Chapter 11: The Notion of Computation

Section 11: The Threshold of Universality in Cellular Automata

[Structures in] rule 41

Various rules like rule 41 below can perhaps be viewed as having localized structures—though ones that apparently always travel in the same direction at the same speed. None of the first million initial conditions for rule 41 yield unbounded growth, though some can still generate fairly wide patterns, as in the pictures below. (The initial condition consisting of repeated, followed by , followed by repeated nevertheless yields a region that grows forever.)

Image Source Notebooks:

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