View source for Testwiki:Featured picture candidates/Image:Mandelbrot Creation Animation (800x600).gif

===[[:Image:Mandelbrot Creation Animation (800x600).gif]]===
====New version====
[[Image:Mandelbrot Creation Animation (800x600).gif|300px|Short description]]
*{{Info}} created by [[User:username|Username]] - uploaded by [[User:Username|Username]] - nominated by [[User:Username|Username]] --[[User:Jarekt|Jarekt]] 12:05, 17 October 2007 (UTC)
*{{Support}} new version of [[:Image:Mandelbrot Creation Animation.gif]] --[[User:Jarekt|Jarekt]] 12:05, 17 October 2007 (UTC)
*{{Support}} '''new version''' I love these animated gifs that illustrate mathematical concepts, too bad many people don't understand them and decline. [[User:Calibas|Calibas]] 06:07, 17 October 2007 (UTC)
:*I moved this line from old version to the new one after separating old and new versions of the file --[[User:Jarekt|Jarekt]] 12:17, 17 October 2007 (UTC)
*{{Oppose}} - Sorry Jarekt, but the story told by the animation is not very interesting. From the 6th to the 20th frames, the image seems to oscillate between two patterns only. Yes, there are differences in the detail but those are too subtle to be noticed at first sight. I really would like to support this animation and I believe there should be some way to make it a little more dramatic - [[User:Alvesgaspar|Alvesgaspar]] 20:52, 17 October 2007 (UTC)
*{{Oppose}} Agree wist Alvesgaspar --[[User:Karelj|Karelj]] 21:32, 18 October 2007 (UTC)
*<s>{{Oppose}}</s> Sorry, but I'm not following what you mean by "the value of the equation". If it means that you instantiate the variable(s?), then it's not an equation anymore... I'm not trying to be pedantic, I just want to be sure I understand how this works. Also, if the coordinates represent the real and imaginary value of z, then how does c vary? If there are different values on different images, it should be made clear. I will consider changing this to a support if a clear and simple explanation of what is going on is added to the image description. --[[User:Nattfodd|Nattfodd]] 22:18, 18 October 2007 (UTC)
:*I added an explanation. Please let me know if it is "clear and simple"--[[User:Jarekt|Jarekt]] 03:33, 19 October 2007 (UTC)
::*It's much better and I think I more or less understand what is now going on, but the explanation still seems to be far from "clear" to someone with no mathematical background. It could probably use a rewrite, for instance putting the explanation of the other method to the end (or completely removing it), making more clear what varies in the different images from the beginning of the explanation, etc. For instance, I think it would be much better to speak of the sequence "z_{n+1} = z_n^2 + c" and then add a label saying z_1, z_2, ... on each frame. What you then mean by "the first 20 iterations of the equation" would become much easier to understand, and you could add that it (sometimes) converges towards a fixpoint which is the solution to the equation. --[[User:Nattfodd|Nattfodd]] 10:51, 19 October 2007 (UTC)
:*{{support}} Changing to support after better rewrite of the explanation. --[[User:Nattfodd|Nattfodd]] 14:15, 22 October 2007 (UTC)
*{{Support}} Personally, I think the story told by this animation ''is'' interesting - it shows that the iterations oscillate between different "classes". The way that the number of dark regions around the edge, just inside the main fractal boundary, increases from frame to frame is also interesting. Just look at how there is a dark spot in the left hand bulge every two frames, spots in the upper and lower lobes every three frames, sports in the next heirachy of lobes every four frames, and then next every fifth and so on. I consider this hidden (you don't see this in a standard, black-inside Brot) pattern that we are being shown to be more interesting than the iterations going wild and doing all sorts of crazy stuff.
:As for the description, here's a minor rewrite that doesn't make any different points but presents the points already there a little more clearly (in my opinion). I think that I have got the meaning of the graphic right, but if I haven't, I apologise.
An animated diagram showing iterations of the equation used to generate the [[w:Mandelbrot set|Mandelbrot set]], a [[w:Fractals|fractal]] first studied by [[w:Benoît Mandelbrot|Benoît Mandelbrot]].
The animation shows the values of ''Z'' for first 20 iterations of the equation 
::<math>Z_{n+1} = Z_n^2+c, \,</math>
where ''c'' is a [[w:Complex number|complex]] variable.

Mandelbrot set graphics are usually generated using the so-called "escape algorithm", where color is assigned according to the number of iterations it took for the equation to diverge past a pre-set limit, and black color is used for regions that never diverge. This, however,  is a plot of a much simpler quantity: the actual values of the equation at the first 20 iterations. Every pixel in the image corresponds to a different value of a complex constant ''c'' ranging from ''-2.2'' to ''1'' on the real axis (horizontal) and from ''-1.2i'' to ''1.2i'' on the imaginary axis (vertical). ''Z'' is initialized to 0. At each iteration, the next value of ''Z'' is calculated using the equation above.

This graphic was generated with 13 lines of code in the [[w:en:R (programming language)|R language]] (see below for the code). For each point, the magnitude of ''Z'' is calculated, than scaled using an exponential function to emphasise fine detail, and finally mapped to color palette (''jetColors''). Dark red is a very low number, dark blue is a very high number. The deep blue region "squeezing" in the boundaries of the fractal is the region where ''Z'' value diverges to very large numbers (which will eventually go to infinity, given enough iterations). The colors inside the fractal shows the absolute ''Z'' value at each value of ''c'' at each iteration.  --[[User:Inductiveload|Inductiveload]] 22:24, 21 October 2007 (UTC)

:Thanks for rewrite, I like it much better than my version. I added it to the graphics description. The only minor differences are in the last 2 sentences. Diverging to infinity (as far as computer accuracy is concerned) happens very fast for some points. Last paragraph talks sometimes about absolute value and sometimes about magnitude of complex numbers, but they are two names of the same quantity. Thanks again--[[User:Jarekt|Jarekt]] 13:38, 22 October 2007 (UTC)

:At one point in the description is calls ''c'' a complex constant, shouldn't this be complex variable? [[User:Calibas|Calibas]] 03:56, 23 October 2007 (UTC)
:: I don't think so. It's not varying in the equation itself, we just happen to study several equations which all have a different value for c, but it doesn't itself vary inside the study. --[[User:Nattfodd|Nattfodd]] 07:55, 23 October 2007 (UTC)
 '''result''': 4 support, 2 oppose, 0 neutral => not featured --[[User:Laitche|Laitche]] 15:02, 30 October 2007 (UTC)