Are decomposed images always centrally symmetric?

The spectrum (image on the right) is centrally symmetric for any real-valued signals.

I'm still a little confused on the symmetry of the spectrum image. According to Quiz 4, "Values near the center of the image correspond to low frequencies...Pixels further along the x-axis correspond to higher and higher frequencies in the horizontal direction, and likewise for the y-axis."

If the center is low frequencies, then wouldn't there be negative x and y axeses (and negative frequencies)? I can kind of see how the central symmetry of the images makes that distinction unimportant, but it's still not entirely clear to me.

@zhaur Here's another way to think about this image.

Let's say that we represent every point in our spectrum in terms of polar coordinates (\theta, r), where the radius r is the distance from the center (i.e., the magnitude of a vector) and \theta is the angle (i.e., the orientation of a vector). The point at the very center is given by r=0, and represents the lowest possible frequency (the DC or constant component).

Here, a low value r represents low frequencies, and a high value r represents high frequencies. The value of \theta corresponds to the orientation of features in our image, e.g., the difference between horizontal, vertical, and slanted features.

What is the difference between coordinates (r,\theta) and (r, \theta+\pi) in the spectrum? If \theta=0, then these coordinate would represent frequencies to the left and right of the center. Both represent the same frequency, but oriented in the opposite direction. For real-valued signals though, the spectrum at coordinates (r,\theta) and (r,\theta+\pi) will be identical; they both respond the same way to vertical features in the image.