what's gaussian noise look like? I am using Matlab function imnoise to add gaussian noise to one image. However, it seems that adjacent samples of the noise is correlated. I am using matlab code below to add noise.

 I = imread('eight.tif');
 J = imnoise(I, 'gaussian', 0, 0.02);
 figure; imshow(I);
 figure; imshow(J);




From the image, it contains many short vertical gray lines which maybe be image structures for some cases. Is the noise really additive white gaussian noise(AWGN)?

histogram of noise:
Yes it is. However, unlike real AWGN which comes mostly from thermal agitation in electronics, matlab's noise is not purely random, this might be the cause of you seeing a deterministic pattern. But this pseudo-random noise is usually random enough to approximate real life noise

If you want to assess the noise "randomness", plot an intensity histogram of In-I, with In being the noised image and I the original image (you are subtracting the deterministic part and keeping the random part).