Talk:Mandelbrot set

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)

There was already one in the system. It was used in earlier versions of the page, but somehow the link got removed at some point. I've put it back in. You can move the picture if you want. Or possibly replace it with another one - personally, I prefer it with the real axis horizontal and the imaginary axis vertical... -- Oliver P. 02:08 Feb 16, 2003 (UTC)

Where's the real axis right now? Also, the self-similarity isn't very well visible in this one. AxelBoldt 03:25 Feb 16, 2003 (UTC)

Why, it goes right through the middle from left to right, of course! I rotated the image, you see. I'm not sure the self-similarity can be shown in a single small image, though, can it? Maybe we should have a sequence of images, gradually zooming in on some point on the boundary... -- Oliver P. 14:12 Feb 16, 2003 (UTC)

Sometimes, if the picture is a bit larger and shows enough detail, one can actually see that parts of it look similar to the whole thing. But a sequence of zoomings would be really nice too. AxelBoldt 21:34 Feb 16, 2003 (UTC)

Check out Mandelbrot1.jpg, Mandelbrot2.jpg ... Mandelbrot6.jpg. I generated them with a program I created using Cycling 74's Max/MSP/Jitter. They are a nice sequence of zoomings. I wonder if anyone might be able to find information about ways to speed up the generation of the mandelbrot fractal, i.e. good, fast algorithms. Snotwong 15:23 1 Jun 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). [mark.dixon@uwa.edu.au]

The contour of the Mandelbrot set is not like a coastline because it is loaded to the brim (and then some) with pinch points (cusps). Coastlines do not have pinch points. --AugPi 01:58, 13 Jun 2004 (UTC)

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)