Talk:Fractal/Archive 2

Hacking

Someone ruined this text with obcenities, so I reverted it to the penultimate saved version.Nikos.salingaros 23:26, 12 May 2007 (UTC)

Hello guys! I made some fractal images for the swedish page: Sv:Fraktal, copy them to here if you like, Sv:User:Solkoll --80.217.177.185 20:11, 10 Jul 2004 (UTC)

Broccoli Image

I think the broccoli image was a most excellent example of fractal-ness in real life. It was removed on 16:06, 3 Apr 2005 by User:Brian0918 without a hint in his edit message ("converted pics to gallery...") that he removed it. I vote for putting the image back into the article. -- Yogi de 20:09, 14 Apr 2005 (UTC)

Speaking of images (Mandelbrot Image at top), I was under the impression that, although the Mandelbrot was highly complex (like a fractal), it was not a fractal because it is not self-similar at all loci Dragoon235 05:34, 27 January 2007 (UTC)

{{attention}}

I see you have listed the featured article fractal on Wikipedia:Pages needing attention with the note "poorly organized; some parts may be expressed better". Can you be more explicit about what further work you think needs to be done on the article ? How can its organisation be improved ? Which parts can be expressed better ? Perhaps if you create a list of specific issues on the article's talk page, then we can try to reach a concensus on the way forward. Gandalf61 15:50, Nov 25, 2004 (UTC)

Really, that's a featured article? That's interesting. It just... doesn't seem to flow very well. The language is a bit odd in places; for example, the intro contains the terrible definition A fractal is a geometric object which is "broken up" in a radical way, which is literal but not accurate (does that definition fit broccoli?); also calculus is said to "zoom in" on "objects" to "gain control of them" (how is anyone supposed to understand that?).

It (zooming) is a metaphor being used in an introduction. People are forever being told about zooming in on Mandelbrot sets. The coastline example argues in terms of zooming by change of scale. It's journalistic but I imagine most readers can cope. As for broken up - that is quite accurate and to the point. It's the broccoli that might be criticised. Charles Matthews 17:42, 26 Nov 2004 (UTC)

[[Image:Gasket14.png|128px|right|thumb|A [[Menger sponge]]]]

But the article doesn't say zooms in on fractal drawings, it says traditional calculus zooms in... which is nonsense.

No. Charles Matthews

Huh? Try adding that statement to the calculus article. --[[User:Eequor|ηυωρ]] 19:38, 26 Nov 2004 (UTC)

It would be a perfectly good approach to calculus, given modern computer graphics, to zoom in on small areas of a graph. In calculus you would see a line, or at worst a corner. That would be the point: after a while it doesn't change when you magnify. Calculus is still taught to serve the needs of mathematical physics of the nineteenth century; so much the worse for it. By the way, please stop it with the page name changes without consultation; whatever the agenda is, it is not appreciated. Charles Matthews 20:15, 26 Nov 2004 (UTC)

It may be a workable approach, but it's a terrible definition. Properly speaking, calculus has already "zoomed in" to the infinitesimal level before anyone examines for themselves. It's meaningless to talk of "zooming" once one understands the underlying principles.

The "agenda" is neutral point of view, a little-known part of Wikipedia policy. --[[User:Eequor|ηυωρ]] 21:08, 26 Nov 2004 (UTC)

NPOV doesn't apply in that way to article titles - that's not an argument. Apply it all you like to the article text. It's a poor reason to start changing things, without discussion, and without authoritative support. Charles Matthews 21:58, 26 Nov 2004 (UTC)

Regarding broken up: who would consider the image at right to be "broken up"?

Broccoli certainly exhibits fractal properties; if we are to say that it is impossible for physical objects to be fractals, we would have to throw out most of the article (Britain's coastline, mentions of trees or ferns, and all the images). The difference between mathematical and physical fractals is only a matter of semantics. --[[User:Eequor|ηυωρ]] 17:54, 26 Nov 2004 (UTC)

No it isn't. Charles Matthews

The order of the sections is jarring; I suspect the anecdote about Britain's coastline could be more clearly connected to the rest of the article. It isn't immediately obvious what the infinite shore has to do with any of the other images on the page aside from the Koch snowflake, and there's hardly any mention of that topic either. Both are related to the Hausdorff dimension in a very specific way, but the article doesn't even touch on their relation. Which is quite unfortunate, because the reader can't find out more at Hausdorff dimension — that article is an abstract lump of ugly math.

