The function gives the same result regardless of the sign of the two components, so there's axes of symmetry around the lines defined by (x ± xi): in the first

The function gives the same result regardless of the sign of the two components, so there's axes of symmetry around the lines defined by (x ± xi): in the first image that gives four axes on the horizontal, vertical, and diagonal lines through the origin. The two zoomed images are along the diagonal extending up to the top left and so there's diagonal symmetry visible. I think that would probably count as it revealing symmetry in the underlying object rather than in the lens, it's not a consequence of rounding or asymptotes or floating point errors or any such.