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)
			(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)

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.