The Categories and Definitions sections are disorderly, and the latter is mostly redundant. A proper definition should be given in the lead section; the extra details can probably be merged into the rest of the article. As it is, it's vaguely like finding Mandelbrot's lecture notes in the middle of his book.

Also note that the Definitions section introduces the (supposedly) correct definition and then dismisses it offhand as being too difficult. Surely some difficulty is to be expected when discussing non-Euclidean geometric objects which have a noteworthy Hausdorff dimension. --[[User:Eequor|ηυωρ]] 17:02, 25 Nov 2004 (UTC)

Would you mind if I copied your comments above to Talk:Fractal ? Both the Introduction and the Definitions sections have been discussed at length there. Their current state is a compromise between two points of view, which could be characterised as the mathematically rigorous view and the understandable to the general reader view. Like all compromises, it is not ideal. Anyway, I think it would be good to see your comments on the talk page. Gandalf61 17:37, Nov 25, 2004 (UTC)

Guys guys guys!? Why don't we just discuss "merging fractal animation"? Silver The Slammer 12:08, 25 October 2006 (UTC)

How Long is the Coast of Britain?

I think most of this section should be moved out. It currently breaks the page up in an odd way. Charles Matthews 10:19, 28 Nov 2004 (UTC)

Yes, I have often this article is not the right place for the Coast of Britain section. Since the section is mostly a description of Richardson's research on the measured lengths of coastlines and borders, I have moved this material to Lewis Fry Richardson. Gandalf61 11:29, Nov 29, 2004 (UTC)

Proposal to remove {{attention}} tag

How would people feel if the {{attention}} tag was now removed from this page ? I think most of the points raised by Eequor when he tagged it in November have been addressed. Gandalf61 14:39, Jan 1, 2005 (UTC)

I just recently read the article for the first time, and I think flows very nicely now, imho. --MPerel 03:01, Jan 6, 2005 (UTC)

I see that Stirling Newberry has now removed the {{attention}} tag, so I have also taken fractal off the list at Wikipedia:Pages needing attention/Mathematics. Gandalf61 10:32, Jan 6, 2005 (UTC)

Nope! It's still there!!!!! Silver The Slammer 12:09, 25 October 2006 (UTC)

Further Reading

I changed the bibliographic sources to standard MLA format which can be autogenerated at this site: http://www.easybib.com/ --MPerel 03:03, Jan 6, 2005 (UTC)

discrete mathematics

The iterative calculative nature of the Mandelbrot set needs to be mentioned to reflect the mathematical relevance of having it there.

If I got it wrong, correct it please.  ;) -- Zalasur 04:48, Mar 25, 2005 (UTC)

Hm I added this comment to the wrong page; please ignore. -- Zalasur 13:48, Mar 25, 2005 (UTC)

First sentence, self-similarity

Sorry, that's just wrong - self-similarity is not the defining property of a fractal.

Charles Matthews 14:10, 25 Mar 2005 (UTC)

So the intro was changed 17 December by User:EastNile, who hasn't edited since. I think we needn't take that as authoritative on fractals. The first para certainly needs to go back to something more like it was before. That's because fractal does now have some strong connotations, but a rather particular actual denotation. (I hope that clarifies a bit what the issue is here: it is not as if self-similarity is irrelevant.)

Charles Matthews 14:22, 25 Mar 2005 (UTC)

I think we should make it clear in the beginning that fractal is NOT a precise mathematical term, like say group. There is NO common definition in mathematics what a fractal is.

Danimey 22:59, 18 January 2007 (UTC)

and so which appears

I don't believe this string of words, found in the first sentence in the article, belongs together. And even if it does somehow belong together, it sounds very awkward.

Here is the sentence:

"A fractal is a geometric object which is rough or irregular on all scales of length, and so which appears to be 'broken up' in a radical way."

