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Archive 1 |
Could you explain shortly how to determine the Hausdorff dimension of the Penrose tiling? In what sense it can be seen as a true fractal? At some scale its geometry is no longer "fine". The citation has no details. Beaumont 21:02, 2 October 2006 (UTC)
Felt a fleeting temptation to link it to Slartibartfast... AnonMoos 19:20, 9 December 2006 (UTC)
I believe that this is discontinuous and thus not a "curve", yet I agree it belongs in this context as it shares other important properties with these curves. See < http://cap-lore.com/MathPhys/Zorder/> for discontinuity argument and also non-differentiability. NormHardy 19:18, 26 December 2006 (UTC)
Several of the listed examples (like the Smith-Volterra-Cantor set, the Mandelbrot set, and the space-filling curves) seem to have the same Hausdorff dimension and topological dimension, and therefore they don't meet the definition of fractal at the beginning of the article. Maybe the definition should be changed to something more like the one on the fractal page. —Preceding unsigned comment added by 160.39.28.117 ( talk) 07:18, 30 November 2007 (UTC)
Ok
You are right for the Mandelbrot set (corrected, the interresting part is the boundary).
For the space-filling curves, the topological and the fractal dimension are actuallay different. Prokofiev. 7 dec 2007. —Preceding
unsigned comment added by
Prokofiev2 (
talk •
contribs) 17:19, 7 December 2007 (UTC)
Reformatted —DIV (
128.250.80.15 (
talk)
02:55, 28 April 2008 (UTC))
The whole point of so-called 'natural, random' aggregates etc. is that they are products of deterministic chaos. The classification used here is misleading. —DIV ( 128.250.80.15 ( talk) 02:57, 28 April 2008 (UTC))
It seems like they would have the same value, as they are both coastlines. 128.232.241.115 ( talk) 00:38, 10 May 2008 (UTC)
It has been mesured (see reference on the article). Coastlines are more or less irregular and Norway's westcoast is particularily irregular. Prokofiev2 ( talk) 08:32, 13 May 2008 (UTC)
The new article titled Casey Lange fractal seems to fail the google test. Does anybody know anything? Michael Hardy ( talk) 04:26, 20 June 2008 (UTC)
New entry on 60o Fibonacci fractal gives a measured dimension of 1.2075. Seems to me that we can calculate an exact Hausdorff dimension. The kth generation Fk consists of 4 copies of Fk-3 and 1 copy of Fk-6, so the area scaling factor is the positive root of
which is
- same as the 90o Fibonacci fractal (as expected). Linearly, two of the Fk-3 copies are at an angle of 60o, so linear scaling factor is the positive root of
which is
So Hausdorff dimension should be
which is close to the give measured value. I don't have a source for this, however, so it might be discounted as OR. Gandalf61 ( talk) 14:19, 29 June 2008 (UTC)
I was looking for that result all the afternoon. I confirm your calculations are right, Gandalf. Well done ! Prokofiev2 ( talk) 19:59, 29 June 2008 (UTC)
The measurements of all the natural things should have some kind of units. Otherwise they are just meaningless numbers. Asmeurer ( talk ♬ contribs) 00:03, 16 October 2008 (UTC)
I agree. But in this case, the units are of length. While the fractals on the top table might be dimensionless, the bottom ones require them. Otherwise, how do I know your coast of Britain refers to the real Britain or the map, and is it in feet or miles or kilometers. Also, I do believe that most dimensionless quantities are ratios of dimensioned quantities that have the same units, so they cancel out. That clearly isn't the case here. Asmeurer ( talk ♬ contribs) 15:13, 16 October 2008 (UTC)
Gandalf, this fractal has been studied under the control of mathematics teachers, as mentionned in his site : [ [1]] "étudiée dans le cadre de mon TIPE" means "Studied in the frameword of my TIPE". TIPE (see [ [2]]) is a research work for French scientific students . Ok, it's not the "Annals of mathematics", but, for me, it is serious enough and does not go against Wikipedia policies regarding reliable sources (if not, then we should delete half of the mathematics contributions in all wikipedias...). Prokofiev2 ( talk) 10:00, 20 December 2008 (UTC)
Let me list some arguments why I decided to propose this entry:
Now for the weak points:
Prokofiev2 ( talk) 13:26, 20 December 2008 (UTC)
I think perhaps someone has the wrong idea about the meaning of cf. (Latin confer): it means 'compare' (not 'see'), so (cf. Stephen Wolfram<ref name="stephenwolfram.com"/>) invites me to compare Doc W to the fractal dimension of a Sierpinski triangle, an exercise of dubious value. Am I missing some point? — Tamfang ( talk) 02:55, 25 December 2008 (UTC)
