Talk:Mandelbulb

Julia formulation

Maybe someone should mention that the julia formulation works for Mandelbulbs too (as in "juliabulbs")? Inhahe (talk) 13:32, 27 May 2010 (UTC)

why was this article

split out from Mandelbrot set into a separate article? 69.228.170.24 (talk) 18:50, 27 May 2010 (UTC)

I split this article out for several reasons:

1. The Mandelbrot Set article is incredibly long, and while very informative, needed some cleaning.
2. The mandelbulb is related to the Mandelbrot set, but it is not a direct derivative and thus is not directly relevant to it. This is why I deemed it acceptable to remove its section from the Mandelbrot Set page and leave a link to Mandelbulb instead.
3. I thought that the Mandelbulb was important enough to warrant its own article, since there have been mentions of it in more that just a few places across the web (and especially since there was a Mandelbox article already).

R0uge (talk) 17:58, 23 July 2010 (UTC)

In response to R0uge: It is actually a direct "derivative" (not in the calculus sense) to the Mandelbrot set, as revealed by the simple complex number formula I came up with a while back, which highlights the mathematical relationship to the 2d Mandelbrot set. Note that the formula is arranged differently than the Mandelbulb formula, a) because that's the way I wrote it when searching for a 3d set and b) for the purpose of highlighting the formula's relationship with the 2d Mandelbrot set. I'd even go as far as saying the formula I'm linking to is the "correct" 3d Mandelbrot formula, but of course Benoit Mandelbrot would have to weigh in on that (or someone else with mathematical authority).

http://www.fractalforums.com/index.php?topic=2081.msg18426#msg18426 —Preceding unsigned comment added by Matthew Benesi (talk • contribs) 19:54, 10 September 2010 (UTC)

In response to Matthew Benesi: There are an infinity of ways to create 3d sets that share properties or a 2d plane with the mandelbrot set. Even just the mandelbulbs have 3 axis-aligned variations and in fact an infinity of variations of choice of polar coordinate angles. This is worth mentioning in the article, but also is good reason for not polluting the Mandelbrot set article with the plethora of 3d "analogs". None are really analogous since the most important property (universality) is not preserved.

In response to above: There are many other 2d sets that are not called the Mandelbrot set as they are variations of the Mandelbrot set, not the Mandelbrot set itself (such as the burning ship fractal, etc.). The 3d set will simply be the most basic extension of the complex arithmetic of the 2d set (see the link above), and this extends to the higher dimensional sets as well (4+ dimensions). The other sets will not be considered to be part of the set, just like the burning ship fractal, etc. are not considered part of the Mandelbrot set.

http://en.wikipedia.org/wiki/Burning_Ship_fractal

hypercomplex algebra

It doesn't seem to use a hypercomplex algebra, nor does your reference refer to a hypercomplex algebra (it just refers to hypercomplex numbers, which is a descriptive term in that context), look up the definition of hypercomplex algebra. —Preceding unsigned comment added by 58.174.106.133 (talk) 03:51, 15 September 2010 (UTC)

"This set"?

Which set is "this set" referring to in the second paragraph? — Preceding unsigned comment added by 146.229.73.85 (talk) 17:25, 9 November 2011 (UTC)

Questions

Are Mandelbulbs edible? Do you need to boil them first?

More importantly, what is the relationship between the "iteration" (what is referred to as such in the article is really just a transformation, which is some function f: R³ → R³), and the set (a subset of R³)? That relationship is not stated in the article. Is it, like for the Mandelbrot set, the collection of points for which the orbit under iteration of the transformation is bounded? If so, that should be explained.

And what is the effect of the additive constant c? Do different values give qualitatively different results? In the special case c = 0 you'll have a ball.  --Lambiam 22:14, 25 August 2012 (UTC)

Would someone mind translating this gibberish into English? As it currently sits, the only people capable of understanding this entry are those that already know what a Mandelbulb is and thus, do not need this entry.--71.218.1.65 (talk) 01:53, 17 May 2013 (UTC)

File:Power 8 mandelbulb fractal overview.jpg to appear as POTD soon

Hello! This is a note to let the editors of this article know that File:Power 8 mandelbulb fractal overview.jpg will be appearing as picture of the day on November 6, 2013. You can view and edit the POTD blurb at Template:POTD/2013-11-06. If this article needs any attention or maintenance, it would be preferable if that could be done before its appearance on the Main Page. Thanks! — Crisco 1492 (talk) 22:59, 20 October 2013 (UTC)

Picture of the day

A mandelbulb is a three-dimensional analogue of the Mandelbrot set, a mathematical set of points whose boundary is a distinctive and easily recognizable two-dimensional fractal shape. This image, for the iteration z ↦ z⁸ + c, is rendered with a volumetric ray tracing and path tracing global illumination algorithm in the Corona renderer. It took about 70 hours to completely render.Image: Ondřej Karlík

most of images much too dark

Except for the first one, the images are all *much* too dark on my monitor.--75.83.65.81 (talk) 06:17, 6 November 2013 (UTC)

I agree...when there are so many nice images in fractal forum, I don't understand why this article has such disappointing imagery. Not only are the images dark, they're lo-res blurry, and they seem to have very low iteration count. Even worse, it may be that the images are not properly computed---I suspect this because I see "taffy-like" strands in these images, and such strands are the hallmark of quaternion-based higher-d Mandelbrot sets...and those objects aren't proper Mandelbulb-type sets at all. My sense of things is that the Mandelbulbs have crisp knobs, as in the image shown higher up on this talk page. So I hope someone with time on their hands and access to a good stash of images can improve the look of this page! Rudyrucker (talk) 21:53, 7 January 2014 (UTC)

Cubic Fractal?

The image in the cubic formula section is just listed as "cubic fractal" with no further explanation, and given the page says there is no canonical 3-dimensional Mandelbrot set, it's kinda unclear whether the fractal is related to the Mandelbrot set or not, or really how it was derived at all. I'm not a mathematician, so I can't really offer much in this case, but someone with more knowledge might want to clarify the image a bit if possible. Asticky (talk) 19:19, 9 March 2024 (UTC)