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A270022
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 54", based on the 5-celled von Neumann neighborhood.
4
1, 5, 8, 20, 28, 40, 44, 76, 100, 100, 124, 160, 196, 212, 204, 276, 324, 344, 380, 428, 456, 492, 492, 616, 700, 700, 696, 784, 908, 816, 1012, 932, 1276, 1148, 1296, 1372, 1572, 1452, 1576, 1640, 1844, 1712, 1972, 1864, 2268, 1912, 2408, 2212, 2644, 2460
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=54; 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: A295901 A143157 A275236 * A271195 A270630 A272217
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 08 2016
STATUS
approved