See You Tube:

]]>I ordered the fractals in the julius Ruis Fractal Sciende and Art gallery.

]]>nice work, as always!

Just one tiny correction for you: the late Adrien Douady’s first name was, well, “Adrien”. Not Adrian.

Best wishes,

Kay

]]>http://www.flickr.com/photos/39445835@N05/sets/

I think the Juliabulbs have been overlooked in the majority. They do create some very nice renderings too.

The variations discovered and explored since continue to grow. The mandelbulb has opened up a whole new genre of fractal (even if it doesn’t create a true new form of algebra in the mathematical sense) that inspires mathematicians and non-mathematicians alike.

Jason.

]]>http://www.fractalforums.com/theory/mandelbrot-pearls/msg10731/#msg10731

]]>A really beautiful paradise-like scene, with a bit of a story framing the images.

http://www.fractalforums.com/mandelbulb-renderings/lost-in-the-mandelbulb/

And a new videos by Dan, zooms into one of the Gateau mountain areas)

http://www.youtube.com/watch?v=cDd8R0xlkNA

The Mandelbulb has really taken off, and there are more posts about it every day.

]]>Thanks much for your passion and pioneering work in the area. The renderings are absolutely incredible!

Any thoughts on why the 8th power works in 3d but not the 2nd? How does an 8th power rendering of the 2d set look?

Thanks!

]]>The Wikipedia article might be a good place to start if you want more info.

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

The earliest fractals along these lines were in fact hand-drawn “Julia sets” by the mathematicians Gaston Julia and Pierre Fatou starting in in 1917.

]]>Just curious…

Thanks,

Oliver ]]>

http://makinmagic.deviantart.com/art/The-Honeycomb-142102904

I think this one is from a degree 8 true 3D mandelbrot. I couldn’t tell which ones of your pix is of the degree 2 version?

By the way (note for casual readers), Daniel White recently posted a longer discussion of these new 3D fractals

http://www.skytopia.com/project/fractal/mandelbulb.html

http://makinmagic.deviantart.com/

Some are from Mandelbrots, others from Julias.

]]>Mathematica Player which is a free download from the

Mathematica website. ]]>

Glad that others have tried to look for the beast. Quite a few have said that such an object is impossible due to the lack of a proper 3D analogue to complex numbers. I’ll say again that I think this would be the most amazing find if it did exist. Like a real ‘holy grail’, but even better in a way, because it’s so universal. And it looks like there may even be various ways to colour the surface rather than keeping it at the default mono-hued colour (one could ‘chop’ off a section of the hypothetical 3D brot, producing awesome colours, though that would lose detail of course).

Paul mentioned your spherical rotation formula on the fractalforums.com site. It’s pretty similar to mine as you know, though I wonder what a higher power version of your formula looks like (Paul found that higher power versions of my formula seem to reproduce some of the incredible deep fractalness of what you’d expect in a 3D brot – see later).

It’s a good idea to weight the rotations like you said – perhaps so that the distance travelled round the sphere is the same no matter what angle. Recently, I was also experimenting with different coord systems as mentioned on the physicsforums.com thread here:

http://www.physicsforums.com/showthread.php?t=331883

(“16 different spherical coordinate systems”).

Finally, as hinted at previously, it already looks as though we’re discovering something 3d-brot-ish. Take a look at some of these pictures. This nice one is of the whole thing (and rendered by Paul of course):

http://www.bugman123.com/Hypercomplex/Mandelbrot-White8-large.jpg

Here’s a zoom-in render by David Makin (lowish 3D resolution):

http://www.fractalforums.com/gallery/?sa=view;id=901

Not too shabby huh?

…and another zoom (around 1000x, shadows are faked)…:

http://www.skytopia.com/stuff/broc.png

Both of those last ones have plain diffuse lighting – love to see them with global illumination.

Anyway, hope one of us finds it in the end!

]]>