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Rule 94


ElementaryCARule94

Rule 94 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 94=01011110_2. This rule is illustrated above together with the evolution of a single black cell it produces after 15 steps (Wolfram 2002, p. 55).

Rule 94 is amphichiral, and its complement is 133.

Starting with a single black cell, successive generations n=0, 1, ... are given by interpreting the numbers 1, 7, 27, 119, 427, 1879, 6827, 30039, ... (OEIS A118101) in binary, namely 1, 111, 11011, 1110111, 110101011, ... (OEIS A118102). A formula for the nthe term is given by

 a(n)={1   for n=0; 7   for n=1; 1/6(10+11·4^n)   for n>1 odd; 1/3(1+5·4^n)   for n>0 even
(1)

(E. W. Weisstein, Apr. 12, 2006), so computation of rule 94 is computationally reducible for evolution from a single black cell, in which case it has generating function

 -((2x+1)(16x^4-5x-1))/((x-1)(x+1)(4x-1)(4x+1)).
(2)

Rule 94 is capable of exhibiting nesting and random behavior for some simple initial conditions (Wolfram 2002, p. 951). In particular, the random behavior is most likely to be computationally irreducible.


See also

Elementary Cellular Automaton, Rule 30, Rule 50, Rule 54, Rule 60, Rule 62, Rule 90, Rule 102, Rule 110, Rule 126, Rule 150, Rule 158, Rule 182, Rule 188, Rule 190, Rule 220, Rule 222

Related Wolfram sites

http://atlas.wolfram.com/01/01/94/

Explore with Wolfram|Alpha

References

Sloane, N. J. A. Sequences A118101 and A118102 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. 90, 55, 870, and 952, 2002.

Referenced on Wolfram|Alpha

Rule 94

Cite this as:

Weisstein, Eric W. "Rule 94." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Rule94.html

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