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Fifteen hundred steps in a cellular automaton

Fifteen hundred steps of rule 30 evolution. Some regularities are evident, particularly on the left. But even after all these steps there are no signs of overall regularity—and indeed even continuing for a million steps many aspects of the pattern obtained seem perfectly random according to standard mathematical and statistical tests. The picture here shows a total of just under two million individual cells.

Image Source Notebooks:

  • Wolfram Language source code for image on page 30

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