But all of these patterns in a sense have the same basic form in every direction. Yet there are many animals whose pigmentation patterns exhibit stripes with a definite orientation. Sometimes these stripes are highly regular, and can potentially arise from any of the possible mechanisms that yield repetitive behavior. But in cases where the stripes are less regular they typically look very much like the patterns generated in the pictures at the bottom of this page using a version of the simple mechanism described in the first caption.

Examples of rules in which cells in the horizontal and vertical directions are weighted differently. In the first case, cells at distances 2 and 3 only have an effect in the vertical direction; in the second case, they only have an effect in the horizontal direction. The result is the formation of either vertical or horizontal stripes.

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From Stephen Wolfram: A New Kind of Science [citation]