The "so which" seems to be superfluous. It adds only awkwardness, and probably causes the sentence to be improper.

Another suggestion, dilational or magnification symmetry is not addressed in the article. This is the angle that Yale takes, although it doesn't seem to be a traditional path for explaining fractals. What I like about the magnification symmetry approach is that it places fractals in context with other mathematical objects/ideas: the butterfly has line symmetry, bricks have translational symmetry, an octahedron has reflectional symmetry, fractals have magnification symmetry. It gives the sense that fractals aren't just a rogue field and have a place in an old and established order of mathematics. It is reminiscent of placing them within an organization chart, and from the hub, or node of magnication symmetry, it is easy to move between the different types of fractals. In one sense, it is good that fractals are set apart, in another, it doesn't help the field to be perceived as an antithesis to standard math. It goes back to the old preschool and kindergarten exercises of identifying in what ways things are different and in what ways they are the same.

I think your magnification symmetry is what the article calls exact self-similarity. As the article explains, this symmetry is a property of some types of fractal, but not of all fractals, which is why the second sentence of the article says that fractals "may ... have a self-similar structure that occurs at different levels of magnification". Various other attempts at an opening paragraph definition of fractal have been attempted, but they have been rejected as being too long, too complex, too mathematical or too inaccurate. The current version seems to sit on the boundary between what is acceptable to specialists and what is accessible to the lay person. Gandalf61 09:43, July 11, 2005 (UTC)

Magnification symmetry does not imply exact replication, it only requires that an object is approximately unchanged under magnification. Although it would apply to self-similarity, it is applicable to multi-fractals. This presentation comes from a credible source, Mandelbrot and Frame on the Yale website. Self-similarity, yes, but not necessarily.

ok guys i need help

ok someone please tell me what a fractal is in english? Explain it too. and define iteration and self similarity. if you get it post it. o by the way, when you explain, please use only around like 6th grade vocabulary, otherwise the words are too complicated for me.-dran

Please NEVER put a flag like that in the main article again, it is very bad form, those of us that monitor these pages also monitor the talk pages too. I would suggest this link: Fractals, in Layman's Terms your questions may be answered there. DV8 2XL 03:50, 17 November 2005 (UTC)

fractal galleries

who decides what fractal galleries are included on the fractal page?

The editors DV8 2XL 03:13, 28 November 2005 (UTC)

It's a concensus situation. There are some Wikipedia policies and gudelines, but most cases are not black and white, so a concensus view emerges. As a rule of thumb, a link to an obviously commercial web-site inserted by an anonymous user with no previous discussion is more likely to be removed than a link to an informative web-site inserted by a signed-up Wikipedia user who has previously discussed his/her intentions on the article's talk page. If you feel strongly that a particular link should be included in this article, I suggest you explain your reasons here on the talk page and invite discussion. Gandalf61 12:40, 28 November 2005 (UTC)

Could we have some more diversity at the top of this article? We currently have two pictures from the Mandelbrot set there, and nothing else. This Mandelbrot set is so common in the article and in this topic so we might confuse readers to the point that they think that Fractal == Mandelbrot set. So let's find a beautiful different example picture to put alongside the beautiful original mandelbrot picture. — Sverdrup 14:21, 28 November 2005 (UTC)

Self-similar

If I recall correctly, the Mandelbrot set isn't self-similar though it has fractal dimension. There are those rigid sticklers that would claim that the Mandelbrot set isn't technically a fractal, though it has fractal characteristics. This is ignored in the article. I was originally going to dispute the facts of the article, but have decided that this objection may be more cosmetic. Thoughts? --ScienceApologist 13:55, 2 February 2006 (UTC)

See Mandelbrot's definition of a fractal and the discussion of definitional problems in the Definitions section, and the different types of self-similarity described in the Categories of fractals section. You could add a sentence to the article to say that some people do not include the Mandelbrot set within their definition of fractal, but I think a reference supporting this statement would be helpful, as it would be a minority view in my experience. Gandalf61 13:34, 3 February 2006 (UTC)

