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## "Mandelbulb," a 3D Mandlebrot Construct, Discovered255

symbolset writes "Many know the beauty and complexity of the Mandelbrot set. For some years now a few enterprising mathematicians / rendering fiends have been seeking a true 3D Mandelbrot set. A month ago a solution was found, and it is awesome to behold."
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## "Mandelbulb," a 3D Mandlebrot Construct, Discovered

• #### Actually, the Mandelbrot set is already 4D (Score:5, Informative)

on Sunday November 15, 2009 @08:22PM (#30110486) Journal

While the Mandelbrot set as usually defined is 2D, each point has an associated Julia set, where instead of the additive constant, the starting point is varied (the original Mandelbrot set always uses zero as starting point). Together, they give a 4-dimensional set, where two dimensions are given by the starting point (zr, zi), and the other two by the additive constant (cr, ci). The original Mandelbrot set is a cut through this 4D set at the plane zr=zi=0, while the Julia sets are cuts orthogonal to theat, at planes with constant cr and ci.

• #### Not a "true" 3D Mandelbrot (Score:5, Informative)

on Sunday November 15, 2009 @08:24PM (#30110496)

It's definitely nifty, the pictures are beautiful, and the creator deserves praise, but the author himself says it's probably not a "true" 3D Mandelbrot:

As exquisite as the detail is in our discovery, there's good reason to believe that it isn't the real McCoy. ... ...
Evidence it's not the holy grail? Well, the most obvious is that the standard quadratic version isn't anything special. Only higher powers (around after 3-5) seem to capture the detail that one might expect. The original 2D Mandelbrot has organic detail even in the standard power/order 2 version. Even power 8 in the 3D Mandelbulb has smeared 'whipped cream' sections, which are nice in a way as they provide contrast to the more detailed parts, but again, they wouldn't compare to the variety one might expect from a 3D version of Seahorse valley.

So, Slashdot, I know this is asking a lot, but can you PLEASE at least read the article before posting? Thanks.

• #### Zooming (Score:4, Informative)

on Sunday November 15, 2009 @08:58PM (#30110708) Journal

• #### Slashdotted (Score:5, Informative)

on Sunday November 15, 2009 @09:06PM (#30110754) Homepage

Seems to be slashdotted, cached version: http://www.skytopia.com.nyud.net:8090/project/fractal/mandelbulb.html [nyud.net]

• #### Re:Not a "true" 3D Mandelbrot (Score:3, Informative)

on Sunday November 15, 2009 @09:21PM (#30110844) Journal

There is a subtle difference between "a solution" and "the solution".

But yeah, I was selling it a bit because the pictures are so lovely.

• #### w00t (Score:5, Informative)

<thomas.ludwig@NOsPam.gmail.com> on Sunday November 15, 2009 @09:27PM (#30110884) Homepage

cool, nice to see my images linked on slashdot :) hopefully we'll have some gpu-accelerated results to show you all soon (and for those with opencl supporting cards, executables).

btw interested parties might like to check out my 3840x2400 resolution render of the 7th degree version here: http://lyc.deviantart.com/art/siebenfach-139038934 [deviantart.com] (it's buried deep in the thread, and fractalforums is creeking a bit)

• #### Fraqtive (Score:5, Informative)

on Sunday November 15, 2009 @11:22PM (#30111618)
A very nice open source app, available through the Ubuntu/Debian repositories. The author's page [mimec.org] even got a windows version.

It supports multi-core CPUs, i.e. if you really want to tax each of your CPU's core to the limit, just use the app to browse through the mandelbrot set. It also supports a 3D extrapolation of the 2D set (OpenGL and software).

Strangely enough it doesn't seem all that popular, as the forum [mimec.org] doesn't seem all that populated..
• #### Re:Looks like a big sea slug. (Score:4, Informative)

on Sunday November 15, 2009 @11:27PM (#30111654)

It's all chemistry, physics and math.

Has anyone actually done this? With even a ''simple'' organism ( yes, those are air-quotes ), like a paramecium? It sounds easy in theory, but I bet when we actually get down to it, there'll be a few speedbumps and unexpected obstacles in the way.

Things are not even close. Look at vcell [uchc.edu] to see what's close to the state of the art in cell simulation. Right now, it's a matter of trying to get a few reactions and cell compartments working correctly. I don't think anyone has even come close to modeling any type of complete cell.

• #### In nature - I give you, Brassica oleracea! (Score:4, Informative)

on Monday November 16, 2009 @02:53AM (#30112594)

These particular fractals remind me of things I hope never to see in nature.

Some of it, at least, has already happened: see this fine example of Brassica oleracea [ubcbotanicalgarden.org], for instance.

Then again, you might have been referring to some of the fractal images that call to mind the work of H. R. Giger... < shiver >.

Cheers,

• #### Re:Not a "true" 3D Mandelbrot (Score:3, Informative)

<blahsebilrazen@blah.com> on Monday November 16, 2009 @08:26AM (#30114082)
Looking at their UID I'd say they were here when here was new.
• #### Re:Actually, the Mandelbrot set is already 4D (Score:2, Informative)

on Monday November 16, 2009 @12:31PM (#30116552) Journal

Ever tried the "Magic Eye" pictures? There's exactly zero visual cues. Unless you manage to look at the image so that the left-eye and right-eye see it with a certain displacement (so different parts of the picture now match), you see not a single trace of the 3D figure hidden in it). The only depth information that is there is the displacement.

• #### Re:Actually, the Mandelbrot set is already 4D (Score:3, Informative)

on Monday November 16, 2009 @01:00PM (#30117022)

Archive.org offers the full .avi file for download (the AVI version is about 4000 times more awesome than the flash version), and it's in public domain, so you are perfectly within your rights to go do it yourself.

• #### Re:Actually, the Mandelbrot set is already 4D (Score:1, Informative)

by Anonymous Coward on Monday November 16, 2009 @02:21PM (#30118556)

It's been proven that there is no normed division algebra over R (real numbers) which has dimension 3 (over R). More specifically, the only normed division algebras over R are R itself, complex numbers, quaternions, and octonions. So, in that meaning of sensible it can't be done.

• #### Re:Actually, the Mandelbrot set is already 4D (Score:1, Informative)

by Anonymous Coward on Monday November 16, 2009 @03:18PM (#30119682)

It's a "Me too!", but for Slashdot. It means "I wanted to say exactly the same, but someone else was first. Rather than saying nothing, I will clutter up the discussion".

The GP (grandparent) did add a bit of his / her own, so it wasn't as bad in this case.

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