A273835 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 966", based on the 5-celled von Neumann neighborhood.

1, 5, 5, 17, 9, 29, 17, 61, 21, 65, 57, 125, 77, 161, 197, 277, 217, 285, 301, 341, 353, 469, 405, 633, 577, 605, 629, 709, 685, 745, 837, 1061, 961, 981, 1049, 1137, 1177, 1285, 1201, 1613, 1497, 1505, 1641, 1773, 1665, 1793, 2037, 2497, 2269, 2357, 2397

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=966; 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: A273326 A273421 A273758 * A246333 A079317 A273482

Adjacent sequences: A273832 A273833 A273834 * A273836 A273837 A273838

Keyword

nonn,easy

Author

Robert Price, May 31 2016

Status

approved