Opening Paragraph
The opening paragraph is too wordy and too technical. Most Wikipedia articles are:
- Title
- Brief summary
- Table of contents
- Detail
I would have fixed it myself, but I can't think of any good way to summarize it briefly -- which I guess is why it's like this in the first place. Does anyone have any ideas? Ravenswood 16:18, August 3, 2005 (UTC)
The new opening paragraph maybe more concise now in terms of a mathematical definition, but it is still way too technical for an opening paragraph. I believe the current opening paragraph should be moved to appear after a new opening paragraph that is more suitable for wider audiences to understand what the Mandelbrot set is.
This encyclopedia exists to spread knowledge as widely as possible and the introductory paragraphs should be understandable by a lay person where possible, especially with something as interesting and beautiful as fractals and the Mandelbrot set.
Also the black and white that was the first image of the article is perhaps the most boring picture of the Madelbrot set I have ever seen in my life. The initial picture ought to be showing the Mandelbrot in all its glory. That black and white image can come later. (I have now done this).
I am not trying to distract from the mathematical aspect of the article at all, I just think this subject will reach a wider audience with the correctly pitched 'front end'. I would gladly write a suitable introductory paragraph myself if I was in a position to do so, but I'm afraid I'm pretty ignorant on the subject. --CharlesC 22:18, 16 June 2006 (UTC)
Bail-out value
I always assumed when I used to play with Fractint that it was "bail-out" value -- as in "after so many iterations, we bail out". The article currently makes it sound as it it's named after something: "Bailout value". Could someone clarify? -- Tarquin 09:22 Aug 24, 2002 (PDT)
It should be "bail out" BEE.It should be "bail-out", with a hyphen. I've changed it. Michael Hardy 01:30 Feb 16, 2003 (UTC)
Now, who donates a nice picture? AxelBoldt 01:51 Feb 16, 2003 (UTC)
"Whilst it is of no mathematical importance, most fractal rendering programs display points outside of the Mandelbrot set in different colours depending on the number of iterations before it bailed out,"
Why is the number of iterations of 'no mathematical importance'? The original definition of the set, ignored the iteration numbers, but this is it, was there any study about the patterns for different interation number classes? Could someone explain what is ment by 'no mathematical importance'?
I also wonder about the lack of mathematical interest. Here's an example of potential mathematical interest: consider the "coastline" example often given as a fractal in nature. If we measure the coastline of an island using gross cartographic techniques we get a certain distance. If we use finer cartographic techniques we get a larger distance. The "closer" we look at the coast, for example, down to the grains of sand on the shore or beyond, the longer the coastline will measure. Now consider a set such as Mandelbrot. If you look at a high iteration number you get an approximation of the circumference of the set, if you take the next lower iteration number you get a larger circumference that sits closer to the edge of the set. This continues as you get closer to the infinitely fractal border of the set. Can we find a mathematical relationship between the difference in circumference and the iteration number? If so there may be applications in Geographic Information Systems (GIS).
Circles, cardioid
AugPi, I have an issue with your June 12 edit. The following statement is false, as can be shown by the infinite number of "mini" Manelbrot sets attached to and surrounding the main set: The Mandelbrot set can be divided into an infinite set of black figures: the largest figure in the center is a cardioid. The rest of the figures are all circles which branch out from this central cardioid. Mackerm 05:49, 26 Aug 2004 (UTC)
I recently found that the circles attached to the central cardiod can be asigned different rational numbers between 0 and 1 in numberical order. What is the mapping from the boundry of the cardiod(excluding the cusp) to the interval (0,1)?--SurrealWarrior 18:19, 1 Jun 2005 (UTC)
Mandel and the bifurcation.
