How do I colour a Mandelbox?

[G]

Hey guys,

So I'm currently writing a program to generate pictures via ray-tracing of the mandelbox by using the distance estimation formula. I was wondering if there was any algorithm that assigned unique/interesting colours to different parts of the Mandelbox. Presumably I would have to work off values of the distance from the screen. Is there any other way to do it?

[Tglad]

Like other 3d escape time fractals you can colour it based on the iteration count of the surface points. This is usually the nicest looking, but I can't give you the details because I forget how you do it exactly.
Another, similar way to colour is to keep a track of how much the point has expanded at the point you draw it (when the max iterations have expired).

[cKleinhuis]

another option is to just use the normalised 3 dimensional point as color

[Rrrola]

Orbit trap: for all iterations, compute the distance from the origin. The color is the smallest distance from these. (It doesn't actually have to be the origin, of course.)

[joeytwiddle]

One interesting way to choose a colour is by counting the number of times each fold was applied during iteration.  Mandelbulber does this but combines all the counts into one value.

I experimented with building a colour out of the 3 fold counts like this:

Code:

//// Weight the colors because some folds occur more often than others
var multr = Math.pow(0.70, foldCounts.fixedSphere);
var multg = Math.pow(0.99, foldCounts.box);
var multb = Math.pow(0.60, foldCounts.minSphere);
//// Note these numbers get smaller with more iterations, so...

//// Normalise the result (find the ratio)
var maxMult = Math.max(Math.max(multr,multg),multb);
multr /= maxMult;
multg /= maxMult;
multb /= maxMult;

//// Apply lighting separately
data[ptr]   = lightness*multr;
data[ptr+1] = lightness*multg;
data[ptr+2] = lightness*multb;

So redness should correspond inversely to the number of fixedSphere folds, greenness to box folds, and blueness to minSphere folds.  The result is:



At higher iterations further variations on these colours can be found.  It seems unlikely we'll ever see pure red this way though! 

The above combination generates somewhat pastel colours as you can see, but I found these reasonably good for picking out bumps with lighting.  But there are many other ways you could visualise the fold counts.

You can try out the application here (Javascript - no WebGL).