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A267679
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Triangle read by rows giving successive states of cellular automaton generated by "Rule 201" initiated with a single ON (black) cell.
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4
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1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0
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COMMENTS
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Row n has length 2n+1.
The fact that only n cells to the left and right of the initially active cell are updated at step n is contradictory to the usual treatment of a "Rule m" automaton, where all cells are updated depending on their neighborhood. See also the illustration of "Rule 201" on the MathWorld page. - M. F. Hasler, Jul 28 2018
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
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LINKS
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EXAMPLE
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The first ten rows:
1
0 0 0
1 0 1 0 1
1 1 0 0 0 1 1
1 1 1 0 1 0 1 1 1
1 1 1 1 0 0 0 1 1 1 1
1 1 1 1 1 0 1 0 1 1 1 1 1
1 1 1 1 1 1 0 0 0 1 1 1 1 1 1
1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1
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MATHEMATICA
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rule=201; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Flatten[catri] (* Triangle Representation of CA *)
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PROG
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(PARI) A267679_row(n)=if(n==1, [0, 0, 0], binary(1<<(n*2+1)-(bittest(n, 0)*2+5)<<(n-1)-1)) \\ M. F. Hasler, Jul 28 2018
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CROSSREFS
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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STATUS
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approved
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