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Value of the one-dimensional radius 2 totalistic 2-color cellular automaton rule 20 after 1 step, with initial condition n.
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%I #17 Aug 27 2023 19:23:24

%S 0,0,15,0,7,15,17,0,3,7,19,15,25,17,45,0,1,3,23,7,27,19,41,15,29,25,

%T 107,17,37,45,85,0,0,1,31,3,31,23,33,7,31,27,99,19,33,41,93,15,31,29,

%U 231,25,99,107,217,17,33,37,155,45,93,85,165,0,0,0,15,1

%N Value of the one-dimensional radius 2 totalistic 2-color cellular automaton rule 20 after 1 step, with initial condition n.

%C The initial pattern is the binary representation of n. A cell becomes live in the next step if either 2 or 4 of its neighbors (including itself) was live in the previous step. The output is interpreted as a binary integer, with factors of 2 removed.

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/TotalisticCellularAutomaton.html">Totalistic Cellular Automaton</a>.

%H Stephen Wolfram, <a href="http://www.wolframscience.com/nksonline/page-281">A New Kind of Science, page 281</a>.

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%F a(2n) = a(n).

%e For n=3, the system's evolution for 1 step is:

%e 001100 = 3,

%e 011110 = 15.

%t input[x_] := RealDigits[x, 2]; step[x_] := Flatten[CellularAutomaton[{20, {2, 1}, 2}, {Part[input[x], 1], 0}, {{1}}]]; a[x_] := FromDigits[step[x], 2]; Table[a[n], {n, 100}]

%K nonn

%O 1,3

%A _Ben Branman_, Dec 25 2011