Chapter 7: Mechanisms in Programs and Nature

Section 7: Origins of Discreteness

2D [discrete] transitions [in cellular automata]

The simplest symmetrical rules (such as 4-neighbor totalistic code 56) which make the new color of a cell be the same as the majority of the cells in its neighborhood do not exhibit the discrete transition phenomenon, but instead lead to fixed regions of black and white. The 4-neighbor rule with totalistic code 52 can be used as an alternative to the second rule shown here. A probabilistic version of the first rule shown here was discussed by Andrei Toom in 1980.

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