A266588 Triangle read by rows giving successive states of cellular automaton generated by "Rule 37" initiated with a single ON (black) cell.

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

Mathematica

rule=37; 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: A189209 A266754 A071982 * A157749 A129407 A267594

Adjacent sequences: A266585 A266586 A266587 * A266589 A266590 A266591

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 01 2016

Status

approved