Wikipedia:Featured picture candidates/Lyapunov fractal

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[edit] Lyapunov fractal

Generalized Lyapunov fractal for the sequence BBBBBBAAAAAA, with growth parameter range (a,b) in [3.4, 4] x [2.5, 3.4], generated with Mathematica 5.

Author: --Wickerprints 08:51, 15 July 2006 (UTC)

Article: lyapunov_fractal

Reason for nomination: I feel that this image is a particularly good example of this type of fractal, and has aesthetic as well as technical merits.

• Nominate and support. - Wickerprints 08:51, 15 July 2006 (UTC)
• Support Interesting...Cab02 13:44, 15 July 2006 (UTC)
• Question: Are all those little black dots along the light ridges part of the fractal, or are they artifacts of the rendering process? —Keenan Pepper 17:10, 15 July 2006 (UTC)

• Answer Some small black regions are rendering artifacts due to the fact that the associated logistic map corresponding to those pairs of values are right on the boundary between order and chaos. With greatly increased precision (and computing time), some of those dots will go away, but in practice it isn't possible to remove them all by further computation, unless you have an infinite amount of time to compute the iterates. I could Photoshop out the more obvious ones, but this raises the question of whether you're really seeing the result of the computation. --Wickerprints 19:08, 15 July 2006 (UTC)

• So they correspond to real features of the fractal? In that case, I support. —Keenan Pepper 19:24, 15 July 2006 (UTC)

• Comment Could you give the source of the Mathematica program (perhaps in the image page), or at least the precise settings for the number of iterations and the generation of colors? Thanks. --Bernard 22:58, 15 July 2006 (UTC)

  Answer Done. Does anyone with a really fast computer want to change the "200" to a "2000" and recompute the image? Or does anyone with more Mathematica experience want to optimize the code? It'll take a few days to compute as it is written. --Wickerprints 21:17, 16 July 2006 (UTC)

• Support per nomination. enochlau (talk) 05:40, 16 July 2006 (UTC)
• Flashback Support Joe I 16:04, 16 July 2006 (UTC)
• Oppose. There are thousands of beautiful fractals out there and even powerful fractal screensavers (cf. Electric Sheep). In order to be featured, a fractal should possess extraordinary aesthetic qualities -- which is, of course, very much a matter of personal taste. This one does not appeal to me at all. While it may represent the type of fractal well, neither the choice of colors (blue/yellow) nor the structures shown (particular in the upper center) seem particularly visually impressive to me.--Eloquence* 17:39, 16 July 2006 (UTC)

• Comment: Your argument, if it simply amounts to personal taste, or that many other fractals are beautiful, can't be rebutted; yet it isn't, in my opinion, sufficient. Why is the Mandelbrot set a FP? It's (1) a canonical image and (2) has illustrative merit. If we're to say that "thousands of fractals are beautiful," then none of them would be allowed FP status, because there will always be a "more beautiful" fractal out there. Indeed, there are only 3 mathematical images that have been given FP status, two of which are related to the M-set. It's like saying, "millions of other photographs are more beautiful," and as a result, none of them are exceptional. The argument for opposition, it seems to me, seems to reflect a lack of understanding of the significance of this type of fractal, which demonstrates that the set of parameter values of a driven logistic map that lead to chaotic behavior is itself fractal. This is not merely another "pretty picture" with some creative coloring scheme; it conveys real information about an important aspect of chaos theory. --Wickerprints 21:06, 16 July 2006 (UTC)

• Possibly. For me, personally, it does not meet Wikipedia:What is a featured picture? criterion 7. Certainly, one can always argue "it could be prettier"; however, any picture should at least cross a certain threshold of beauty. This one does not cross mine and I'm certain that the same information could be conveyed in a way which does. YMMV.--Eloquence* 21:54, 16 July 2006 (UTC)

• Oppose per Eloquence. I could imagine this being on the main page as an 'invitation' to check out an article on fractals. However, there are many images I could imagine doing that, some (perhaps) a better introduction than this one. -- moondigger 20:43, 16 July 2006 (UTC)
• Support. Aesthetic value, as well as significance explained by Wickerprints. — BRIAN0918 • 2006-07-16 21:09
• Support per above--Vircabutar 01:02, 17 July 2006 (UTC)Insert non-formatted text here
• Support Wikid! So often fractals use dodgy color schemes. This one looks good. --Abdominator 01:33, 17 July 2006 (UTC)
• Support my edit. Recomputation with a C program. I tried to keep the same colors; I notice they are a little different but I could fix that. Downsampled from a 9000x6000 image to 3000x2000, still 4 times bigger than previous one (has the file become too big?). Also I increased to 10000x12 iterations maximum (compared to 200x12), but I have optimizations to stop before most of the time. I kind of like the colors of Wickerprints, but something like in this page might be more impressive. I particularly like the second, where the color transition between order and chaos is smooth, and the picture looks like a landscape. Maybe we could adapt this, I'm not sure. --Bernard 04:58, 17 July 2006 (UTC)

  Support edit Wow, nice job! You and I need to have a discussion about how you did that. Truly, I would like to know as much as possible about how you implemented this image. I know Mathematica isn't the fastest way to do this, but you totally blew me away with your version! Regarding your comment about the color palette, I chose a sharp boundary because it reveals the fine details in the structure, and this is qualitatively important. But you're more than welcome to select alternative color schemes. --Wickerprints 05:43, 17 July 2006 (UTC)

  • I more or less fixed the color difference problem. It was a sad story of PNG gamma correction. I don't know if it is the best solution, but I just modified the gamma value in my file to match the value in Wickerprint's file. --Bernard 07:43, 17 July 2006 (UTC)
• Oppose per Eloquence. Dionyseus 07:08, 17 July 2006 (UTC)
• Oppose. While interesting, not exceptional. Are there better specimens? AJ24 14:37, 17 July 2006 (UTC)
• Support. Wow, I'm using this one as my new desktop background. Does anyone else see an old sailing ship on the right engaged in a arrow battle with another one on the left, which is mostly obscured by the waves crashing around them, or is my imagination too wild? And kudos on the colour scheme, per Abdominator. --Aramգուտանգ 08:13, 18 July 2006 (UTC)
  • Salvador? Is that you? — BRIAN0918 • 2006-07-19 02:17
• Support the second version (the C program is a nice bonus) BrokenSegue 17:06, 19 July 2006 (UTC)
• Neutral - While it is cool-looking, I've done a lot of fractal work, and this one doesn't especially stand out. --Cyde↔Weys 17:17, 19 July 2006 (UTC)
• Oppose. This image is not iconic for Lyapunov fractals in the same way that the "bug" pic is for the Mandelbrot set. Aside from that, it's not particularly compelling compared to any of the 10 bazillion other large "pretty" fractals that one can generate quite handily. --Dante Alighieri | Talk 17:52, 21 July 2006 (UTC)

Not promoted Raven4x4x 06:33, 23 July 2006 (UTC)