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Rule 190
Rule 190 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 246, 130, and 144, respectively.
Starting with a single black cell, successive generations 
, 1, ... are given by interpreting the numbers 1, 7, 29,
119, 477, 1911, 7645, 30583, ... (OEIS A037576)
in binary, namely 1, 111, 11101, 1110111, 111011101, ... (OEIS A118111).
The 
th term is given by the first 
terms of the quaternary sequence
131313..., or, more explicitly, by
 |  |  |
(1)
|
 |  | ![1/(15)[-10-3(-1)^n+7·4^(n+1)]](https://mathworld.wolfram.com/images/equations/Rule190/Inline10.svg) |
(2)
|
(E. W. Weisstein, Apr. 13, 2006). Rule 190 is therefore computationally reducible for an initial configuration consisting of a single black cell. It has generating function
 |
(3)
|
See also
Elementary Cellular Automaton, Rule 30, Rule 50, Rule 54, Rule 60, Rule 62, Rule 90, Rule 94, Rule 102, Rule 110, Rule 126, Rule 150, Rule 158, Rule 188, Rule 220, Rule 222Related Wolfram sites
https://atlas.wolfram.com/01/01/190/Explore with Wolfram|Alpha
References
Sloane, N. J. A. Sequences A037576 and A118111 in "The On-Line Encyclopedia of Integer Sequences."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.Referenced on Wolfram|Alpha
Rule 190Cite this as:
Weisstein, Eric W. "Rule 190." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Rule190.html