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A273502
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 774", based on the 5-celled von Neumann neighborhood.
4
1, 5, 5, 17, 5, 25, 17, 61, 9, 45, 45, 125, 41, 157, 73, 221, 57, 141, 129, 309, 125, 305, 125, 405, 133, 481, 245, 597, 333, 597, 397, 793, 429, 681, 613, 969, 561, 893, 669, 993, 821, 1061, 893, 1313, 873, 1429, 993, 1657, 1105, 1697, 1109, 1661, 1509
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=774; 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: A195465 A173464 A072272 * A273606 A273544 A273703
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 23 2016
STATUS
approved