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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.

Patterns generated by rules shown on previous page

Patterns generated by rules of the type shown on the previous page, with a range of choices for the weights of cells at distances 2 and 3. Weights vary from -0.9 to 0 down the page for distance 2, and from -0.7 to 0.4 across the page for distance 3. In all cases the evolution starts from the same random initial condition, and is continued until it stabilizes. Note that pigmentation patterns for actual animals may contain either larger or smaller numbers of elements than the patterns shown here.

Rules in which horizontal and vertical cells are weighted differently

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]