Coloring the Mandelbulb

[trafassel]

Classic overlay coloring for all i

[trafassel]

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

[trafassel]

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.

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

[M Benesi]

  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: