I'm new to Discrete Cosine Transform (DCT) and I have a question relating to basis functions. In DCT, basis functions are defined by:
$$\alpha_p\alpha_q\cos\frac{\pi \left(2m+1\right)p}{2M}\cos\frac{\pi \left(2n+1\right)q}{2N},\quad \begin{align}0&\leq p\leq M-1\\0&\leq q\leq N-1\end{align}$$
If $M = N = 64$, we'll have $64$ basis functions. These functions have two variables including $p$ and $q$. Now, to verify, I take the first basis function with $m = n = 0$. Clearly, this function changes with different values of $p$ and $q$. Why it's drawn with same color in the following image (the upper left gray square)?