Rule 220 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).
The mirror image, complement, and mirror complement are rules 206, 196, and 140, respectively.
Starting with a single black cell, successive generations 
, 1, ... are given by interpreting the numbers 1, 3, 7, 15,
31, 63, 127, 255, ... (OEIS A083420) in binary,
namely 1, 11, 111, 1111, .... Or including leading zeros, 1, 011, 00111, 0001111,
... (OEIS A118175). The 
th term is given by
 |
which are alternate Mersenne numbers, so rule 220 is computationally reducible for an initial configuration consisting of a single black cell.
