A266843 Triangle read by rows giving successive states of cellular automaton generated by "Rule 70" initiated with a single ON (black) cell.

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

Offset

0

Comments

Row n has length 2n+1.

This sequence is also generated by Rule 198.

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

Mathematica

rule=70; 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: A240025 A100923 A050073 * A373486 A353491 A120474

Adjacent sequences: A266840 A266841 A266842 * A266844 A266845 A266846

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 04 2016

Status

approved