Rule 188 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 230, 194, and 152, respectively.
Starting with a single black cell on an otherwise white infinite row, successive generations ,
1, ... are given by interpreting the numbers 1, 3, 5, 15, 29, 55, 93, 247, 477, ...
(OEIS A118173) in binary,
namely 1, 011, 00101, 0001111, 000011101, ... (OEIS A118174).
The th iteration has generating
function
. This rule is illustrated above together with
the evolution of a single black cell it produces after 15 steps (Wolfram 2002, p. 56).
,
1, ... are given by interpreting the numbers 1, 3, 5, 15, 29, 55, 93, 247, 477, ...
(OEIS A118173) in binary,
namely 1, 011, 00101, 0001111, 000011101, ... (OEIS A118174).
The 
th iteration has generating
function
![a(n)={1/(30)[55·2^n+3i(2i)^n-14] for n odd; 1/(15)[25·2^n+3(2i)^n-13] for n even.](/images/equations/Rule188/NumberedEquation2.svg)
is the imaginary
unit.
