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Found on top of the spine (view is from inside the set).

Let (x,y,z) be the coordinate of the last point in the iteration.

The rgb-Values of the surface color is given by red=x*x; green=y*y and blue=z*z.

Zoom in the last scene with 13 iterations.

Interesting notion. It seems to only yield coherent patterns in the sections where the iteration rate's too low to show all the details, but the pattern that it does yield looks sort of like a picture of what's going to be there as you iterate. I assume the pattern changes slightly as you modify the iteration count, but are there substantial changes? All in all, I like the idea.

Yes, definitely an interesting coloring method going on there.    :D

It would have been quite unique to use a photograph used for the coloring, for example somebody's face.  
Imagine all of those little faces at the end of those "stalks".
 :rotfl:
 

Instead of faces i would prefer a strawberry.

Same Mandelbulb scene (its exactly the same 3D body), but 1 more iteration steps for coloring.

how does this perform on a smooth iteration animation?

That would work just as well.  Whatever image a person wanted to use for the coloring of an area would make for some very interesting "bulbs".  


These additional images were interesting also.
 

Why does there not seem to be areas where the colors are more blended? Everything looks like it's either red, green or blue and not mixed.

That's true. It looks like the transitions between colors are just so fast you can't really see them, probably because of the normal behavior of the points as they iterate--it looks like the points tend to stay near axes.

Colored combination of the last 2 pictures ( with Paint.Net ).

Ahhhh...  now we are getting somewhere!!!    :)
 

looks like the colouring could be iteration-additive or something, so that you automatically mix all the colours per iteration to do a final either nice and smooth or boring (that has to be tried out^^) gradient :)

The color combination works, but some drawings are are weird.

looks a lot like a wave pattern :)

Same color method; 10 iterations.

Wow, very nice! Looks amazing.

That looks pretty good :)

WOW, it looks like those fabrics which changes "metallic" colours due to the light angle.

Really amazing!

Soap bubble!

Color combination is given by (Gestaltlupe formula):

        public override void Init() {
          base.Init();
          additionalPointInfo=new AdditionalPointInfo();
          gr1=GetDouble("Formula.Static.Cycles");
          int tempGr=(int)gr1;
          gr1=gr1- tempGr;
          gr1=1-gr1;
          gr1*=2.4;
        }

 double gr1=0;

        public override long InSet(double ar, double ai, double aj,  double br, double bi, double bj, double bk, long zkl, bool invers) {
            double aar, aai, aaj;
            long tw;
            int n;
            int pow = 8; // n=8 entspricht dem Mandelbulb
                double gr =Math.Pow(10,gr1)+1.0;  //   10; // Ab diesem Wert liegt mit Sicherheit Nichtzugehörigkeit zur Menge vor.
            double theta, phi;

            double r_n = 0;
            aar = ar * ar; aai = ai * ai; aaj = aj * aj;
            tw = 0L;
            double r = Math.Sqrt(aar + aai + aaj);

             double      phi_pow;
             double       theta_pow;
             double    sin_theta_pow;
              double  rn_sin_theta_pow;

additionalPointInfo.red=0;
additionalPointInfo.green=0;
additionalPointInfo.blue=0;

double red=0; double green=0; double blue=0;

            for (n = 1; n < zkl; n++) {

                theta = Math.Atan2(Math.Sqrt(aar + aai), aj);
                phi = Math.Atan2(ai, ar);
                r_n = Math.Pow(r, pow);

                phi_pow=phi*pow;
                theta_pow=theta*pow;
                sin_theta_pow=Math.Sin(theta_pow);
               rn_sin_theta_pow=r_n* sin_theta_pow;


                ar =  rn_sin_theta_pow * Math.Cos(phi_pow)+br;
                ai = rn_sin_theta_pow * Math.Sin(phi_pow)+bi;
                aj = r_n * Math.Cos(theta_pow)+bj;

                aar = ar * ar; aai = ai * ai; aaj = aj * aj;
                r = Math.Sqrt(aar + aai + aaj);

if(n>2) {
/*
double arPos=ar; if(arPos<0) arPos=-ar;
double aiPos=ai; if(aiPos<0) aiPos=-ai;
double ajPos=aj; if(ajPos<0) ajPos=-aj;
red+=Math.Abs(ar)/r;
green+=Math.Abs(ai)/r;
blue+=Math.Abs(aj)/r;
*/

if(ar>0)
  red+=ar/r;
if(ai>0)
  green+=ai/r;
if(aj>0)
  blue+=aj/r;

}

                if (r > gr) { tw = n; break; }

            }

additionalPointInfo.red=red;
additionalPointInfo.green=green;
additionalPointInfo.blue=blue;


            if (invers) {
                if (tw == 0)
                    tw = 1;
                else
                    tw = 0;
            }

            return (tw);

        }

Colors on a flat surface.

also nice but obviously, the shape adds a lot to it. :)

I don't think so. It seems, as the color "knows" how the shape looks in higher iterations. And perhaps this is fundamental for all variants of the mandelbulb fractal.

