A276966 Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 33", based on the 5-celled von Neumann neighborhood.

1, 0, 1, 12, 1, 60, 1, 244, 1, 1012, 1, 4084, 1, 16340, 1, 65364, 1, 261972, 1, 1048404, 1, 4194132, 1, 16777044, 1, 67108180, 1, 268432724, 1, 1073730900, 1, 4294923604, 1, 17179825492, 1, 68719433044, 1, 274877863252, 1, 1099511584084, 1, 4398046467412, 1

Offset

0,4

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 the 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

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=33; 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[1, i]], 2], {i, 1, stages-1}]

Crossrefs

Cf. A276708, A276768, A277773.

Sequence in context: A013619 A092527 A085840 * A277799 A278468 A280975

Adjacent sequences: A276963 A276964 A276965 * A276967 A276968 A276969

Keyword

nonn,easy

Author

Robert Price, Nov 16 2016

Status

approved