Rule 222
Rule 222 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 222 is amphichiral, and its complement is rule 132.
Starting with a single black cell, successive generations 
, 1, ... are
given by interpreting the numbers 1, 7, 31, 127, 511, 2047, 8191, ... (OEIS A083420)
in binary, namely 1, 111, 11111, 1111111, 111111111, .... The 
th term is given
by
 |
which are Mersenne numbers, so rule 222 is computationally reducible for an initial configuration consisting of a single black cell.
Contact the MathWorld Team
rule 222
