A266608 Triangle read by rows giving successive states of cellular automaton generated by "Rule 41" initiated with a single ON (black) cell.

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

Mathematica

rule=41; 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: A267463 A264442 A266243 * A066288 A333818 A111412

Adjacent sequences: A266605 A266606 A266607 * A266609 A266610 A266611

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 01 2016

Status

approved