The greek letter delta is used both for the Haussdorff dimension and the Feigenbaum constant. Use different symbol for the Haussdorff dimension, e.g. capital D? —Preceding unsigned comment added by 193.174.246.168 ( talk) 09:01, 6 January 2009 (UTC)
Anyone considered nominating this fine list at Wikipedia:Featured lists? -- œ ™ 07:57, 5 June 2009 (UTC)
Does any source qualify rational numbers as a fractal? The example with the box dimension is quite interesting, but it belongs in a diffferent place ( Box dimension, say). I find the rational numbers on this list a bit surprising, so please give some references as to their fractal nature. ptrf ( talk) 15:10, 5 June 2009 (UTC)
MISTAKE —Preceding unsigned comment added by 85.221.173.203 ( talk) 20:17, 9 September 2009 (UTC)
Hausdorff dimension of Menger sponge is log(20)/log(3)!!! —Preceding unsigned comment added by 85.221.173.203 ( talk) 20:19, 9 September 2009 (UTC)
There are some fractal vegetables more wonderful than a simple white cauliflower, as a Search on Google will show. I was past 50 before I first saw a Romanesco brocolli or cauliflower - what a wasted life! P.r.newman ( talk) 10:15, 16 April 2010 (UTC)
Is it me or does it scale really badly? Maybe we need a custom thumbnail? -- 80.175.250.220 ( talk) 11:07, 24 January 2011 (UTC)
http://icpr.snu.ac.kr/resource/wop.pdf/J01/2005/046/R02/J012005046R020474.pdf stated the dimension to be ~2.8, can someone proof that? —Preceding unsigned comment added by 88.65.198.120 ( talk) 19:28, 19 May 2011 (UTC)
Shouldn't the interval removed from the Cantor set be γ((1-γ)/2)m-1 instead, in contrast to the Smith-Volterra-Cantor set?
-- User:Dom 220.255.1.136 ( talk) 13:27, 25 May 2011 (UTC)
The list shows two fractals next to each other (3d Greek Cross and Octahedral), these are two different ways of creating the same limit set. So, I don't think they should be listed as two different fractals. — Preceding unsigned comment added by 98.225.20.68 ( talk) 17:21, 12 November 2012 (UTC)
Hi all, the same method used to calculate analytically dimension of the boundary of twindragon is also used for infinite family of such simple IFS - for example I've just seen that one of them is called 'tame twindragon' in the table: just use
Solve[Det[fin - IdentityMatrix[ie]*x] == 0, x]
and take 2Log[x]/Log[n] of the only reasonable solution in the demonstration getting another nasty formula for 'tame twindragon':
These formulas can be written in plenty of ways - maybe there is some nicer(?)
Cheers, Jarek —Preceding unsigned comment added by Jarek Duda ( talk • contribs) 07:04, 18 July 2010 (UTC)
Titus III ( talk) 05:05, 15 May 2013 (UTC)
Are there estimated fractal dimensions of galaxies, galactic superclusters, or the current model of the known universe? If so, those would be excellent additions to the natural fractals section.
Rememberlands ( talk) 18:23, 15 November 2011 (UTC)
Subsequent measurements have revealed that on larger scales, the power spectrum of galaxies fails to follow the (R/R0) ~ R^1.8 curve. Therefore, the distribution is not a fractal. — Preceding unsigned comment added by SCS137 ( talk • contribs) 14:31, 14 February 2015 (UTC)
Could the Infinity mirror and Kaleidoscope by added to this list? Also Harmonograph and Spirograph. - Shiftchange ( talk) 01:08, 7 May 2017 (UTC)
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I haven't quite understood why a space-filling curve is considered a fractal. Ok, I have an iterative procedure yielding a self-similar geometric object. But in the limit, I end up just with the unit square, which is defnitely not a fractal since topological and Haussdorff dimension both equal 2.
I'm a little puzzled both by the inclusion of this shape and it's linked picture. The limit of the fractal described is just a square. It seems a little strange to consider this a fractal. I know some 'fractal curves' cover the unit square in the limit, but these have other interesting properties in general (continuity, parametrization of the square..) I'm not sure the 'greek cross fractal' needs to be mentioned so much given that it doesn't seem to be a particularly interesting shape in any obvious way. Furthermore, the picture of the 2d greek cross fractal shows an early stage approximation to it. As mentioned the limit would just be a square. Obviously it's not possible to represent the limit strictly, but I find the picture is a little misleading given the above points. A mathematically unsophisticated reader might think the 'fractal' has some fine structure not present in the square. I'll review the page on this fractal and consider changing or removing it from here.