I think that strictly speaking the Mandelbrot set itself is not fractal, but the boundary of the Mandelbrot set is fractal. The same applies to the Koch snowflake where the set itself is measured in m² while the circumference is measured in m^1.2. Anybody know the exponent for the circumference of the Mandelbrot set? Another thing. When the complex plane is drawn with 1 to the right, then the symmetry axis of complex conjugation is horisontal, and the Mandelbrot set is shown lying down. It is more pleasing to the eye to see the monster standing up, with 1 upwards. Bo Jacoby 07:58, 3 February 2006 (UTC)

Please read this forum thread between me and my friend about this topic, and make some changes.--Max 10:41, 3 June 2006 (UTC)

Removed "book review"

This is for Gandalf61: Who are you? the tin god of references? This is called an annotated bibliographic entry and there's nothing wrong with it. I'm putting it back. It's not a "review" its an annotation. It's useful for folks who want to read more. wvbaileyWvbailey 18:13, 27 February 2006 (UTC)

This is such a nice page

I like the animation, the beautiful fractals. I sent my nephew here (he's taking 8th grade algebra, was doing a project on fractals) for a look-see. Nice work is going on here. wvbaileyWvbailey 23:53, 7 March 2006 (UTC)

What's wrong with the random fractal? Is it not a fractal? If not, discard it. If so, what's wrong with it? If it helps the 8th-grade nephew understand, then put it back. Thanks. wvbaileyWvbailey 23:58, 7 March 2006 (UTC)

I liked the fern, the colored one. Why did it have to go away? I don't like all this page-hopping. Sigh. wvbaileyWvbailey 03:02, 8 March 2006 (UTC)

I don't think it belonged on this page--too much detail in a niche area for a general article on fractals. Sorry about the page hopping, but I really think it's more at home in the IFS article, which actually badly needed an example. --Experiment123 03:10, 8 March 2006 (UTC)

I am the author of the animation and IFS colored fern... and I aggree the fern is better in the IFS article. Tó Campos 12:23, 8 March 2006 (UTC)

Agreed. Thanks for the explanation.wvbaileyWvbailey 17:30, 8 March 2006 (UTC)

Reorganization and rewrite

I just reorganized this article and rewrote some bits. I'd like this article to stay accurate mathematically while recognizing the colloquial uses of the term fractal. --Experiment123 01:36, 8 March 2006 (UTC)

I see some etymology was added back to the intro. Not sure how critical the etymology is, but I'm still learning my way around Wikipedia style. I did move the bit about "monster curves" to the paragraph on the Koch snowflake, since "monster curve" was never synonymous with fractal, but instead used to describe a particular set of examples.

One of the books that I cited, Fractals for the Macintosh, (Jones, section titled "A Gallery of Monsters") definitely refers to "monster" curves -- specifically the Koch "snowflake" and the Peano "space-filling" curve. According to this book, the Peano curve led Hausdorff to his definition of "dimension" -- the snowflake has Hausdorff dimension of 1.26, the Peano curve has dimension 2.0 etc. so:

"...these are both fractals by Mandelbrot's definition" (Fractals Definited 8)

The other book, Fractals (Lauwerier), refers to the snowflake as an example of a "pathological" curve:

"Now, nearly a century later, such 'pathological curves' (as they were called) turn out to occur everywhere in pure and applied mathematics" (p. 33).

This book corroborates its Hausdorff dimension of 1.26.

So there you go. Whether or not these books are accurate is another question. So is the snowflake a "monster" or just "pathological"? I think one or both words would be fine (kids love the word "monster" so I vote for that one). I liked the intro before it was changed. wvbaileyWvbailey 17:52, 8 March 2006 (UTC)

The books are right, the Snowflake and its cousins were called "monster curves." But they are just a small set of examples, curves whose metric properties are surprising. Cantor dusts and Sierpinski carpets also predate Mandelbrot, but certainly weren't called curves. Various dynamical-systems-related fractals(Julia sets, etc.) were also known well before Mandelbrot. In other words, it is misleading to say that fractals were called "monster curves," though it is true that monster curves were fractals by today's definition.