(http://files.me.com/trafassel/ovqp7l)

With adding a lot to it, I meant things like shadow.
That colour pattern lacks of shadow. No wonder: Where should it come from? :)

Same picture as the spine in the gallery, but with post processing (Paint.Net).

nice :D A metallic soap bubble :)

Stereo image

(http://files.me.com/trafassel/fm3zww)(http://files.me.com/trafassel/vnk2lm)

hard to think of it as stereo with this arrangement :P
But it looks very nice :)

use CTRL - +/-
to lower the zoom, to see it side by side

I can't seem to make it go side-by-side... but I can turn my head just enough to make it work. Cool!

Next time i combine both pictures in one bitmap. You can also use two webbrowsers side by side.

The Ctrl - idea works but the text now is ridiculously small xD

Then you should press CTRL-0 (that's a zero) to reset the zoom-factor ;)

Cool!

klixon: I know. I'd just like to read and see images at the same time :)

Color distribution inside the mandelbulb.

http://www.youtube.com/watch?v=j4_9rtHfDDU

Same coloring method, other fractal (formula 21 type).


The solution of a 2 coloring problem on a fractal map.

it seems underexposured (dark) to me but it looks nice :)

I've been using the orbital color scheme since I discovered how to implement it in ChaosPro, and it's pretty nice.  I decided to mess around today, and changed the values I picked out of the iterations.  

  First, I'm using what I call a "complex triplex" formula type.  It runs quite a bit faster than the trig versions, and I just threw in some further optimizations that shaved an extra second off of a small (444x444) zoomed in 10 iteration z^9 bulb.  

  I was using the values r (the magnitude of x,y and z at the end of an iteration), x, y, and z to assign colors.  Well, I decided to simply take the components of the 2 complex numbers after I take them to the nth power, and ended up with a similar, but slightly more interesting color scheme (will put code after image):

z^3:
(http://lh5.ggpht.com/_gbC_B2NkUEo/TCanhYaJ-YI/AAAAAAAAAg0/muECr6NKCkU/pretty%20coloring%20tree.jpg)
z^7 4d:
(http://lh6.ggpht.com/_gbC_B2NkUEo/TCaprRFKEbI/AAAAAAAAAg8/aOV2AB8aRdo/disco%20ball.jpg)
z^9:
(http://lh6.ggpht.com/_gbC_B2NkUEo/TCaq9N3P87I/AAAAAAAAAhE/trg1Fj99D2Y/quick%20and%20prett.jpg)

as said in the other thread:
Great :D

Stereo Images (cross eye).

O.o
What a colourful danger for the eyes lol

Same scene, higher iterations. Prostproduction is done with Paint.Net.

Classic overlay coloring for all i

Classic overlay coloring for all i

Overlay coloring for the weighted sum of (x,y,z) in the iteration step i-2,i-1 and i.

Coloring (r,g,b) as weighted sum of (x,y,z) in the iteration step n-2,n-1 and n in a smooth iteration movie.

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

  I've written some algorithms for ChaosPro, capturing various parts of the mathematics for various coloring styles. 

  As I use complex triplex algebra rather than trig to do my calculations (for speed, 2x as fast on my comp), I have the option of using parts of the complex numbers (rather than simply using x,y, and z components after an iteration, I can use the parts of the complex numbers).  Using the complex portions (prior to adding in pixel values/finishing the iteration calculation) makes for some very distinct coloring patterns.

  I also "average" the components (not simply taking the last component, or a specific iteration's component values).  It's not really an average, rather it's the total magnitude of the component over all iterations:
x_component =sqrt (new_x^2 + x_component^2)   // same for y, z, or whatever...

  I like doing this, instead of calculating standard average because... I don't know.  I just do.

  Anyways, you can get awesome contrasts when using HSLA lighting mode (hue/saturation/luminosity/alpha channel) by using the correct component to assign luminosity.  It really helps enhance the details of the fractal. 

  Following are a couple images:
(http://lh4.ggpht.com/_gbC_B2NkUEo/TIRT6ox5MaI/AAAAAAAAAoc/kh8uvAfilJY/alive.jpg)
(http://lh3.ggpht.com/_gbC_B2NkUEo/TIRT6kRQLEI/AAAAAAAAAoY/AA9dcqMytmc/space%20platform.jpg)
  (http://lh6.ggpht.com/_gbC_B2NkUEo/TIRT6Vr8kLI/AAAAAAAAAoQ/a2MMpyQfDnc/happy%20fun%20ball.jpg)

  (http://lh4.ggpht.com/_gbC_B2NkUEo/TIKuZMDdp5I/AAAAAAAAAnM/sddZ-zB3INY/8th%20order%20mandelbrot%20gold%20big.jpg)