the Mandelbulb

[fourier jr]

This is AWESOME!!! & 1000x awesomer if you know about the math behind it. How could a painter or sculptor come up with something like this? Math is much better:

http://www.wired.com/images_blogs/wiredscience/2009/12/mandelbulb_1a.jpg

see more pics here, but it's not very interesting because there's no explanation:
http://www.wired.com/wiredscience/2009/12/mandelbulb-gallery

& more theory & many more pics here:
http://www.skytopia.com/project/fractal/mandelbulb.html

cDd8R0xlkNA eKUh4nkmQbc

[lisab]

Oh wow...that's very, very cool!

[fourier jr]

there are some good questions on the 2nd page also:

Further exploration of the creature
There are so many questions we can ask about the structure and nature of the object (we'll stick mostly to the power 8 version for now):
•What's the formula of this thing? (see the page)
•What does it look like on the inside? (see the page)
•Any interesting analogues to the 2D Mandelbrot set? (yes)
•Is this thing really new? (as far as the author knows it is)
•What variations of the formula are possible?
•What happens at infinity iterations? (unknown)
•Is the object completely connected, and maybe path, locally, or simply connected? (also unknown)
•Why do lower powers exhibit less fractal-like detail than higher powers? (unknown)
•Does fractal detail really go on forever when you zoom in? (probably)
•Any Julia equivalent for it? (yes)
•What is its volume and Hausdorff dimension? (unknown)
•Are there near exact copies of the object deep inside the structure? (as of right now, no)
•Any way to colour the object, to replace its mono-ish appearance?
•Any decent 3D software to render the beast?
•If the 2D Mandelbrot is the thumbprint of God, what does that make the 3D Mandelbulb?

[Phrak]

They first called it a "Broccoli Virus".

A fellow going by the name of Twinbee (Daniel White) was posting here on PF in August, asking about various spherical coordinate systems (http://www.physicsforums.com/showthread.php?t=331883&highlight=Twinbee), eventually directing us to FractalForums (http://www.fractalforums.com/index.php). Including Daniel, there are variously, up to about 5 other major contributors attempting to discover "The True 3D Mandelbrot" (http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/150/). Look about halfway down the page for the first appearance of this object. Together, these guys are amazing, and have been in dogged persuit of a 3D Mandelbrot-like object since September 2007!

[Phrak]

Here's a close-up photograph of the inspirational broccoli romanesco (http://scienceblogs.com/chaoticutopia/upload/2006/11/broccoli.jpg).

Daniel White's web site is hosted here (http://www.skytopia.com/project/fractal/mandelbulb.html).

David Makin hosts his own site, so frequent visits could cause him some dispair unless you want to purchase his art.

[Loren Booda]

Makes a good argument for extraterrestrial life.