One straightforward way of doing this is to consider arbitrarily-sized patches of the image. For example, let's say we are interested in all 9*9 regions of pixels that can be taken from the image. Extract each of these image patches, and transform each image patch to a row vector. Consider the entire set of image patches (8464 row vectors for a 100*100 pixel image) as a matrix M.
Compute the correlation (or covariance, corr(M) and cov(M) in Matlab) between each of the columns in M. For your specific question, look at the three columns of the correlation/covariance matrix corresponding to the central pixel in the image. Reshape these back to the size of the image patch, and plot these. For natural images, you should find that the central pixel is highly correlated with adjacent pixels, and that the correlation decreases as distance from the central pixel increases across each of the three color channels.