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A273683
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 841", based on the 5-celled von Neumann neighborhood.
4
1, 4, 17, 37, 61, 97, 124, 177, 228, 309, 337, 409, 492, 613, 628, 753, 860, 1045, 1048, 1177, 1348, 1565, 1552, 1705, 1916, 2125, 2236, 2417, 2640, 2949, 2900, 3177, 3472, 3773, 3852, 4049, 4348, 4725, 4724, 4985, 5244, 5589, 5836, 6057, 6404, 6749, 6888
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=841; 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: A031092 A120884 A267766 * A173511 A218925 A356347
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 27 2016
STATUS
approved