If you want to emphasize the strange properties of fractals in the introduction, you could say something like, "Some early examples of fractal sets were referred to as 'monsters,' due to their seemingly paradoxical properties." --Experiment123 18:05, 8 March 2006 (UTC)

applications

i didn't want to edit the page without getting people's opinions on whether financial analysis should be added to the applications section. i've just finished mendelbrot's "the (mis)behavior of markets," and while he isn't able to replace the valuation formulae stemming from the efficient capital market hypothesis, he makes some very lucid suggestions that others appear to have followed in their research. while the pure number of citations does not tell us whether they agree or disagree, his financial work has at least been taken seriously. thoughts?afuturehead 22:39, 29 March 2006 (UTC)

There's dispute as to how much credit Mandelbrot deserves for finding fractal patterns in financial markets. Some say he hasn't done much other than attach the label "fractal" to analysis done by other people.

Page Layout

The fractal fern overlaps with the broccoli and the page has a horizontal scrollbar at 1280x1024, Ubuntu, Firefox 1.5

I'm afraid it rarely renders well for me either. Unfortunately, I don't know enough about image formatting and wikipedia to understand why. I am also using Ubuntu at the same resolution but firefox 1.0.7. --Richard Clegg 21:46, 4 April 2006 (UTC)

Possible Copyright violation in history section

While searching on google for "Anklets of Krishna" I found the following webpage:

http://classes.yale.edu/Fractals/Panorama/Art/Kolams/Kolams.html

The material about kolams seems to be a word for word copy of that material.

This seems to be a likely copyright violation. So I removed it.

Can anyone show that it isn't?

Plus even if it isn't, I'm not sure it belongs in the history section, perhaps it belongs in an examples section.

TheRingess 17:47, 16 April 2006 (UTC)

Colour?

How are generated fractals coloured? Every image of fractals I've seen is in a kaleidoscope of colour, but I can't find an explaination of which bits of the image get which colour.

I'll explain how it's done for the Mandelbrot fractal. This is a set generated by taking a point in the complex plane and repeatedly performing the same operation on it. Most points end up whizzing off into the distance, but some stay close to where they started. These are part of the Mandelbrot set and are colored one color (usually blue or black). If a point isn't in the set, it will diverge to infinity and you can tell a point isn't in the set once it reaches a certain distance from the origin, a circle of radius 2. The number of steps it takes to cross that boundary is the color it gets. So if it takes only one step, it's given color #1. If it takes ten steps, color #10. Points that start close to the edge of the Mandelbrot set take a long time to move past the boundary. That's where the complicated colored bands come from. Other fractals are colored in a similar way. I hope this explanation helps. Reyk _YO! 01:45, 4 June 2006 (UTC)

Quasicrystals and fractals

The pinwheel tiling, as its name suggests, is known generally as an aperiodic tiling but it is also a fractal. It is obtained by dividing a 1:2:sqrt(5) triangle into five smaller triangles of the same shape or conversely by inflation - surrounding one such'seed' by four copies and repeating the procedure with the larger figure. Thus tilings are 'extended' to infinity while fractals are usually thought of as divided down to infinity. Anyway, I believe that the topics of fractals and quasicrystals should be perceived as typical for the end of 20th century mentality.

The infinite aperiodic sequence 101000101000000001010001010... is the Cantor set written up from the atom '1', but I am not sure if it is 'fractal' in a meaningful way. However many aperiodic sequences are 'fractal' in the disputed self-similar way: if you strike out every other term you get the same sequence, e.g. in 0110100110010110...(Thue-Morse; you can see it in the list of self-similar sequences in the OEIS). Aperiodic tilings are easily constructed out of such sequences. This could be an other argument for the link between aperiodic and fractal structures. al 17:03, 13 July 2006 (UTC)

Good article nomination

Hi all,

I'm happy to promote this article to be a good article but I made some changes to the article in line with what I thought the article was trying to say. Specifically I tried to highlight comparisons between the topological/Hausdorff dimension. If someone can verify my changes are correct I will promote this article.

