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A271301
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 350", based on the 5-celled von Neumann neighborhood.
4
1, 5, 12, 17, 37, 28, 76, 45, 112, 80, 153, 141, 188, 168, 277, 229, 348, 296, 409, 381, 500, 464, 569, 605, 632, 688, 765, 805, 888, 916, 977, 1081, 1116, 1200, 1201, 1413, 1340, 1556, 1433, 1753, 1632, 1840, 1837, 2093, 1996, 2108, 2293, 2385, 2460, 2504
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=350; 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: A237669 A022137 A271121 * A282696 A314288 A314289
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 03 2016
STATUS
approved