Harmonics in 2-D FFT Signal
Your diagram is incorrect. Computing the 2D-FFT of a 8x8 matrix is not the same as computing the 1D-FFT of a 1x64 vector. A 2D-FFT is "probing" your signal with templates which have both an horizontal and vertical frequency. A signal with a low horizontal frequency and a null vertical frequency is a progressive horizontal gradient. A signal whose vertical and horizontal frequency are both the nyquist frequency is a checkerboard pattern...

If you take an image and perform a 2D-FFT on it, you will find in the resulting matrix the following elements:


Cell (1, 1): DC component (average of all values in the matrix).
Cell (2, 1): first horizontal harmonic; frequency 1/8.
Cell (3, 1): second horizontal harmonic; frequency 2/8.
Cell (4, 1): third horizontal harmonic; frequency 3/8.
Cell (5, 1): fourth horizontal harmonic; frequency 4/8 (Nyquist).
Cell (6, 1): third horizontal negative freq. harmonic; frequency -3/8.
Cell (7, 1): second horizontal negative freq. harmonic; frequency -2/8.
Cell (8, 1): first horizontal negative freq. harmonic; frequency -1/8.
Cell (1, 2): first vertical harmonic; frequency 1/8.
Cell (1, 3): second vertical harmonic; frequency 2/8.
...
Cell (5, 5): fourth horizontal/vertical harmonic (Checkerboard pattern).
...


A good way to visualize this is to compute the 2D IFFT of a single pixel at each of the 64 positions of the matrix, and look at the real part.