A272252 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 449", based on the 5-celled von Neumann neighborhood.

1, 4, 9, 24, 21, 72, 45, 112, 93, 224, 117, 320, 173, 464, 205, 528, 293, 848, 225, 1100, 145, 1488, 361, 1396, 593, 1744, 561, 2012, 637, 2384, 669, 2336, 1053, 2952, 861, 3600, 589, 4208, 1073, 4140, 1241, 4876, 1145, 5176, 1573, 5556, 1509, 6008, 1621

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=449; 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: A196034 A196037 A270685 * A067801 A062775 A288105

Adjacent sequences: A272249 A272250 A272251 * A272253 A272254 A272255

Keyword

nonn,easy

Author

Robert Price, Apr 23 2016

Status

approved