Talk:Julia set

From Wikipedia, the free encyclopedia

What's a "waist", as defined in the article?

A place where the Mandelbrot set constricts to a point, then expands again. Precisely, it is a point such that two disjoint open neighborhoods whose boundaries are circles tangent at the waist lie inside the Mandelbrot set, while a line segment or arc of a circle whose midpoint is the waist, and which is tangent to said circles at the waist, lies outside the set except for the waist. -phma 21:11, 9 Mar 2004 (UTC)

I want to introduce the Julius Ruis set, being a smart presentation of 400 Julia sets, showing that the Mandelbrot set is the parameter basin of all closed Julia Sets.

Sorry, but this is not the place to do it: our no original research policy forbids this sort of content. - jredmond 21:44, 11 Apr 2005 (UTC)

I do not understand your remark. See Image:Julius-Set.jpg. This is an example of the Julius Set for z'=z^2+c.

From WP:NOR:

If you have a great idea that you think should become part of the corpus of knowledge that is Wikipedia, the best approach is to publish your results in a peer-reviewed journal or reputable news outlet, and then document your work in an appropriately non-partisan manner.

Basically, it says that we're sorry but this is not the appropriate place to publicize your new approach to Julia sets. - jredmond 22:24, 11 Apr 2005 (UTC)

Why then published the image with 121 Julia sets?

I am very sorry. I thought I was giving a service to Wikipedia.

[edit] Simplicity of Article

I remember the previous versions of the mandelbrot set and julia set articles, that were far more accessible to those not schooled in advanced mathematics. The mandelbrot and julia sets are of great interest to the less mathematically trained, and the article should reflect this. --86.141.94.84 16:34, 1 August 2006 (UTC)

[edit] Original?

I read in Fractal Geometry: Mathematical Foundations and Applications by Kenneth Falconer, that the set of all points c for which the Julia set of f(z) = z^2 + c is connected was the definition of the Mandelbrot set, and the definition in the article was later proven (in the book, at least). I can't submit any more, for fear of copywright infringement.

Yes, when Benoît Mandelbrot first plotted the Mandelbrot set, he was investigating the values of c for which the Julia set of z^2+c is connected (in fact, he was originally investigating a related question concerning the values of c for which stable limit cycles exist). But Mandelbrot already knew that the Julia set is connected if and only if the critical point at z=0 does not lie in the domain of attraction of the super-attracting fixed point at infinity i.e. if and only if the forward orbit of 0 does not tend to infinity - this is a special case of more general results about rational maps proved by Pierre Fatou and Gaston Julia around 100 years ago. This equivalent definition of the Mandelbrot set is more suited to numerical computation, as well as being more easily understood (it does not involve the concepts of "connected" or "Julia set"), so it is the one that is usually given today. For Mandelbrot's own account of his early work on the Mandelbrot set see Fractals and the Rebirth of Iteration Theory in The Beauty of Fractals; Peitgen and Richter, 1986. Gandalf61 11:32, Jun 4, 2005 (UTC)

[edit] Quaternion Julias

There is no mentioning of any Quaternion Julia Set in this article. Can someone kindly contribute more information on Quaternions? Doomed Rasher 23:05, 13 September 2006 (UTC)