Higher Iterations

[grundraisin]

Hi Everyone,

It was two weeks ago my brother send me an email with the link of Skytopia where I discovered these incredibles images of the mandelbulb world.
Immediatly I told myself: I want to do the same, to build a beautiful mandelbulb and make an animation where I can travel all around the mandelbulb, go deeper and deeper in this world with a good music on the background.
I found this forum where I saw these same images. And I have a question, I found lot of software to generate mandelbulb but I never can't generate a beautiful mandelbulb like Twinbee on the first page of this post or like here:
 http://www.fractalforums.com/mandelbulb-renderings/improved-lighting/
I spend all my nights on it and I can't find the formulas parameters to obtain this kind of romanesco shape.
I work with ChaosPro, and I play with the lights, change some parameters of the mandelbulb formula, I never find the way to increase the interation and obtain the pictures like I see on this forum. When the number of iterations increase the details became more and more complex (it's normal of course) but too much fretful, not the same way I can saw on the Twinbbe's iterations example where all the results are very soft.

So, my question is simple: With which software you work to obtain this deepness on the pictures (it is like some fog-shadow on the background) and to increase iteration and keep smooth details? I know it will be time consuming to obtain these beautiful pictures but I am not afraid to work on it.
Thank you for your help.

[LesPaul]

Why does it appear that higher iterations are adding to the set?  Doesn't iteration normally remove from the set?

These were views from inside the set looking out, i.e. the outside was solid and the inside hollow.

Ah, of course.  Easier to see the deep parts that way.

[Timeroot]

Great! So smooth iteration building is possible. I'm guessing it uses the same kind of idea that the 'smooth colouring' does for the normal 2D Mandelbrot?

That's exactly how it works - a kind of "bailout extrapolation", if you will. In fact, it works for any fractal whose value of z grows like a^(Power^iter), where a is dependent upon the pixel. This means for Mandelbrot sets, Julia Sets, and (for example) the perpendicular slice of the power 1 MBulb, this works. Or, since newton iteration has quadratic convergence (usually), using power=-2 also gives smooth coloring. It's  very general formula indeed.

P.S. after I read this thread a couple days ago I implemented this formula with several fractal types in ahm.ucl in UF formula library, thinking it was something new. A few hours after uploading I discover the regular "Smooth (Mandelbrot)" did the exact same thing. 

[LesPaul]

So, my question is simple: With which software you work to obtain this deepness on the pictures (it is like some fog-shadow on the background) and to increase iteration and keep smooth details? I know it will be time consuming to obtain these beautiful pictures but I am not afraid to work on it.
Thank you for your help.

Hi, grundraisin, and welcome to the forum.  The answer to your question is a little tricky.  Many here are using software that they've written themselves.

Some are using UltraFractal with quite a bit of custom "programming" done in the form of plug-ins (for 3D rendering, or lighting, for example).  I don't believe that there's a one-size-fits-all solution to doing this sort of rendering, yet, mainly because the mandelbulb itself is such a recent discovery.

Your best option might be to choose a specific image or animation from a particular member, and ask him or her what software or method was used in that instance.

[trafassel]

The same scene with my new renderer (source code available at github, project "Gestaltlupe").

Compile this project on Visual Studio 2008 (or sharpdevelop), load "settings\animation\varIterations\eins.xml" and press start to render one picture.

[trafassel]

All 3 parts in one film:

<a href="http://www.youtube.com/v/FavM9Y4d4FY&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/FavM9Y4d4FY&rel=1&fs=1&hd=1</a>

[kram1032]

it's like liquid that crystalizes in stunning shapes

[trafassel]

For smooth iteration in this video i used the following computations. No much math here, just playing with parameters and comparing results.

//Initialisation:
double gr1=GetDouble("Formula.Static.Cycles"); // Number of iterations
int tempGr=(int)gr1;
double gr1Frac=gr1- tempGr;
gr1=1-gr1Frac;
gr1*=2.4;

double gr =Math.Pow(10,gr1)+1.0;  // Bailout

// ... in iteration:

double r= Math.Sqrt(x*x+y*y+z*z);
if (r > gr) { tw = n; /* abort iteration: no inner point */ break; }

<a href="http://www.youtube.com/v/xZeHSzGCSfg&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/xZeHSzGCSfg&rel=1&fs=1&hd=1</a>