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Rule 126


ElementaryCARule126

Rule 126 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 126=01111110_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 126 is amphichiral, and its complement is rule 129.

Starting with a single black cell, successive generations n=0, 1, ... are given by interpreting the numbers 1, 7, 27, 127, 387, 1935, 6579, 32767, ... in binary, namely 1, 111, 11011, 1111111, 110000011, ....


See also

Elementary Cellular Automaton, Rule 30, Rule 50, Rule 54, Rule 60, Rule 62, Rule 90, Rule 94, Rule 102, Rule 110, Rule 150, Rule 158, Rule 182, Rule 188, Rule 190, Rule 220, Rule 222

Related Wolfram sites

http://atlas.wolfram.com/01/01/126/

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References

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 126

Cite this as:

Weisstein, Eric W. "Rule 126." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Rule126.html

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