Chapter 9: Fundamental Physics

Section 10: The Sequencing of Events in the Universe

Intrinsic synchronization in cellular automata

Taking the rules for an ordinary cellular automaton and applying them sequentially will normally yield very different results. But it turns out that there are variants on cellular automata in which the rules can be applied in any order and the overall behavior obtained—or at least the causal network—is always the same. The picture below shows how this works for a simple block cellular automaton. The basic idea is that to each cell is added an arrow, and any pair of cells is updated only when their arrows point at each other. This in a sense forces cells to wait to be updated until the data they need is ready. Note that the rules can be thought of as replacements such as "A><B" "<AB>" for blocks of length 4 with 4 colors.

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