This problem is traditionally solved by attempting to teach the aliens how to decode the pattern inside the pattern itself. For example a rendering might look like

    x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
    x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ x
    x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
    x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ x
    x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
    x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ x
    x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
    x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ x
    x _ _ x _ x _ x x x _ x _ x _ _ x _ x _ x x x _ x _ x _ _ x
    x _ _ x _ x _ x _ _ _ x _ x _ _ x _ x _ x _ x _ x _ x _ _ x
    x _ _ x x x _ x x _ _ x x x _ _ x x x _ x _ x _ x _ x _ _ x
    x _ _ x _ x _ x _ _ _ _ x _ _ _ _ x _ _ x _ x _ x _ x _ _ x
    x _ _ x _ x _ x x x _ _ x _ _ _ _ x _ _ x x x _ x x x _ _ x
    x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ x
    x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
    x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ x
    x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
    x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ x
    x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
    x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ x
    x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

The idea is that the aliens can figure out first that these opening and closing sections have periodicity 30, and because they are so repetitive they do not contain the actual data bits, but then there is a central section which does contain complexity.

So then they will hopefully alight upon the idea of looking at the code two-dimensionally, and adjust their browser width until the lines all line up, at which point they get the custom message.