A266659 Triangle read by rows giving successive states of cellular automaton generated by "Rule 47" initiated with a single ON (black) cell.

1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1

Offset

0

Comments

Row n has length 2n+1.

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
                1 1 0
              0 0 0 1 1
            1 1 1 1 1 0 0
          0 0 0 0 0 0 0 1 1
        1 1 1 1 1 1 1 1 1 0 0
      0 0 0 0 0 0 0 0 0 0 0 1 1
    1 1 1 1 1 1 1 1 1 1 1 1 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0

Mathematica

rule=47; 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 *)

Crossrefs

Sequence in context: A157022 A016362 A016415 * A214960 A127693 A129405

Adjacent sequences: A266656 A266657 A266658 * A266660 A266661 A266662

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 02 2016

Status

approved