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The fractal dimension of an object is clearly not always, and never is, greater than the dimension of the space containing it. By definition the dimension of an object is less than the dimension of the space containing it.
The attempted analogy to lines and planes is utter nonsense; the length of the Koch curve is the same as any line: infinite, and the dimension in the conventional sense (coordinates ~ degrees of freedom) is precisely 1. Fractal dimension is an entirely different concept. Augur ( talk) 06:29, 10 January 2011 (UTC)
Expand and make simpler please Alan2here 23:06, 5 November 2006 (UTC) I agree. Please define terms such as "attractor" for non-mathematicians. Also in figure 1 should r be l? —Preceding unsigned comment added by 71.164.135.92 ( talk) 05:16, 20 December 2007 (UTC)
I thnk the article is not bad. One suggestion for improvement: there are many definitions alluded to, and some discussed. Is it possible to show how differently the various definitions would quantify the fractal character of a given object? If there is some well-known (to mathematicians, at least) object where you could say, "Now by definition (1) we get 1.23 and by definition (2) we obtain 1.27, but definition (3) actually goes to infinity", or some such. —DIV ( 128.250.80.15 ( talk) 06:45, 26 April 2008 (UTC))
Can the parenthetic comment in the article "(which is more or less the Hausdorff dimension)" be elaborated on just a little more, perhaps in a footnote? —DIV ( 128.250.80.15 ( talk) 06:48, 26 April 2008 (UTC))
The parenthetic comment has been modified and the required footnote added. ( 87.4.47.185) — Preceding unsigned comment added by 87.4.47.185 ( talk) 19:56, 1 October 2011 (UTC)
I would think that the introduction could be more general, in that regular dimension are a 'subset' so to speak of fractal dimensions, since they can be represented when D is not a fraction or irrational number (i.e. and integer). This would nicely connect fractal dimensions to 'regular' dimensions, since they probably have something to do with one another, but most of the time they are treated as 'disjoint' areas of knowledge. Rhetth ( talk) 21:54, 4 March 2009 (UTC)
It is not really clear how you get from the expression D=log N(l)/ log l to D=lim epsilon->inf log N(epsilon)/log 1/epsilon. Could you please explain this more in detail? Thank you. —Preceding unsigned comment added by 134.221.149.67 ( talk) 08:36, 20 August 2010 (UTC)
I ran into that problem as well, and I think, looking at the later equations, that "log l" should be "log 1/l". Since no one has answered your question, I'm inclined to go ahead and fix it, and hope that if I'm wrong, someone who understands better will correct the problem. Huttarl ( talk) 21:43, 20 October 2010 (UTC)
There seems to be a sign problem here. The expression, N=L^D, seems right. e.g. the square in fig 1 divided into 4 has N=4, L=2 and D=2 which fits OK (I'm writing L, not l which looks like 'one'). Taking logs gives logN=D.logL, whence D=logN/logL, not D=logN/log(1/L) as written in the article. With the same example from fig 1, D=log(4)/log(2)=+2 (right) whereas D=log(4)/log(1/2)=-2 (wrong sign). One could write D=-logN/log(1/L) instead but I prefer to leave amending the article to someone who knows about fractals. Ajrc ( talk) 22:51, 7 November 2010 (UTC)
Akarpe, your recent edits have created a broken layout and an introduction section that is too long. It also includes too many changes at once, making it impossible to fix them one by one. I've reverted the article to the previous version and saved your edits here so that it can be properly fixed, before placing them into the main article. Please refrain to include them again until we discuss them here. Diego ( talk) 14:22, 6 February 2012 (UTC)
Akarpe ( talk) 14:48, 6 February 2012 (UTC)
I wonder if this gives a lot of readers the impression that fractal sets exist in a mysterious dimension, cuz it did to two people I asked to read the page. But fractal sets have 0 or 1 or 2 or 3 topological dimension just like the rest of the sets in geometry do. Having a fractional dimension doesn't change the set's topological dimension but the phrase seems to say it does. Would it be better reworded? — Preceding unsigned comment added by Akarpe ( talk • contribs) 07:05, 8 February 2012 (UTC)
The lead says "a fractal dimension is greater than the dimension of the space containing it". This seems wrong: it is greater than the object's topological dimension, and (AFAICT) never greater than the dimension of the space containing it. Comment? — Quondum ☏ 19:09, 14 July 2012 (UTC)
http://gosper.org/wikifrac.gif Bill Gosper ( talk) 13:13, 2 November 2013 (UTC)
