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The simplest system based on constraints that is forced to exhibit a non-repetitive pattern. The constraint requires that the arrangement of colors around each cell must match one of the 12 templates shown, and that at least somewhere in the pattern a template containing a pair of stacked black cells must occur. In the numbering scheme used on preceding pages, the constraint is number 18762389. The pattern shown is unique, in that no variations of it, except for trivial translations, will satisfy the constraints. The nested structure on the diagonal essentially corresponds to a progression of base 2 digit sequences for positive and negative numbers.

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