A267679 Triangle read by rows giving successive states of cellular automaton generated by "Rule 201" initiated with a single ON (black) cell.

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

Offset

0

Comments

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

References

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

Robert Price, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Example

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

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A267681 (value of row n read as binary number). - M. F. Hasler, Jul 28 2018

Sequence in context: A089011 A267043 A266444 * A267868 A288733 A095111

Adjacent sequences: A267676 A267677 A267678 * A267680 A267681 A267682

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 19 2016

Status

approved