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A272153
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 437", based on the 5-celled von Neumann neighborhood.
4
1, 8, 5, 44, 9, 112, 21, 220, 25, 344, 41, 492, 57, 712, 53, 900, 105, 1176, 77, 1444, 149, 1780, 165, 2108, 193, 2476, 245, 2884, 309, 3312, 361, 3776, 401, 4288, 357, 4840, 417, 5392, 473, 5984, 513, 6608, 561, 7296, 585, 7924, 669, 8668, 745, 9320, 701
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=437; 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: A272350 A271812 A272416 * A272564 A271689 A272111
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 21 2016
STATUS
approved