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A273482
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 742", based on the 5-celled von Neumann neighborhood.
4
1, 5, 5, 17, 9, 29, 21, 65, 25, 77, 37, 113, 57, 141, 69, 225, 89, 253, 101, 305, 121, 333, 133, 417, 169, 477, 205, 569, 257, 709, 309, 897, 361, 845, 333, 1001, 377, 989, 381, 1081, 385, 1077, 461, 1129, 465, 1349, 509, 1609, 601, 1613, 653, 1817, 697
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=742; 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: A273835 A246333 A079317 * A273792 A273855 A175614
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 23 2016
STATUS
approved