I haven't thought about it a lot, but here is my understanding of the effect.  A symmetry axis (e.g., 2-fold) basically is the same as having 2 identical cells on top of each other, rotated 180 degrees. Imagine that cell 1 has random density.  Then cell 2 has the same random density, rotated 180 degrees. Now add them together. At most points, the density from cell 1 and cell 2 are different, and the RMS of their sum is about sqrt(2) times the RMS of either one.  On the other hand, at the symmetry axis, the density from cell 1 and cell 2 are identical, so that they always add constructively and the RMS is 2 times the RMS of either one.  As you move away from the axis, the effect is smaller, and it decays away over the resolution of the map.  Note that if you have a 3-fold, 4-fold or 6-fold, then the effect is even bigger.

All the best,

Tom T