This image intrigues me quite a bit, since the dimension of the Koch curve seems to be , not . These seem to be fundamentally different ways for defining fractal dimension. Or perhaps there is just imprecision in the picture and I am right to be sceptical about it. Warichnich ( talk) 09:39, 26 June 2017 (UTC)
There is no such thing as a synchronized limit of two variables in mathematics, there are actually some examples why this is not possible. This means that the definition of the correlation dimension is not well-defined. I changed it to a twice limit, the one that actually could make sense, but since I am not sure of this at all I added a citation needed. I was reluctant to remove it since the general idea is clear nevertheless, even with errors in the formula. Hope this is in line with all the Wikipedia policies I don't know too much about yet. The other thing is, I don't really see the point of putting in the formula of a definition without defining the elements in it (cf. Higuchi dimension) but perhaps ideally someone who is fit in such matters could do that. I don't understand the source well enough. Warichnich ( talk) 09:39, 26 June 2017 (UTC)
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In the "Estimating from real-world data" section, the statement, "Nonetheless, the field is rapidly growing..." is not anchored to any dates. Was this written 10 years ago? It likely will not be correct 15 years from now. And I'm just curious about the answer anyway. EvolutionOfTruth ( talk) 03:01, 12 July 2020 (UTC)
The section heading "D is not a unique descriptor" is wrong.
Here a few ways to correctly describe D.
D is a unique descriptor
D is a fractal descriptor
D is a property of a given fractal
D is not a complete specifier
D is one descriptor of a fractal, but is insufficient to define the fractal
Feel free to wordsmith but make the heading conceptually correct! Wcmead3 ( talk) 16:55, 6 January 2022 (UTC)
"It has also been mythologized as a measure of the space-filling capacity of a pattern that tells how a fractal scales differently and in a fractal dimension, i.e. one that does not have to be an integer" What does this sentence mean? Is it incorrect to say that the fractal dimension is a measure of space-filling capacity? Why is it a myth? 2601:18A:C67F:D540:DE2:6CA4:8A5A:594D ( talk) 01:57, 28 January 2023 (UTC)
This article is rated B-class on Wikipedia's
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The fractal dimension of an object is clearly not always, and never is, greater than the dimension of the space containing it. By definition the dimension of an object is less than the dimension of the space containing it.
The attempted analogy to lines and planes is utter nonsense; the length of the Koch curve is the same as any line: infinite, and the dimension in the conventional sense (coordinates ~ degrees of freedom) is precisely 1. Fractal dimension is an entirely different concept. Augur ( talk) 06:29, 10 January 2011 (UTC)
Expand and make simpler please Alan2here 23:06, 5 November 2006 (UTC) I agree. Please define terms such as "attractor" for non-mathematicians. Also in figure 1 should r be l? —Preceding unsigned comment added by 71.164.135.92 ( talk) 05:16, 20 December 2007 (UTC)
I thnk the article is not bad. One suggestion for improvement: there are many definitions alluded to, and some discussed. Is it possible to show how differently the various definitions would quantify the fractal character of a given object? If there is some well-known (to mathematicians, at least) object where you could say, "Now by definition (1) we get 1.23 and by definition (2) we obtain 1.27, but definition (3) actually goes to infinity", or some such. —DIV ( 128.250.80.15 ( talk) 06:45, 26 April 2008 (UTC))
Can the parenthetic comment in the article "(which is more or less the Hausdorff dimension)" be elaborated on just a little more, perhaps in a footnote? —DIV ( 128.250.80.15 ( talk) 06:48, 26 April 2008 (UTC))
The parenthetic comment has been modified and the required footnote added. ( 87.4.47.185) — Preceding unsigned comment added by 87.4.47.185 ( talk) 19:56, 1 October 2011 (UTC)
I would think that the introduction could be more general, in that regular dimension are a 'subset' so to speak of fractal dimensions, since they can be represented when D is not a fraction or irrational number (i.e. and integer). This would nicely connect fractal dimensions to 'regular' dimensions, since they probably have something to do with one another, but most of the time they are treated as 'disjoint' areas of knowledge. Rhetth ( talk) 21:54, 4 March 2009 (UTC)
It is not really clear how you get from the expression D=log N(l)/ log l to D=lim epsilon->inf log N(epsilon)/log 1/epsilon. Could you please explain this more in detail? Thank you. —Preceding unsigned comment added by 134.221.149.67 ( talk) 08:36, 20 August 2010 (UTC)
