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A272280
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 457", based on the 5-celled von Neumann neighborhood.
4
1, 4, 9, 28, 21, 92, 57, 168, 65, 244, 81, 352, 97, 536, 165, 656, 233, 892, 221, 1124, 277, 1432, 361, 1676, 425, 1924, 441, 2348, 585, 2616, 777, 2840, 905, 3180, 777, 3788, 933, 4212, 1045, 4604, 1173, 5008, 1225, 5640, 1593, 6000, 1833, 6532, 1981, 7036
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=457; 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: A272016 A272089 A270720 * A087726 A270891 A272313
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 24 2016
STATUS
approved