How can I efficiently determine where in a radial gradient the bands are really close together?

Question

When using my radial gradient algorithm with the Spread property set to Reflect or Repeat, I get crazy ass moiré when the bands are too close together. This is normal.

What I have been trying to understand is how to figure out where this happens, or if it's at all possible to figure this out. If I can determine some kind of "distinct<->muddled" value, I can use it as a weight to blend between the gradient color at a given pixel and a weighted average of all the colors, thereby mitigating the moiré.

I know this is quite an obscure topic, and maybe this is more of a math question, but does anybody have any ideas?

For reference, my algorithm is similar to this implementation.

Here is what my code gives now:

Answer 1

Use a 3x3 filter and for each 3x3 pixel patch compute the color variance. E.g. for each two adjacent pixels in the patch ( e.g pix( 0,0 ) and pix(0,1)) get the absolute value of the difference between each color channel, square it and sum.

So something like:

double pixelVariance( pix a, pix b )
{
    double variance = 0;
    variance += ( a.red   - b.red   ) * ( a.red   - b.red   );
    variance += ( a.green - b.green ) * ( a.green - b.green );
    variance += ( a.blue  - b.blue  ) * ( a.blue  - b.blue  );
    return variance;
}

Then variance for the 3x3 patch:

double patchVariance( Patch patch )
{
   double variance = 0;
   variance += pixelVariance( patch( 0, 0 ), patch( 0, 1 )); 
   variance += pixelVariance( patch( 0, 0 ), patch( 1, 0 )); 
   // etc.
   return variance;
}

Patches with high variance are not smooth gradients and are almost certainly going to be high moire areas.