A267053 Triangle read by rows giving successive states of cellular automaton generated by "Rule 93" initiated with a single ON (black) cell.

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

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

Mathematica

rule=93; 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: A267800 A373993 A322980 * A359591 A359592 A257477

Adjacent sequences: A267050 A267051 A267052 * A267054 A267055 A267056

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 09 2016

Status

approved