A118102 Triangle read by rows giving successive states of cellular automaton generated by "Rule 94" initiated with a single ON (black) cell.

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

Offset: 0

Author

Eric W. Weisstein, Apr 12 2006

Keywords

• nonn
• tabf

Comments

Totals for row k, starting with k = 0, are {1, 3, 4, 6, 6, 8, 8, 10, 10, 12, 12, ...}, i.e., {1, 3} followed by A052928(k + 3). - Michael De Vlieger, Oct 08 2015

Examples

			From _Michael De Vlieger_, Oct 08 2015: (Start)
First 12 rows, replacing "0" with ".", ignoring "0" outside of range of 1's for better visibility of ON cells:
                        1
                      1 1 1
                    1 1 . 1 1
                  1 1 1 . 1 1 1
                1 1 . 1 . 1 . 1 1
              1 1 1 . 1 . 1 . 1 1 1
            1 1 . 1 . 1 . 1 . 1 . 1 1
          1 1 1 . 1 . 1 . 1 . 1 . 1 1 1
        1 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 1
      1 1 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 1 1
    1 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 1
  1 1 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 1 1
1 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 1
(End)
		

References

• S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

• Robert Price, Table of n, a(n) for n = 0..9999
• Michael De Vlieger, Visualization of rows 0 - 31 of Rule 94
• Eric Weisstein's World of Mathematics, Rule 94
• Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
• S. Wolfram, A New Kind of Science
• Index to Elementary Cellular Automata
• Index entries for sequences related to cellular automata

Crossrefs

Cf. A052928.

This sequence, A118101 and A071033 are equivalent descriptions of the Rule 94 automaton.

Programs

Mathematica

clip[lst_] := Block[{p = Flatten@ Position[lst, 1]}, Take[lst, {Min@ p, Max@ p}]]; FromDigits[#, 2] & /@ Map[clip, CellularAutomaton[94, {{1}, 0}, 24]] ; clip /@ CellularAutomaton[94, {{1}, 0}, 9] // Flatten (* Michael De Vlieger, Oct 08 2015 *)