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Examples of patterns produced by two-dimensional Turing machines whose heads have four possible states. In each case, all cells are initially white, and one of the rules given on the left is applied for the specified number of steps. Note that in the later cases shown, the head often visits the same position on the grid many times.

Examples of patterns produced by two-dimensional Turing machines whose heads have four possible states. In each case, all cells are initially white, and one of the rules given on the left is applied for the specified number of steps. Note that in the later cases shown, the head often visits the same position on the grid many times.


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