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A271148
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 297", based on the 5-celled von Neumann neighborhood.
4
1, 4, 5, 32, 13, 88, 17, 168, 33, 276, 29, 432, 81, 580, 41, 800, 125, 968, 53, 1344, 141, 1560, 89, 1888, 241, 2100, 117, 2640, 281, 2892, 205, 3352, 413, 3704, 229, 4348, 437, 4632, 317, 5284, 549, 5644, 369, 6424, 737, 6816, 373, 7884, 649, 8172, 633
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.
MATHEMATICA
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=297; 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: A271160 A269872 A270075 * A271200 A335526 A373190
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 31 2016
STATUS
approved