I ran into that problem as well, and I think, looking at the later equations, that "log l" should be "log 1/l". Since no one has answered your question, I'm inclined to go ahead and fix it, and hope that if I'm wrong, someone who understands better will correct the problem. Huttarl ( talk) 21:43, 20 October 2010 (UTC)
There seems to be a sign problem here. The expression, N=L^D, seems right. e.g. the square in fig 1 divided into 4 has N=4, L=2 and D=2 which fits OK (I'm writing L, not l which looks like 'one'). Taking logs gives logN=D.logL, whence D=logN/logL, not D=logN/log(1/L) as written in the article. With the same example from fig 1, D=log(4)/log(2)=+2 (right) whereas D=log(4)/log(1/2)=-2 (wrong sign). One could write D=-logN/log(1/L) instead but I prefer to leave amending the article to someone who knows about fractals. Ajrc ( talk) 22:51, 7 November 2010 (UTC)
Akarpe, your recent edits have created a broken layout and an introduction section that is too long. It also includes too many changes at once, making it impossible to fix them one by one. I've reverted the article to the previous version and saved your edits here so that it can be properly fixed, before placing them into the main article. Please refrain to include them again until we discuss them here. Diego ( talk) 14:22, 6 February 2012 (UTC)
Akarpe ( talk) 14:48, 6 February 2012 (UTC)
I wonder if this gives a lot of readers the impression that fractal sets exist in a mysterious dimension, cuz it did to two people I asked to read the page. But fractal sets have 0 or 1 or 2 or 3 topological dimension just like the rest of the sets in geometry do. Having a fractional dimension doesn't change the set's topological dimension but the phrase seems to say it does. Would it be better reworded? — Preceding unsigned comment added by Akarpe ( talk • contribs) 07:05, 8 February 2012 (UTC)
The lead says "a fractal dimension is greater than the dimension of the space containing it". This seems wrong: it is greater than the object's topological dimension, and (AFAICT) never greater than the dimension of the space containing it. Comment? — Quondum ☏ 19:09, 14 July 2012 (UTC)
http://gosper.org/wikifrac.gif Bill Gosper ( talk) 13:13, 2 November 2013 (UTC)
This image intrigues me quite a bit, since the dimension of the Koch curve seems to be , not . These seem to be fundamentally different ways for defining fractal dimension. Or perhaps there is just imprecision in the picture and I am right to be sceptical about it. Warichnich ( talk) 09:39, 26 June 2017 (UTC)
There is no such thing as a synchronized limit of two variables in mathematics, there are actually some examples why this is not possible. This means that the definition of the correlation dimension is not well-defined. I changed it to a twice limit, the one that actually could make sense, but since I am not sure of this at all I added a citation needed. I was reluctant to remove it since the general idea is clear nevertheless, even with errors in the formula. Hope this is in line with all the Wikipedia policies I don't know too much about yet. The other thing is, I don't really see the point of putting in the formula of a definition without defining the elements in it (cf. Higuchi dimension) but perhaps ideally someone who is fit in such matters could do that. I don't understand the source well enough. Warichnich ( talk) 09:39, 26 June 2017 (UTC)
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I have just modified 2 external links on Fractal dimension. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
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Cheers.— InternetArchiveBot ( Report bug) 03:38, 5 October 2017 (UTC)
In the "Estimating from real-world data" section, the statement, "Nonetheless, the field is rapidly growing..." is not anchored to any dates. Was this written 10 years ago? It likely will not be correct 15 years from now. And I'm just curious about the answer anyway. EvolutionOfTruth ( talk) 03:01, 12 July 2020 (UTC)
The section heading "D is not a unique descriptor" is wrong.
Here a few ways to correctly describe D.
D is a unique descriptor
D is a fractal descriptor
D is a property of a given fractal
D is not a complete specifier
D is one descriptor of a fractal, but is insufficient to define the fractal
Feel free to wordsmith but make the heading conceptually correct! Wcmead3 ( talk) 16:55, 6 January 2022 (UTC)
"It has also been mythologized as a measure of the space-filling capacity of a pattern that tells how a fractal scales differently and in a fractal dimension, i.e. one that does not have to be an integer" What does this sentence mean? Is it incorrect to say that the fractal dimension is a measure of space-filling capacity? Why is it a myth? 2601:18A:C67F:D540:DE2:6CA4:8A5A:594D ( talk) 01:57, 28 January 2023 (UTC)