A271129 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 291", based on the 5-celled von Neumann neighborhood.

1, 5, 9, 32, 9, 101, 41, 164, 33, 316, 61, 433, 53, 600, 141, 825, 76, 1097, 160, 1285, 92, 1629, 268, 1809, 273, 2325, 252, 2589, 264, 2889, 421, 3349, 396, 3809, 440, 4209, 393, 4793, 665, 5124, 553, 5992, 649, 6321, 629, 6968, 985, 7580, 773, 8345, 1081

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..128

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=291; 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}];
Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)

Crossrefs

Sequence in context: A049602 A350280 A119031 * A271152 A271164 A266206

Adjacent sequences: A271126 A271127 A271128 * A271130 A271131 A271132

Keyword

nonn,easy,changed

Author

Robert Price, Mar 31 2016

Status

approved