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Hello

So I saw a mandelbulb and was bitten!

So I wrote a program that renders mandelbulbs on the GPU and adds some primitive volume rendering.

One very interesting thing I discovered was that if you generalize (David Whites) MandelBulb equation setting the scaling of r theta and phi to different values like this r^Na theta*Nb phi*Nc you can get the ordinary MANDELBROT back!! But bulby!! and beefy!!  ;D  :D using Na=2.0,Nb =1.0 and Nc=2.0. Center slice is identical to mandelbrot.

The Lurking spider uses Na=2.0 Nb=1.5 Nc=2.5. Classic mandelbulb would be Na=Nb=Nc=8.0.

The colorful display on the right in the videos shows...the 3D vector in r g b for each slice being rendered.

Bulby mandelbrot and lurking spider!

http://www.youtube.com/watch?v=gai1kSkAOfE (http://www.youtube.com/watch?v=gai1kSkAOfE)

http://www.youtube.com/watch?v=Hw0mwtUa9TU (http://www.youtube.com/watch?v=Hw0mwtUa9TU)

Bulby mandelbrot snapshot!

(http://img135.imageshack.us/img135/1204/bulby.jpg)

My rendering can improve a lot I do not have any lights yet.. I think I have an aliasing problem though dunno what to do??

Also I do not know exactly how to improve volume rendering to work for all viewing angles..I use planes that slice the 3d texture
and then alpha blending.. but keeping planes perpendicular to viewer does not help the 3d texture follows around.

Finally to have something to compare with: Na=8,Nb=8,Nc=8 the mandelbulb... (needs antialiazing badly i think?)
(http://img513.imageshack.us/img513/2736/mandelbulb.jpg)

Ah great I actually tried the same thing today, but not in voxels but in a raytracer ;)  Welcome to the fractal forums.

Here is a sample of my voxel experiments from a couple of days ago. Looks surprisingly similar to your "bulby brot" but mine was the result of a programming error (bad rotation code).

(http://img42.imageshack.us/img42/2805/voxelfront.jpg)

Thank you!

Your result, sure looks related :)

How do you do the volume rendering ?

nVidia CUDA SDK 2.3 - volume render demo - hence requires an nVidia graphics card to run

Slightly modified to compute a fractal instead of loading a predefined data set - and slightly tweaked the
color parameters to give a nice red aura over a blue body

Christian

Thanks I think they show how to multisample properly!  :evil1:
Using Cuda seems easier, I am using shaders and FBO ping pong.

This is fun..setting Na=2.0 Nb=1.0 Nc=-2.0 thus exatly as for the mandelbrot but!! a change in rotation direction
we get this:
(http://img706.imageshack.us/img706/1585/trinary.jpg)

Trinary mandelbrot thingys  :o
It is difficult to see but all three points are the same.

ah, I see, so that's how the whole thing relates... :)

(http://fc06.deviantart.net/fs51/f/2009/333/b/8/Hyperspacelotus_cut_through_by_kram1032.png)

This is one of three possible space-lotus versions of one variant of the mandelbrot :)

wow! nice... how does it relate to the space-lotus ?

read yourself ;)

It's my basic attempt on one triplex algebra and what you see is of course just the xy crosssection of the whole 3D object...

http://kram1032.deviantart.com/art/Hyperspacelotus-cut-through-145154948 <- there you can read it ;)

I see, its all about changing signs.. or direction of rotation in spherical coordinates.
How come the three bars are not identical in your image ?

first of all, I'm not sure wether my formula will actually return a symmetrical 3D object (though that's rather likely) and second, don't forget that this is only a cut through.
Probably this will look different when you see the full 3d object which I wasn't able to do ^^

So you are slicing through it at some angle ?

at the simplest possible angle.

if your new coordinate is z, then the plane I use is the xy plane. (So, z==0)
My current program doesn't allow for much more.
Though the results already archeived by that is nice :)

and the z coordiate is the one I "reverse the direction" of in the picture above :)
I just chose that variant because it looked visually the most appealing to me ;)

Greetings, and a belated Welcome to this particular Forum !!!     :D

I think just about everybody in this Forum has been "bitten" by the MandelBulb !!!!    ;)   :D