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The complete collection of all 171 patterns needed to satisfy constraints of the type shown on the previous page. If none of these 171 patterns satisfy a particular constraint, then it follows that no pattern at all will satisfy the constraint. The patterns are labelled by numbers which specify the minimal constraint which requires the given pattern. Patterns differing by overall reflection, rotation or interchange of black and white are not shown.

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