Cedars 01:25, 14 July 2006 (UTC)

Since my changes weren't verified this article will not become a good article. Overall though I think this article could benefit from some more insight into the mathematics of fractals. Also the "might (or might not)" statements should be removed from the article and rephrased if necessary. Cedars 08:52, 23 July 2006 (UTC)

Fractal Art Galleries Section

I deleted this section because there seems to be no criteria for what constitutes a notable link. TheRingess 00:31, 22 July 2006 (UTC)

Problems with Cantor Set paragraph?

(In the Examples section.)

As far as I can tell, we don't ever explain what "a Cantor set" is. The linked article is mostly about the standard Cantor set, with allusions to alternatives. Presumably a Cantor set is something like "Anything obtained from an interval by repeatedly removing middle portions from segments"? And the "might (or might not)"s are about the fact that you can get something with Hausdorff dimension zero by increasing how much you remove, or Hausdorff dimension 1 by decreasing how much you remove? I think we should clarify this somehow.

Also, the last sentence is inconsistent with the rest of it: "By comparison the topological dimension of any Cantor set is 0 and hence all Cantor sets are fractals."

And I agree with the above about "might (or might not)." Maybe deleting the "(or might not)" achieves the desired effect. Or something else?

--Dchudz 14:31, 28 July 2006 (UTC)

This stuff is all gone now anyway. As good a way to deal with my problems as any. Thanks, Beaumont. Dchudz 17:42, 3 August 2006 (UTC)

Well, actually I find that the examples section should be rewriten and expanded. A list of (more) examples within some important categories should do (curves, planar IFS, Mandelbrot-Julia, logistic-map-related, strange attractors, stochastic fractals...). Detailed discussion of each example could be moved to a separate article. IMHO, at the present the examples are the core of the actual "definition" of what fractal really is. --Beaumont 18:53, 3 August 2006 (UTC)

New Definition, Real Line...

This new definition in the opening paragraph better matches my experience with the word "fractal" than the strict. But it's still not quite right: As we say in a later paragraph, the real line wouldn't be called a fractal, but it does have three of the five ("most") of the characterizing properties... What to do? -- Dchudz 18:42, 3 August 2006 (UTC)

Formally you're right. And formally, we may split the first feature into two (as in the source) and define "most of" to be 4. Personally, I find this unsatisfactory. Maybe it is better to refer explicitly to the examples? Anyway, this is the best definition I've heard about. --Beaumont 19:00, 3 August 2006 (UTC)

After a while I added an interpretation that may help. Actually, natural look excludes staight lines, squares etc. In nature we have no straight lines. --Beaumont 15:42, 4 October 2006 (UTC)

Fractal animation

I am trying to start this(Fractal animation) article, and I have a crude beginning. I feel it would benifit from more minds. Thanks! HighInBC 21:07, 3 August 2006 (UTC)

It's nice, but I'd like to propose that Fractal animation be merged into this article. I don't really think animation alone warrants its own article. Gregly 15:15, 6 September 2006 (UTC)

I originally did not include it here because this article is rather long. I don't object to the merge. I admit the current article is sparse, but the subject is rather extensive. HighInBC 16:17, 6 September 2006 (UTC)

Concave/convex

Is it possible to have a convex fractal? I think this would be an interesting property to exclude, if it's so.

I guess so. Take a Cantor set and wrap it round a circle, construct a convex polygon by joining the points. --Salix alba (talk) 11:08, 16 October 2006 (UTC)

I'm not sure... Well, when we take the convex hull of just 4 points (0,1/3,2/3,1) wraped anyhow, we get the filled quadrilateral. Adding some more points outside results in a strange figure; maybe fractal, but I can not see this. Anyway, possible "fractal behaviour" could be observed just at the boundary and, at the first sight, the boundary looks like a Lipshitz curve a.e. (Cantor has gaps of length 1/3, 2*1/9 etc). To compare with a simple example of von Koch snowflake - fractal bounded convex domain, not a real fractal inside though.Beaumont 12:31, 16 October 2006 (UTC)

I think the "Cantor polygon" described would not be fractal since its length would be finite (less than the circumferenece of cricle) and its area would be finite (less than area of circle). The curve of the Koch snowflake is infinite. I doubt we could create a convex curve which is fractal though I cannot prove it. --Richard Clegg 13:16, 16 October 2006 (UTC)

