pixels in the same image are correlated but how can I visualize it?
If you would like to show that in natural images, neighboring pixels tend to have similar values, you can use the cooccurrence matrix. The values in the matrix will be distributed mostly along the diagonal.

In the snapshot below, the second image is random and non-correlated. For that image the cooccurrence matrix is pretty much a constant.  I'm not showing the matrices themselves, but a plot of their values such that white means '0'.