A month ago an unknown user removed half the page with no reason and no discussion I can find. Why? It seems like such a large change to the page should have some discussion first. 173.229.9.179 ( talk) 18:06, 1 February 2019 (UTC)
I propose expanding List of fractals to include more information so that it looks like this and then moving the page to Table of fractals. Thoughts? ➧ datumizer ☎ 19:07, 5 July 2021 (UTC)
The standard parameters for the Lorenz attractor are σ = 10, β = 8/3, ρ = 28.
So: What is the point of listing the Lorenz attractor in this article with the non-standard parameters σ = 16, β = 4, ρ = 40 ???
(To make matters even more confusing, the parameters are listed in nonstandard order: first ρ, then σ, then β.)
That makes no sense at all.
I understand the sentiment. However, note that the meaning that humans attribute to unordered sequences of symbols are purely a matter of culture and that, for example, in cultures that read in different directions than English, such as from right to left, the "natural" order would be reversed. In short, there is no notion of absolute correctness.
It is nice when an offspring source maintains the symbological standard of its citation. I encourage you to be bold and make these changes whenever you encounter them and simply check the box that says "minor edit" and make a note in the change field summary that you have re-ordered the parameters or renamed them to fit a certain style or source. If it is based on a source, please cite that source both in the change and in the article. The change form can just have the URL/DOI; the article obviously needs to have the citation inserted more carefully, and in the format that is currently used for that article.
Thank you for reading, and thank you for caring. As a fellow human, your insights and observations are equally important to us all. I also encourage you to sign your edits and talk-entries. The signing contains the time stamp that allows others to know the rough timeline and history of the development of an article. In short, it is a key piece of the historical record of changes and suggestions, which is very important. (Incidently, the information is still there; it is just not on the page, but rather in the metadata. Putting it on the page helps only humans.) MMmpds ( talk) 17:02, 4 May 2023 (UTC)
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 |
Could you explain shortly how to determine the Hausdorff dimension of the Penrose tiling? In what sense it can be seen as a true fractal? At some scale its geometry is no longer "fine". The citation has no details. Beaumont 21:02, 2 October 2006 (UTC)
Felt a fleeting temptation to link it to Slartibartfast... AnonMoos 19:20, 9 December 2006 (UTC)
I believe that this is discontinuous and thus not a "curve", yet I agree it belongs in this context as it shares other important properties with these curves. See < http://cap-lore.com/MathPhys/Zorder/> for discontinuity argument and also non-differentiability. NormHardy 19:18, 26 December 2006 (UTC)
Several of the listed examples (like the Smith-Volterra-Cantor set, the Mandelbrot set, and the space-filling curves) seem to have the same Hausdorff dimension and topological dimension, and therefore they don't meet the definition of fractal at the beginning of the article. Maybe the definition should be changed to something more like the one on the fractal page. —Preceding unsigned comment added by 160.39.28.117 ( talk) 07:18, 30 November 2007 (UTC)
Ok
You are right for the Mandelbrot set (corrected, the interresting part is the boundary).