It's not clear to me why the "Cantor polygon" is not a fractal. It is self-similar under the two polar co-ordinate transformations

$\theta \rightarrow {\frac {\theta }{3}}\quad \theta \rightarrow {\frac {4\pi +\theta }{3}}$

and its boundary contains fine structure at all scales. It's not a very sexy fractal, since it can't (by definition) have any winding fjords or inlets, but I think it is a fractal nonetheless. Gandalf61 14:15, 16 October 2006 (UTC)

Its Haussdorff dimension is equal to its topological dimension is it not? I guess many people do not consider that a strict requirement though. --Richard Clegg 15:06, 16 October 2006 (UTC)

The question provoked some interesting (original?) research, so let's get back to the origins. If you want some properties of fractals, we have tons of them, see any book by Falconer, Mandelbrot or others. And, apparently, convexity (or concavity) is not the the big issue. We may think of another way of enriching the article (projections, products, you name it).

To conclude, I believe that not-too-sexy examples of fractal bounded domains are the only possible convex fractals. On the other hand, I have never heard about such a statement in the literature and, unless someone finds an actual reference, we have no reason to discuss it further, no reason to insert our research into the article (actually, I suspect that from math point of view the question may be somehow trivial and was not really studied; but any proof of the contrary by some refs will be welcome).Beaumont 15:25, 16 October 2006 (UTC)

young

Why don't they aim for a younger crowd?

Silver The Slammer 12:02, 25 October 2006 (UTC)== !@$#%@$ ==

WHO UNEDITED MY PAGE?! —Preceding unsigned comment added by Power Gear (talk • contribs) October 23, 2006

Please understand you do not own this page and anybody is allowed to edit it, or unedit it. HighInBC ^{(Need help? Ask me)} 13:52, 23 October 2006 (UTC)

People! Stop fighting and check out the article on Silver The Hedgehog.

Usage of the word euclidean

All known fractals are acceptable in euclidean geometry (opposing what many "applied" students say), and all of them are constructed using euclidean geometry (the original article presenting the koch snowflake, for an instance, uses nothing but eucidean geometry to derive their properties). It may be incredibly hard to describe in terms of simple drawings like lines and circles, but they are euclidean;

Expressions like "non euclidean" or "contrary to euclidean" should be changed to "not traditional".

--200.17.137.71 22:18, 25 October 2006 (UTC)

Reordering Sections

I have to agree with some of the other comments on here that the article doesn't flow very well, and I'd quite like to see the article upgraded in status, so can I suggest the following (they're not minor changes, so I thought it better to discuss them first). I'm quite happy to do it myself, but I know that some people have already put a lot of effort in, so there may be some reasoning (e..g- behind the ordering as it stands), that I'm unaware of:

1. Change the ordering of the sections (numbers reflect thier current ordering):

• 0 Intro
• 1 History

• n "Demonstration of how fractals were discovered" (& * 3 Self-similarity dimension) - This would cover the concepts that are now considered to be typical of fractals. I know that the 'Coastline of Britain' article now has it's own page, but it would be useful to show at least an overview of how fractals typically demonstrate some 'infinite length' behaviour. This could then be tied into the Koch curve as a more rigorous mathematical treatment. Perhaps some reference should also be made back to the Falconer's points that are mentioned in the intro paragraph.

• 5 Classification of fractals (& * 2 Examples) - These ought to be combined into one topic so e.g.- the ordering would be title -> definition -> examples

• 4 Generating fractals

• 6 Fractals in nature - This should perhaps be moved to it's own page as it doesn't add much to the article as an overview of fractals. Perhaps mention such a page in the 'applications' section (since Pollock crops up)

• 7 Applications
• 8 See also
• 9 References
• 10 Further reading
• 11 External links

         o 11.1 Multiplatform generator programs
         o 11.2 Linux generator programs
         o 11.3 Windows generator programs
         o 11.4 Mac generator programs
         o 11.5 MorphOS generator programs

Apart from that it's just the links that need weeding and/or re-ordering in terms of usefulness since there are such a large number of them (which may be more appropriate in the fractal art page?).

