I think what is happening is that interior detection is taking precedence over boundary detection. Instead, just flag the point as interior, then outside the loop, check the boundary first, then if interior return interior color, else return exterior color.

While your derivative is correct, it can be simplified to -2z/(z²-1)² by multiplying out the numerator instead.

I missed that you are iterating z = z2/(z2 +c ). Shouldn't it be z2/z2m1 + c?

What should work is something like this (I don't use c or c++ so may not be correct):

  boolean IsInterior;
...
      if (cabsz< PixelWidth) IsInterior = true;

...

  if (distance <distanceMax) return iColorOfBoundary;
  if (IsInterior) return iColorOfInterior;
  return iColorOfExterior;


As I generally combine DE and other methods into one procedure for iteration, the general hierarchy I use for checking after iteration is orbit traps, boundary, other. The other is classified by the iteration as interior/exterior/in set.