For the space-filling curves, the topological and the fractal dimension are actuallay different. Prokofiev. 7 dec 2007. —Preceding
unsigned comment added by
Prokofiev2 (
talk •
contribs) 17:19, 7 December 2007 (UTC)
Reformatted —DIV (
128.250.80.15 (
talk)
02:55, 28 April 2008 (UTC))
The whole point of so-called 'natural, random' aggregates etc. is that they are products of deterministic chaos. The classification used here is misleading. —DIV ( 128.250.80.15 ( talk) 02:57, 28 April 2008 (UTC))
It seems like they would have the same value, as they are both coastlines. 128.232.241.115 ( talk) 00:38, 10 May 2008 (UTC)
It has been mesured (see reference on the article). Coastlines are more or less irregular and Norway's westcoast is particularily irregular. Prokofiev2 ( talk) 08:32, 13 May 2008 (UTC)
The new article titled Casey Lange fractal seems to fail the google test. Does anybody know anything? Michael Hardy ( talk) 04:26, 20 June 2008 (UTC)
New entry on 60o Fibonacci fractal gives a measured dimension of 1.2075. Seems to me that we can calculate an exact Hausdorff dimension. The kth generation Fk consists of 4 copies of Fk-3 and 1 copy of Fk-6, so the area scaling factor is the positive root of
which is
- same as the 90o Fibonacci fractal (as expected). Linearly, two of the Fk-3 copies are at an angle of 60o, so linear scaling factor is the positive root of
which is
So Hausdorff dimension should be
which is close to the give measured value. I don't have a source for this, however, so it might be discounted as OR. Gandalf61 ( talk) 14:19, 29 June 2008 (UTC)
I was looking for that result all the afternoon. I confirm your calculations are right, Gandalf. Well done ! Prokofiev2 ( talk) 19:59, 29 June 2008 (UTC)
The measurements of all the natural things should have some kind of units. Otherwise they are just meaningless numbers. Asmeurer ( talk ♬ contribs) 00:03, 16 October 2008 (UTC)
I agree. But in this case, the units are of length. While the fractals on the top table might be dimensionless, the bottom ones require them. Otherwise, how do I know your coast of Britain refers to the real Britain or the map, and is it in feet or miles or kilometers. Also, I do believe that most dimensionless quantities are ratios of dimensioned quantities that have the same units, so they cancel out. That clearly isn't the case here. Asmeurer ( talk ♬ contribs) 15:13, 16 October 2008 (UTC)
Gandalf, this fractal has been studied under the control of mathematics teachers, as mentionned in his site : [ [1]] "étudiée dans le cadre de mon TIPE" means "Studied in the frameword of my TIPE". TIPE (see [ [2]]) is a research work for French scientific students . Ok, it's not the "Annals of mathematics", but, for me, it is serious enough and does not go against Wikipedia policies regarding reliable sources (if not, then we should delete half of the mathematics contributions in all wikipedias...). Prokofiev2 ( talk) 10:00, 20 December 2008 (UTC)
Let me list some arguments why I decided to propose this entry:
Now for the weak points:
Prokofiev2 ( talk) 13:26, 20 December 2008 (UTC)
I think perhaps someone has the wrong idea about the meaning of cf. (Latin confer): it means 'compare' (not 'see'), so (cf. Stephen Wolfram<ref name="stephenwolfram.com"/>) invites me to compare Doc W to the fractal dimension of a Sierpinski triangle, an exercise of dubious value. Am I missing some point? — Tamfang ( talk) 02:55, 25 December 2008 (UTC)
The greek letter delta is used both for the Haussdorff dimension and the Feigenbaum constant. Use different symbol for the Haussdorff dimension, e.g. capital D? —Preceding unsigned comment added by 193.174.246.168 ( talk) 09:01, 6 January 2009 (UTC)
Anyone considered nominating this fine list at Wikipedia:Featured lists? -- œ ™ 07:57, 5 June 2009 (UTC)
Does any source qualify rational numbers as a fractal? The example with the box dimension is quite interesting, but it belongs in a diffferent place ( Box dimension, say). I find the rational numbers on this list a bit surprising, so please give some references as to their fractal nature. ptrf ( talk) 15:10, 5 June 2009 (UTC)
MISTAKE —Preceding unsigned comment added by 85.221.173.203 ( talk) 20:17, 9 September 2009 (UTC)
Hausdorff dimension of Menger sponge is log(20)/log(3)!!! —Preceding unsigned comment added by 85.221.173.203 ( talk) 20:19, 9 September 2009 (UTC)
There are some fractal vegetables more wonderful than a simple white cauliflower, as a Search on Google will show. I was past 50 before I first saw a Romanesco brocolli or cauliflower - what a wasted life! P.r.newman ( talk) 10:15, 16 April 2010 (UTC)
Is it me or does it scale really badly? Maybe we need a custom thumbnail? -- 80.175.250.220 ( talk) 11:07, 24 January 2011 (UTC)
http://icpr.snu.ac.kr/resource/wop.pdf/J01/2005/046/R02/J012005046R020474.pdf stated the dimension to be ~2.8, can someone proof that? —Preceding unsigned comment added by 88.65.198.120 ( talk) 19:28, 19 May 2011 (UTC)
Shouldn't the interval removed from the Cantor set be γ((1-γ)/2)m-1 instead, in contrast to the Smith-Volterra-Cantor set?