Anyone to add a note about this in the article, (it is pretty large and a bit messy so I want try to do that. If I do, somebody (maybe you) WILL change it, I'm sure (because I'm Swedish and my writing in English is not perfect, somebody (maybe you) always change the addings I have done to the fractal articles here at en: ), better you write it from scratch =) // Solkoll 20:58, 8 Jun 2005 (UTC)
Are the filiments of the Mandelbrot set infinitly thin or do they have a finite thickness?--SurrealWarrior 29 June 2005 20:16 (UTC)
Questions
Moved following paragraph from article page, as it consists mainly of questions. Gandalf61 09:30, August 12, 2005 (UTC)
- Why are captial Z and minor z in the formulas mixed?
- What, exactly, is meant by "infinite set"?
Scope and limitations of Mandelbrot art
One can wonder how long it would take a room full of monkeys with computers to reproduce the works of van Gogh. He painted with a finite number of molecules of paint which have a finite number of permutations, while the set has an infinite range of coordinates, so they all may be in there somewhere. Or are there mathematical limits on what a Mandelbrot picture can look like?David R. Ingham
My brother wrote a program to write poetry that had one accepted for publication. When he admitted how he wrote the poem, the periodical changed its mind and rejected it.David R. Ingham 04:07, 1 December 2005 (UTC)
Simply connected / path connected?
The article contains the sentence: "...the Mandelbrot set is connected, and even simply connected. It is conjectured but unproven to be path connected."
According to the simply connected space, a set is simply connected if it is path connected and all loops can be continuously shrunk to points. Therefore, it seems absurd to say that the Mandelbrot set is simply connected but may or may not be path connected. Is this a typo? Or is there another definition of simple connectedness that does not include path connectedness? Reedbeta 01:09, 12 December 2005 (UTC)
It appears, from looking at it, that the connections do not always have finite width. That is, spirals can be zoomed in on by almost a factor of 10**20 and still remain spirals with apparently point vertices. Does anyone know mathematically if that is true? David R. Ingham 19:18, 10 January 2006 (UTC)
Ideal computer
Except for "accelerator" short cuts, it is a point by point calculation, so it would be best done with parallel arithmetic units. The the requirements for memory and connectivity are minimal. David R. Ingham 04:43, 17 December 2005 (UTC)
Better yet would be a field programmable gate array. David R. Ingham 19:08, 6 January 2006 (UTC)
Change in formula
(I also posted this question on the Talk:Benoît Mandelbrot page) The formula as originally presented by BBM was z -> z 2 - c but almost every single current reference uses z -> z 2 + c. Anybody know when and why this was changed? Khim1 14:23, 17 January 2006 (UTC)
Pseudo code vs QBASIC
An anon user User:86.129.85.127 replaced the pseudo code with this (as being more compact):
QBasic code for plotting a Mandelbrot set.
SCREEN 12 FOR sy% = 0 TO 479 FOR sx% = 0 TO 639 x = (sx% - 320) / 160: ox = x y = (sy% - 240) / 160: oy = y FOR c% = 15 TO 1 STEP -1 xx = x * x: yy = y * y IF xx + yy >= 4 THEN EXIT FOR y = x * y * 2 + oy x = xx - yy + ox NEXT PSET (sx%, sy%), c% NEXT NEXTI've rolled it back, (and notified the anon) please discuss here. Rich Farmbrough . 23:46, 21 February 2006 (UTC)
I agree with the revert. I know a lot of programming languages and assembly languages, and one hardware design language, but the QBasic is not clear to me. I once would have assumed that everyone using computers would know Fortran. David R. Ingham 06:13, 22 February 2006 (UTC)
I agree that QBASIC is unreadable, but it would be a nice way if the article could have a pointer to where to find it, since it does serve the purpose of being code that can be run by the reader as a demonstration. However, I wouldn't really select QBASIC as my first choice for this purpose, either. Senatorpjt 12:25, 28 February 2007 (UTC)
illustration of sequences
That makes the mathematics much more intuitive. I only wonder whether it is 5 or 6 cases. David R. Ingham 05:18, 4 March 2006 (UTC)
Visibilty of Image:Mandelset hires.png
I can't see it, when viewing the Mandelbrot set page, on Safari or Netscape, on my Mac. (I read that FireFox is more "politicly correct" but h
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