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A273855
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 998", based on the 5-celled von Neumann neighborhood.
4
1, 5, 5, 17, 9, 29, 21, 65, 33, 69, 69, 141, 129, 201, 233, 325, 309, 337, 353, 465, 525, 649, 673, 789, 825, 937, 989, 1169, 1257, 1421, 1453, 1677, 1657, 1729, 1777, 1945, 2053, 2261, 2405, 2625, 2705, 2829, 2901, 3181, 3285, 3557, 3709, 4017, 4041, 4145
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=998; 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: A079317 A273482 A273792 * A175614 A214022 A125256
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jun 01 2016
STATUS
approved