Rule 158 is one of the elementary cellular automaton rules described by 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. 56).
The mirror image, complement, and mirror complement are rules 214, 134, and 148, respectively.
Starting with a single black cell on an otherwise white infinite row, successive generations 
,
1, ... are given by interpreting the numbers 1, 7, 29, 115, 477, 1843, 7645, ...
(OEIS A118171) in binary,
namely 1, 111, 11101, 1110011, 111011101, ... (OEIS A071037).
The decimal value of the 
th
iteration is given in closed form by
![a(n)=1/(30)[-16+(-4)^n-10(-1)^n+55·4^n]](/images/equations/Rule158/NumberedEquation1.svg) |
(E. W. Weisstein, Apr. 13, 2006), so computation of Rule 158 is computationally reducible for an initial
configuration consisting of a single black cell. 
has generating function
 |