-- User:Dom 220.255.1.136 ( talk) 13:27, 25 May 2011 (UTC)
The list shows two fractals next to each other (3d Greek Cross and Octahedral), these are two different ways of creating the same limit set. So, I don't think they should be listed as two different fractals. — Preceding unsigned comment added by 98.225.20.68 ( talk) 17:21, 12 November 2012 (UTC)
Hi all, the same method used to calculate analytically dimension of the boundary of twindragon is also used for infinite family of such simple IFS - for example I've just seen that one of them is called 'tame twindragon' in the table: just use
Solve[Det[fin - IdentityMatrix[ie]*x] == 0, x]
and take 2Log[x]/Log[n] of the only reasonable solution in the demonstration getting another nasty formula for 'tame twindragon':
These formulas can be written in plenty of ways - maybe there is some nicer(?)
Cheers, Jarek —Preceding unsigned comment added by Jarek Duda ( talk • contribs) 07:04, 18 July 2010 (UTC)
Titus III ( talk) 05:05, 15 May 2013 (UTC)
Are there estimated fractal dimensions of galaxies, galactic superclusters, or the current model of the known universe? If so, those would be excellent additions to the natural fractals section.
Rememberlands ( talk) 18:23, 15 November 2011 (UTC)
Subsequent measurements have revealed that on larger scales, the power spectrum of galaxies fails to follow the (R/R0) ~ R^1.8 curve. Therefore, the distribution is not a fractal. — Preceding unsigned comment added by SCS137 ( talk • contribs) 14:31, 14 February 2015 (UTC)
Could the Infinity mirror and Kaleidoscope by added to this list? Also Harmonograph and Spirograph. - Shiftchange ( talk) 01:08, 7 May 2017 (UTC)
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I haven't quite understood why a space-filling curve is considered a fractal. Ok, I have an iterative procedure yielding a self-similar geometric object. But in the limit, I end up just with the unit square, which is defnitely not a fractal since topological and Haussdorff dimension both equal 2.
I'm a little puzzled both by the inclusion of this shape and it's linked picture. The limit of the fractal described is just a square. It seems a little strange to consider this a fractal. I know some 'fractal curves' cover the unit square in the limit, but these have other interesting properties in general (continuity, parametrization of the square..) I'm not sure the 'greek cross fractal' needs to be mentioned so much given that it doesn't seem to be a particularly interesting shape in any obvious way. Furthermore, the picture of the 2d greek cross fractal shows an early stage approximation to it. As mentioned the limit would just be a square. Obviously it's not possible to represent the limit strictly, but I find the picture is a little misleading given the above points. A mathematically unsophisticated reader might think the 'fractal' has some fine structure not present in the square. I'll review the page on this fractal and consider changing or removing it from here.
A month ago an unknown user removed half the page with no reason and no discussion I can find. Why? It seems like such a large change to the page should have some discussion first. 173.229.9.179 ( talk) 18:06, 1 February 2019 (UTC)
I propose expanding List of fractals to include more information so that it looks like this and then moving the page to Table of fractals. Thoughts? ➧ datumizer ☎ 19:07, 5 July 2021 (UTC)
The standard parameters for the Lorenz attractor are σ = 10, β = 8/3, ρ = 28.
So: What is the point of listing the Lorenz attractor in this article with the non-standard parameters σ = 16, β = 4, ρ = 40 ???
(To make matters even more confusing, the parameters are listed in nonstandard order: first ρ, then σ, then β.)
That makes no sense at all.
I understand the sentiment. However, note that the meaning that humans attribute to unordered sequences of symbols are purely a matter of culture and that, for example, in cultures that read in different directions than English, such as from right to left, the "natural" order would be reversed. In short, there is no notion of absolute correctness.
It is nice when an offspring source maintains the symbological standard of its citation. I encourage you to be bold and make these changes whenever you encounter them and simply check the box that says "minor edit" and make a note in the change field summary that you have re-ordered the parameters or renamed them to fit a certain style or source. If it is based on a source, please cite that source both in the change and in the article. The change form can just have the URL/DOI; the article obviously needs to have the citation inserted more carefully, and in the format that is currently used for that article.
Thank you for reading, and thank you for caring. As a fellow human, your insights and observations are equally important to us all. I also encourage you to sign your edits and talk-entries. The signing contains the time stamp that allows others to know the rough timeline and history of the development of an article. In short, it is a key piece of the historical record of changes and suggestions, which is very important. (Incidently, the information is still there; it is just not on the page, but rather in the metadata. Putting it on the page helps only humans.) MMmpds ( talk) 17:02, 4 May 2023 (UTC)