Rule 126

Rule 126 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its color and its immediate neighbors. Its rule outcomes are encoded in the binary representation . This rule is illustrated above together with the evolution of a single black cell it produces after 15 steps (Wolfram 2002, p. 55).

Rule 126 is amphichiral, and its complement is rule 129.

Starting with a single black cell, successive generations , 1, ... are given by interpreting the numbers 1, 7, 27, 127, 387, 1935, 6579, 32767, ... in binary, namely 1, 111, 11011, 1111111, 110000011, ....

REFERENCES:

Wolfram, S. "Statistical Mechanics of Cellular Automata." Rev. Mod. Phys. 55, 601-644, 1983.

Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, pp. 55, 90, and 952, 2002.