A281523 Binary representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 374", based on the 5-celled von Neumann neighborhood.

1, 11, 1, 111, 10001, 111111, 1001, 111111, 10100001, 1111101111, 101001, 11111111, 1000100001, 111111101111, 10010000101001, 1111110011111111, 11000100001, 1001011101111, 111111010101001, 10000001111111111, 1110000101000100001, 100010111111011101111

Offset

0,2

Comments

Initialized with a single black (ON) cell at stage zero.

References

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

Links

Robert Price, Table of n, a(n) for n = 0..126

Robert Price, Diagrams of first 20 stages

N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Wolfram Research, Wolfram Atlas of Simple Programs

Index entries for sequences related to cellular automata

Index to 2D 5-Neighbor Cellular Automata

Index to Elementary Cellular Automata

Mathematica

CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code = 374; stages = 128;
rule = IntegerDigits[code, 2, 10];
g = 2 * stages + 1; (* Maximum size of grid *)
a = PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca = a;
ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k = (Length[ca[[1]]] + 1)/2;
ca = Table[Table[Part[ca[[n]] [[j]], Range[k + 1 - n, k - 1 + n]], {j, k + 1 - n, k - 1 + n}], {n, 1, k}];
Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}]

Crossrefs

Cf. A281522, A281524, A281525.

Sequence in context: A281309 A282306 A282603 * A282420 A282683 A038315

Adjacent sequences: A281520 A281521 A281522 * A281524 A281525 A281526

Keyword

nonn,easy

Author

Robert Price, Jan 23 2017

Status

approved