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A269918
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 822", based on the 5-celled von Neumann neighborhood.
4
1, 5, 9, 25, 37, 49, 57, 105, 117, 153, 161, 229, 253, 297, 289, 417, 397, 545, 585, 661, 709, 745, 737, 949, 909, 1073, 1033, 1309, 1285, 1425, 1289, 1657, 1509, 1881, 1985, 2269, 2237, 2449, 2537, 2725, 2693, 2953, 2929, 3245, 3277, 3409, 3241, 3805, 3445
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=822; 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: A273561 A273746 A234277 * A354775 A273827 A024825
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 27 2016
STATUS
approved