a short article on fractal generators is appropriate, and I have begun work on this.

If there are good reasons why this is unnecessary or inappropriate then please add them here, rather than just deleting. Soler97 (talk) 02:05, 4 October 2008 (UTC)

I do still object to its inclusion. Mostly on the grounds that it is so obvious of an observation as to be meaningless. No one writes their own fractal programs or uses the mathematics to draw their own fractals. Of course everyone uses a fractal generator. This section merely presents the mathematics that those fractal generators use. If it isn't made clear earlier that most people use generators then it could be, but the sentence does not belong in a section discussing the algorithms, in my opinion.TheRingess (talk) 22:02, 6 October 2008 (UTC)

Do you object if I put the same sentence at the end of the introductory section? In my experience, the obvious should be pointed out, especially to people who have no knowldege of fractals and very little of computers. It may be obvious to you and me, but people routinely ask me "How are fractals made?" These people are satisfied with the answer, "using a program". An encyclopedia article should presume the absolute minimum of knowledge on the topic in question.

Also, do you object to the addition of a short article on fractal generators? Soler97 (talk) 22:40, 7 October 2008 (UTC)

Fractal program on NOVA

NOVA recently aired a television program on fractals. (the full video of which is available to be viewed online, as well as other things pertaining to fractals) Perhaps the link should be mentioned in the External links section? http://www.pbs.org/wgbh/nova/fractals/ Cardsplayer4life (talk) 09:45, 13 November 2008 (UTC)

More Examples from Nature

I wonder if anyone thinks it worthy of mention in the "In Nature" list of examples that gecko toes and feathers are fractal in structure? Pammalamma (talk) 23:02, 29 November 2008 (UTC)

Certainly you could mention these examples if you have a reliable source for both of them. Gandalf61 (talk) 17:21, 30 November 2008 (UTC)

• Picture collection of natural fractals

Hilbert Curve

It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve). As far as I know Hilbert Curve has Haussdorf dimension=2 and topological dimension=1. Is that correct ? Lbertolotti 8 febb

No, the Hilbert curve (i.e. the image of the Hilbert map in R²) has a topological dimension of 2, equal to its Hausdorff dimension. I checked this at the Mathematics Reference Desk. Gandalf61 (talk) 18:00, 15 March 2009 (UTC)

nonfractals?

by the definition given in this article, the last five images, interesting as they are, are not fractals. why are they in this article?· Lygophile has spoken 15:12, 14 May 2009 (UTC)

Perhaps you could expand on that a little. Which specific images do you mean ? Why exactly do you think they are not fractals ? Gandalf61 (talk) 15:24, 14 May 2009 (UTC)

well, the very last five images in the article. the "poenix set" seems to merely contain a bunch of spirals (which are inherently perferct fractals), so i don't think that's really notable as a fractal image (but you don't get to see much of it). the "Pascal generated fractal" and the "fractal flame" are a in essence bunch of lines. if you zoom in, the lines get thicker and less curly, and it doesn't resemble itself in different zoom-scales. the Sterling fractal uses overlapping copies of an image, like a bunch of fractals do, but in contrast with those fractals, these images are not ordered in a way, that they collectively resemble that image, nor does that image have parts that resemble that image. it's basically the same for the julian one.· Lygophile has spoken 15:53, 14 May 2009 (UTC)

With regard to "zooming in", those images are just screen-shots of images created by fractal generating software programs. When you "zoom in" on the image, you are just expanding pixels - you cannot "zoom in" to show more detail. You seem to be expecting to "zoom in" in the image as if you were using the fractal generating program itself - that is just not possible. With regard to having "parts that resemble that image", I think you are talking about the property of self-similarity. That property can be quite difficult to determine from a single image - just because an image does not have any visually obvious self-similarities does not mean that it is not a fractal. Gandalf61 (talk) 08:16, 15 May 2009 (UTC)

Aros

I would like to add this to External links. It is freeware. It is an excellent and simple mandelbrot generator/zoomer.

Aros Magic

Any thoughts? --Anna Frodesiak (talk) 09:54, 2 June 2009 (UTC)

Generation / Beginner's Help

I want to add, for anyone who does not understand this topic, that a FRACTAL IS:

The 'SET' (look up Mathematical sets) of all the Points, on the COMPLEX PLANE (look up complex numbers) which when iterated through a fractal equation, does NOT escape to infinity. (For example, the Mandelbrot is , z(n+1) = z(n)*z(n) + c Where 'c' is the point you are testing......).

If this is any help, please say so!

74.199.8.90 (talk) 22:45, 8 August 2009 (UTC)

No, I'm afraid that is not helpful. The sets you describe are only one example of fractals. The definition in the article is good.--seberle (talk) 17:59, 12 August 2009 (UTC)

I'm thinking I meant more of a specific ALGORITHM explanation, how to actually visually generate a fractal. Mostly, because this does not exist in articles about specific fractals. —Preceding unsigned comment added by 74.199.8.90 (talk) 21:33, 27 October 2009 (UTC)

Featured article again?

Now that the article has references and has been improved in various ways, perhaps we should reclassify it as a "featured article" again? Soler97 (talk) 09:00, 1 November 2009 (UTC)

The article would have to go through the featured article review process first - see WP:FAC for details. Getting an article successfully passed to FA status often involves a lot of work - take a look at Wikipedia:Featured article candidates/Euclidean algorithm/archive1 for a fairly recent example. Gandalf61 (talk) 16:12, 1 November 2009 (UTC)

Self similar?

Not all fractal sets are self similar, some are only self affine. (see for example Faloner's "Fractal Geometry: Mathematical Foundations and Applications".Wilmot1 (talk) 19:44, 1 November 2009 (UTC)

The concept of self-similarity includes self affine transformations. The "similariies" in self-similarity can be more general than geometric similarities. Gandalf61 (talk) 09:41, 2 November 2009 (UTC)

Links to other topics

I've linked the text concerning Fractal Art and Fractal Music to their associated articles in the "Applications" section. However this means that Fractal Art is now linked to in three places: in it's own "In Creative Works" section, in the "Applications" section and in the "See Also" section. Surely only one location is necessary? I propose to remove the link from the latter two sections. FatPope (talk) 00:23, 6 March 2010 (UTC)

No immediate objections so I've gone ahead with this change FatPope (talk) 09:48, 8 March 2010 (UTC)

Criticalmess (talk) 21:10, 24 March 2010 (UTC) History of Mandelbrot fractal Think this might be useful for putting fractals and their history in perspective - http://classes.yale.edu/Fractals/MandelSet/MandelMonk/MandelMonk.html Apparently, the first occurence of a calculated fractal is earlier than thought. Should this be incorporated somehow? Before editing the article, thought I'd talk this through with the editors here?

Seriously? That was an April Fool's joke. Look it up.TheRingess (talk) 21:22, 24 March 2010 (UTC)

Criticalmess (talk) 19:39, 4 April 2010 (UTC) Ah indeed - my bad -- saw it referenced elsewhere, and no April 1st date was listed. My apologies - nice catch! Nice example of iterated function system animation, trough not for an article: IFS fractal 1 Edo 555 (talk) 13:45, 11 September 2010 (UTC)