-- Submanifold 26/12/2006

Koch Snowflake

In the article it talks about the snowflake having a finite area, isn't it infinite? As the triangular area is added to the existing shape no other areas are taken away, meaning that every step it gains area and perimeter. Thanks Onefournine 10:56, 30 January 2007 (UTC)

The area is not infinite since a koch snowflake is enclosed in a finite region in the cartesian plane.TheRingess (talk) 14:37, 30 January 2007 (UTC)

Topological dimension of space-filling curves

I don't understand why things in brackets are necessary in the fourth feature:

• It has a Hausdorff dimension that is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).

Well, my "main" question would be: "Isn't topological dimension of any curve = 1?" Because the brackets say that topological dimension of Hilbert curve is 2 (or more). 89.164.4.146 15:07, 2 February 2007 (UTC)

Should the example of "Shikhar" of the Hindu Temple be included or not?

I feel the shikhar of the Hindu temple, which is the most visible form of fractal in its architectural form, that derives itself from the meaning and form of the "temple" be portrayed in some relevant section of the article[1]. The history section begins with the mathematical history. The examples from nature section limits itself to imagery from nature. If we take just the imagery the temple "shikhar" can be placed in it, by renaming it to something like "visible examples of fractal" or create a new section on "Application of fractals"(?).

To quote references from the net, there is one example that uses 2 different examples of the Hindu temple as examples of "fractals in architecture" [2]

The philosophical base of "self similarity" and its meaning is provided in Stella Kramrisch's The Hindu Temple. --Nikhil Varma 05:16, 21 April 2007 (UTC)

Here are some detailed studies related to Shikhar:

1. A Computational Approach to the Reconstruction of Surface Geometry from Early Temple Superstructures [3]

2. The Generation of Superstructure Geometry in Latina Temples: A Hybrid Approach [4]

3. ON RECOVERING THE SURFACE GEOMETRY OF TEMPLE SUPERSTRUCTURES [5]

--Nikhil Varma 05:46, 21 April 2007 (UTC)

Facinating stuff. Cross checking with the def of fractile at to of page

A fractal as a geometric object generally has the following features:

• It has a fine structure at arbitrarily small scales. No - there is a limit to the scalling applied
• It is too irregular to be easily described in traditional Euclidean geometric language. Maybe - it does have a recursive/procedural method of definition - however the limit to scalling mean that there is onlya finite number of each element so it can be define in a traditional manner
• It is self-similar Yes - to a limited degree
• It has a Hausdorff dimension that is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve). No - the limit to scaling prohibs this
• It has a simple and recursive definition. Yes

So whether it really classes as fractal is not clear cut. Further the above assesment would be WP:OR on my behalf.

What we would really need is something in the litrature identifying it as fractal. The webpage link is by Michael Frame and Benoit B. Mandelbrot so that probably counts, in their common mistakes page they discuss that no physical fractal can exhibit scaling over infinitely many levels, nevertheless to make a plausible claim of fractality, a pattern must be repeated on at least a few levels. So with this vesied characterisation it would count as fractal.

I think rather than just this one example it might be worth discussing all the examples in the Architecture page. --Salix alba (talk) 14:53, 21 April 2007 (UTC)

what about fractals in architecture?

This being the main page for Fractal, to make it more complete, I think the example of the Hindu temple and also other architectural forms [6]that resemble the imagery[7], if not as systematic as the geometry of the Hindu temple, should be included to provide the reader of the extent of "fractals" in our world.

I am still scavenging to fetch resources from the net that provide more detail studies of the fractal geometry and its mathematics involved in the Hindu Temple architecture. More than imagery it is the mathematics behind the design that can more strongly demonstrate the application of the concept to design.

We can even provide further links to aspects of fractals and its "need" or effect on people, from an architectural point of view.[8]

Question: Should we have a separate page on "Fractals in Architecture"? and provide a link on the main page (with an inspiring image) to that page?

--Nikhil Varma 05:11, 21 April 2007 (UTC)