Suggestion: stack the images vertically or horizontally. Frequency spectrum compression schemes like JPG will see the similarity in the fine details.
Could it be possible that jpg also exploits the repetition at the wavelength of the width of a single picture, so to say? E.g. 4 pictures side-by-side with the same black dot in the center, can all 4 dots be encoded with a single sine wave (simplifying a lot here..) that has peaks at each dot?